Conceptual Considerations

1
INTRODUCTION

2
BACKGROUND

3
STANDARD COSMOLOGICAL MODEL
*
SCM Closure Problem*
*
SCM Horizon Problem*
*
SCM Symmetry Problem*
*
SCM Smoothness Problem*

4
CONTINUUM COSMOLOGICAL MODEL
*
World Form*
*
Friedmann-Lemaître Spacetime*
*
Spectral Shift*
*
Singularity*
*
Pseudo-Stellar Fireball*
*
Planck Interface*
*
Spacetime Curvature*

5
SYNTHESIS
*
Fermiosynthesis*
*
Leptosynthesis*
*
Baryosynthesis*
*
Baryon Symmetry Violation*
*
Critique of Evidence for Baryon Symmetry Violation*

6
INTERACTIONS
*
Gravitational Potentials*
*
Potential Form*
*
Baryonic Clustering*
*
Freeze-Out*
*
Large-Scale Structure*
*
Nucleosynthesis*
*
Decoupling*
*
Dicke Coincidence*
*
Black Holes, White Holes, and Other Anomolies*
*
Cosmic Background Radiation*

7
CCM CONCERNS
*
Closure*
*
Horizon*
*
Symmetry*
*
Smoothness*
*
Homogeniety*

8
VERIFICATION
*
Lepton Experiment*
*
Baryon Experiment*

9
DISCUSSION
*
Cosmogony and Eschatology*

10
SUMMARY

**1
INTRODUCTION**

The evolution of cosmological models is almost as fascinating a study as that of cosmological evolution itself, and speculation on cosmology are of course as old as man's imagination. However, greater strides have been made in the last half-century to place cosmology on a firm analytical foundation than all of the conjectures presented since ancient Assyria. This progress has occurred because of our ability to look both inwards and outwards has increased so greatly in this period: both downward to the depths of the sub-nuclear universe and upward to the furthest extent of the astronomical universe; for only in the beginning did these universes coincide. Cosmology simply could not have been studied with any rigor until the processes underlying both particle physics and astrophysics could be understood with some degree of certainty and their findings correlated with some degree of confidence.

Modern*
analytical *cosmology was fathered by Friemann
and independently by Lemaître
during the 1920s. They derived a series of simple solutions to Enstein's
General Relativity field equations involving highly spherically-symmetrical
spacetime geodesics that were time-dependent and could be interpreted as
descriptions of an expanding universe. Such a dynamic universe must have
expanded from a smaller universe, in direct contrast to the prevalent static
models developed by Einstein
and de
Sitter. The Friedmann-Lemaître evolutionary
model could not predict explictly the curvature of the expansion however,
permitting three possible solutions: either hyperbolic, flat or spherical
expansion, all of which are unbound but only the latter is closed.

In terms of Riemannian space these solutions predict monotonic spacetime divergence of hyperbolic and flat universes. The spherical universe alone provides a cusp beyond which spacetime reconverges to an unfortunate conclusion: either a final crunch or perhaps a rebound, resulting in either an unending cycle of birth and death or a gradual running down of the universe with each cycle.

Modern*
empirical *cosmology was sired by Hubble,
who correlated the spectrometric red-shifts of distant celestial objects
with the radial velocity of such objects, albeit poorly, but with enough
verve to pronounce the correlation a fact. Hubble proposed a linear correlation
between red-shift and receding velocity whose slope H has since been denoted
Hubble's Constant. However this correlation did not necessarily point to
the Friedmann-Lemaître model as opposed to the Einstein-de Sitter
model, either of which could accommodate this finding inasmuch as spectrometric
red-shifts need not be related to spacetime expansion (gravitational effect)
but to radial motion in a static framework (Doppler effect).

However,
in the light of the excellent empirical observations of Humason
and reconsideration of the theoretical conclusions of Wirtz
the Hubble observations were generally interpreted to be considerably more
consistant with a dynamic model which would encompass both gravitational
and Doppler effects than a static model which would accommodate only the
latter. When both Einstein and de Sitter also accepted the dynamic interpretation
of the red-shift expansion achieved acceptability. Accordingly Hubble's
Constant became a time-dependent variable related to spacetime expansion,
the determination of whose present value H_{o}
still involves much difficulty. Hubble never fully reconciled himself to
an expansion model because such a model must presuppose a past smaller
universe, and therefore logically a beginning. In agreement Eddington
professed that *"the notion of a beginning of the present order of nature
is repugnant to me",* while, in contrast to Hubble, Eddington paradoxically
supported the Friedmann-Lemaître model as the model most closely
supported by observations.

The
three solutions to the Friedmann-Lemaître model can be quantized
by normalizing the Riemannian expansion factor K with K=-1 for hyperbolic
space, K=0 for flat space, and K=+1 for spherical space. Because spacetime
curvature depends on the density of the enclosed space D relative to a
critical density for closure D_{c}, the present density ratio W_{o}
can be defined as W_{o}=D_{o}/D_{c}.
Hence K=-1 for W_{o}<1,
K=0 for W_{o}=1,and
K=+1 for W_{o}>1.

Within
this framework H>0 for a hyperbolic universe, H=0 for a flat universe,
and H<0 for a spherical universe. However there is simply too much uncertainty
in the red-shift velocity observations to fix the variance in H, let alone
its current value H_{o}. The present value
of H_{o} ranges from 40 to 100 km/s-Mpc, depending
on the investigator, each reporting an error of no greater than ±10
km/s-Mpc. This unseeming uncertainty arises from the method of measurement,
the objects observed, and particularly the reliability of standard candles
required for absolute distance determinations at great displacements. The
Cepheid variables, the most reliable candles, can be calibrated to less
than 1% of the present Hubble radius: c/H_{o}.

**2
BACKGROUND**

Only after it was generally accepted by astronomers that the present universe evolved from a smaller precursor was the concept of expansion seriously considered by cosmologists. During the 1930s Tolman suggested that intergalactic radiation would cool in an expanding universe, though maintaining its Planck distribution, permitting its temperature to be determined. During the late 1940s two cosmologies ostensibly consistant with the Friedmann-Lemaître model were introduced that have attained sufficient recognition to have been studied seriously by cosmologists.

In
large measure the hot *big-bang* as the origin from which the universe
expanded was placed on a quantitative basis by the seminal work of Gamov
concerning the relative abundance of the elements in the universe. If a
big bang is a fact then remnent cosmic background radiation would fill
the universe, and if its temperature could be measured it would reveal
quantitative information as to the age of the universe. The work
was extended by Alpher
& Herman and although the big-bang scenario
is still burdened with some difficulties it is still considered the most
promising approach, evolving into the Standard Cosmological Model (SCM).

The steady-state model proposed by Bondi, Gold & Hoyle introduced spontaneous matter generation and is now largely discredited, but occasionally resurrected. Both models accounted for the perceived expansion of the universe.

A rather offbeat model was proposed by Lemaître which could be denoted the "Oscillating Universe Model". Assuming that the mass density of the universe was sufficient for closure, the collapse from the maximum volume would follow bounce back and expansion from the minimum volume: endless cycles, but only if no information whatsoever could transit the bounce back. Presumably the universal kinetic energy would be at a maximum and the potential energy at a minimum at the bounce with the situation reversed at maximum expansion. Tolman took the bounce model seriously enough to investigate its implications. If entropy were preserved through a bounce each cycle would be longer than the previous cycle, essentially destroying the oscillation concept. The duration of each cycle would be shorter than the subsequent cycle, requiring an initial cycle, presumably without duration; and likewise the duration of each cycle would be longer than the previous cycle, essentially resulting in a final cycle of endless duration.

The steady state theory proposed a flat universe (K=0) whose matter density remains constant because matter is spontaneously created between galaxies at a constant rate proportional to the constant rate of expansion. This approach thereby avoids the need for a genesis: the universe had forever existed and forever will. This view presumably failed on two counts: it could not account for the relatively anisotropic distribution of galaxies in the observable universe nor the measured microwave background radiation or neutrino background flux.

Although other sources of the background radiation have been proposed by Hoyle, the blackbody distribution of this radiation most strongly suggests a sufficiently-distant past period in which this radiation was in thermal equilibrium with matter: a hot big-bang. However, there may be a more substantial fault with the steady-state universe. According to steady-state theory to maintain the density of the expanding universe constant the aggregate mass of the universe must be increasing, indicating an evolutionary process. In the past the mass of the universe was less than at present, and accordingly at some substantially distant past the mass must have approached zero, destroying any steady-state scenario.

**3
STANDARD COSMOLOGICAL MODEL**

The SCM in its most elementary form proposes that universal expansion is the precise and proper interpretation of observed red shifts of stellar and galactic spectrum and that physical laws have remained unchanged at least since radiation-mass equilibrium and presumably from Planck time. The universe is larger than it was and perhaps smaller than it will eventually be, depending on the appropriate model of spacetime curvature. Consequently, on extrapolating back the universe would be substantially smaller and far enough backward the universe would have been an immensely dense collection of hot matter and radiation: perhaps the primordial Lemaître quantum singularity from which sprung the present universe.

This evolutionary model has been comprehensively studied and sufficient agreement has been achieved among cosmologist concerning certain basic predictions - particularly the observed abundances of He and D - that this model has been canonize the Standard Cosmological Model (SCM). Frankly it is a little short of astonishing just how well the universe follows the SCM scenario: at least from nucleosynthesis to the furthest extent of the visible universe. However there are certain basic difficulties that have only recently been addressed: principally the closure problem, the horizon problem, the symmetry problem, and the smoothness problem. Attempts have been made to graft the steady-state scenario onto the SCM to somewhat alleviate these difficulties, such as the proposal of King that continuous mass creation within an expansing space-time framework would go far in explaining the apparent distribution of galaxies, a major stumbling block in the SCM.

Closure would really not be a problem if cosmologists had not made it one. Using Kepler's 3rd Law, mass-luminosity relationships related to selected galaxies indicates that the present critical density ratio is on the order of W

What
must be addressed first however is just why it is so important to cosmologists
for W_{o}-->1.
On a visceral level there is just something indescribably unsatisfactory
about a hyperbolic K=-1 universe with a definite cosmogony but an uncertain
eschatology: a forever-expanding spacetime of diminishing curvature populated
by the cold ashes of bygone stars. Perhaps it is simply too assymetrical
to be taken seriously: lacking the symmetry of definite beginning and definite
end. The flat K=0 universe fares no better, simply attracting more adherents.
Thus the incessant search for additional matter might be no more than exhibitions
of the predilections of some cosmologist's (Kolb).

Hence,
the quest for W_{o}>1.
A very strong probability in this direction is a possible halo of cold
matter surrounding galaxies. Wherein the radial velocity of galaxies at
radial distance v(r) should diminish with r^{1/2},
instead roughly constant velocities are found out to luminous cut-off,
indicating an increase in mass with radial distance r. This mass is undetected,
hence denoted cold dark matter. If this matter is baryonic, then W_{o}
might at best increase by a magnitude to W_{o}=0.1,
or perhaps W_{o}=0.2:
still far short of criticality. This is certainly the upper limit of the
baryonic density which would have been coupled with radiation in accordance
with the SCM, otherwise the superbly predicted abundance of light elements:
the great triumph of SCM, would be adversely affected. For W<1
deuterium would be underproduced and helium and lithium overproduced during
nucleosynthesis.

What
is left is non-baryonic dark matter, which would not have coupled with
radiation. Such matter might be relics of the primordial universe: the
stable Weakly-Interacting Massive Particles (WIMP). These might range from
magnetic monopoles, pyrgons, maximons and newtorites with masses between
10^{16} and 10^{19}
GeV to quark nuggets with masses up to 10^{30}
GeV: a circus of massive relics proposed without even a shred of emperical
support. Although such WIMP can exist within a consistent theoretical framework,
the only problem with this scenario is that the physical processes necessary
to form them, their lifetimes, and the processes responsible for their
annihilation, are unknown. Although for closure the mass of all such existing
WIMP would have to be roughly a magnitude greater than all of the detectable
mass of the universe, in fact the survival of just the WIMP with masses
on the order of the Planck mass would drive W_{o}
to several magnitudes greater than unity, a nonsensical outcome.

As
has been noted, there is no empirical evidence whatsoever for the present
existence of any such non-baryonic matter. Nevertheless, there are those
who's predispositions favor a closed universe and they still infer that
such non-baryonic matter exists, much as did the adherents of the luminiferous
ether of bygone days (Strauss
& Davis). A disinterested observer must assume
however from all of the evidence at hand that W_{o}<<1
and hence the SCM universe is decidedly hyperbolic and will go on expanding
forever.

According to the Cosmological Principle there exists no special viewing point in the universe, our position notwithstanding, and in general over a sufficiently large volume of the universe any observed volume is representative of the whole: the universe is essentially isotropic. This supposition however would require that all of the universe was causally related at some time so that any conditions giving rise tooc some possible particularity in some portion of the universe would eventually influence all of the universe, giving rise to the essential isotropy. However, this requirement is not met in the SCM universe: any characteristic distance L was always, and still is, longer than the causal distance R

Accordingly regions causally connected are always smaller than the furthest extent of the universe: the event horizon is always smaller than the SCM universe. For example, the essentially uniform temperature of the cosmic background radiation (CBR) in any observed quadrant would naturally lead to the assumption that the conditions which originally lead to the emission and quantization of the radiation extended over the entire universe. However the horizon is too small in the SCM universe at quantization to accommodate such an assumption. Although R --> L in the present epoch, with the horizon at most roughly a kiloparsec, at earlier times the horizon would been significantly smaller than the greatest extent of the universe.

To circumvent this problem a modification
of the SCM of the early universe denoted the Inflationary Standard Model
(ISM) was originally proposed by Gliner
and further developed by Guth.
Essentially the breakdown in the electromagnetic and electroweak symmetry
in the primordial universe according to the Grand Unification Theories
(GUT) is accompanied by a phase transition in the thermodynamic sense.
The primordial universe for a short period is isothermal rather than cooling
with SCM expansion due to the release of the latent heat of transition,
followed by a limited superheating of the universe subsequent to which
the SCM scenario is followed to the present epoch. The result of superheating
is a sudden and uncharacteristic inflation. To accommodate this inflation,
the primordial ISM universe must have been significantly smaller than the
classical SCM universe before inflation and hence smaller than the horizon.
However, the ISM requires that the critical density W_{o}=1±10^{6},
a condition that is not presently supported by any observational evidence
whatsoever, all of which evidence still supports W_{o}<<1,
as has been discussed. Setting aside this detail the ISM has attracted
much serious thought.

This problem involves certain conservation relationships, the sum of whose terms one would expect to vanish, for example charge balance: the number of positive charges and negative charges are supposedly equal in the universe. Without exception all cosmological models arbitrarily provide for charge balance, yielding a charge number C=0. Accordingly, one would then expect

The reason this logical outcome is unacceptable is not due to any convincing observations but rather arises intrinsically from the SCM, according to which matter is in thermal equilibrium with radiation at nucleosynthesis. However the SCM provides no means that could account for the segregation of matter from antimatter under these severe conditions: a necessary requirement for separate matter and antimatter nucleosynthesis without mutual annihilation. Accordingly, a condition of B>0 must be provided prior to nucleosynthesis so that matter density exceeds antimatter density. Thus after annihilation some matter particles will survive to nucleosynthesis: accounting for all of the mass of the observable universe.

Models based on GUT do provide an out: for example non-conservation mechanisms by which anti-baryons can be converted to baryons, thereby allowing an original B=0 condition to subsequently become B>0 before nucleosynthesis. Of course all such processes require a causal connection throughout the early universe, a condition provided by the ISM scenario. What mitigates against this approach, and other mechanisms proposed by which the antimatter density can be diminished is that all such processes involve reactants and products whose chemical potentials are identical, such as equivalent baryons and antibaryons. Any equilibrium process that would favor baryosynthesis would have the same probability of favoring antibaryosynthesis.

Even under nonequilibrium GUT conditions all such models must not only provide for the formation of baryons at the expense of antibaryons, but simultaneously must provide for means of suppressing equivalent antibaryon formation. As a further difficulty, loss of electromagnetic and electroweak symmetry can lead to the formation of WIMP at the assymmetry transition, the number of which would dominate the mass of the universe, but which have not been observed. Needless to say, much difficulty have been encountered with the GUT approach to systematically provide baryon assymmetry, resulting in a plethora of GUT to circumvent these difficulties.

Essential to the SCM is a homogeneous universe with matter and radiation in thermal equilibrium before decoupling, the strongest evidence for which is the uniformity of the Cosmic Background Radiation (CBR), yet this uniform soup gave rise to the large scale structure of the observed universe. That is, the primordial SCM universe was exceedingly homogeneous yet the present universe, although denoted isotropic, exhibits much large-scale structure. Galaxies are found in clusters and clusters are found in superclusters, the latter separated by vast voids, with the clusters and superclusters themselves are often arranged in chains.

Hence the isotropy of the universe is a matter of scale. Nevertheless there is sufficient anistropy to be of concern. In fact, the CBR now appears to be too uniform. Although perturbations are observed, some are smaller than the resolution of the measuring equipment, being mentally magnified by ingenious investigators using esoteric methodologies to account for the required anisotropy.

**4 CONTINUUM COSMOLOGICAL MODEL**

It is evident that all of these described problems are interconnected, either requiring special pleading, arbitrary initial conditions, or avoidance of empirical realities; and all of them are intrinsic to the SCM. However the SCM has been so overwhelmingly successful despite these difficulties that any alternative cosmology must at best encompass the Standard Model or at least be consistent with it. What will now be described is such alternative model.

Basic Assumption

According to
the Continuum Cosmological Model (CCM) the big bang singularity did not
occur some 15 billion years in the past but rather resides some 15 billion
lightyears distance from us. Essentially, the temporal processes
involved before decoupling are assumed to be an on-going concern.
Surprisingly the SCM formalism can be employed to describe the CCM universe,
or more accurately the co-moving portion of our observable universe which
is assumed to have been expelled some 15 billion years or so ago.

In terms of lookback time astronomers can only see back a few billion years, which effectively limits the observable extent of our co-moving portion of the universe. Although claims have been made that objects some 10 billion or so lightyears distance have been observed in the infrared by the HST, these claims has not yet been confirmed. According to the CCM these latter objects would be relatively young, perhaps five billion years old. Hence even this period and distance is still much too short to observe the temporal singularity.

*World
Form*

What will be assumed is that the universe takes the world form shown in
Figure 1, a rather inadequate two-dimensional rendition of four-dimensional
spacetime. According to the CCM the singularity has a temporal existence.
From this singularity spacetime geodesics diverge and eventually converge.
Hence the singularity exists not only at the origin of spacetime but for
all time: it is the origin from which the discernible universe expanded
and the destination to which it will contract. Hence the observable universe
is a small portion of a continuum universe of fixed volume with timeless
duration.

Before considering an analytical description of the CCM universe, it would be advantageous to further describe the world form because of the difficulty in rendering 4-dimensional spacetime in two dimensions. The most difficult concept to describe is the continuum singularity in asmuch as it has a temporal existance.

.

.

Essentially
the past universe in contraction is continuously passing through the singularity
to the future universe in expansion. The photonic energy density and hence
the temperature increases during contraction to infinite at the singularity
and then decreases during expansion.
.

.

.

As
an analogy consider a light ray passing through an ideal lens system. The
ray moves from the past through the focal point (at which point the radiation
energy density is infinite) to the future. Consider now an analytical description
of the CCM.
The coordinates of the CCM universe described in Friedmann-Lemaître spacetime (FLS) can be so chosen that the line element

(4.1) *
d*s^{2}
= *d*t^{2} - R(t)^{2}*d*s^{2}

where t is local time, R(t) is a
measure of the local time-dependent spacetime curvature and *d*s^{2}
is the line element in Riemannian 3-space. Recognizing this distinction
the line element can be described in general terms for both the SCM and
the CCM. According to the SCM (c)=sin(c)
for the case of K=+1, resulting in a closed system with greatest expansion
at c=p/2 where 0<c<p
for a single cycle, with convergence at c=p.

(4.2)*
d*s^{2}
= *d*c^{2}
+ É2(c/2) (*d*q^{2}
+ sin^{2}q*d*j^{2})
.

In contrast, for the CCM (c)=sin(c/2)
as shown in equation (3), resulting in a closed system with greatest radial
extent at the cusp c=p(t_{c},s_{c})
where 0<c<2p.
For continuum spacetime the geodesic folds back on itself: c=0
simultaneously at c=2p.
Thus the same singularity exists at c=0 and
c=2p.

.

.

Hence a CCM elapsed time measures strictly
the local time t(4.3a)
t_{o} = (4pGD_{o}/3)
[c/2-sin(c/2)]

where D_{o}
is the local density within our local comoving spherical shell at our Present
Local Epoch (PLE) as shown in Figure 4.4. The local radius of curvature
R_{o }shown in Figure
4.4 can be expressed as

(4.3b)
R_{o} = (4pGD_{o}/3)
[1-cos(c/2)] .

Hence R_{o}=0
at both c=0 and c=2p.
Consequently
there exists a singularity from which spacetime diverges (c=0)
and to which it converges (c=2p).
Thus, in passing through the singularity at convergence the original point
of divergence is reattained. The characteristic length for each epoch
is shown shorter at the earlier local epoch than at the present local epoch
and shorter again at the future local epoch as t_{o}-->
t_{W}.

.

.

The CCM universe is a continuum, with
the singularity having a temporal existence. Hence, as shown in Figure
4.4, only a local time tAccordingly, any concept of an absolute
cosmological time t is meaningless. All that can be measured is t_{o}
for our local epoch. The local epoch (t_{o},s)
expands from the past singularity (0,0) to the cusp at (t_{c},s_{c})
and thence contracts to the future coincident singularity (t_{W},s_{W}).
The CCM universe is closed because the density D in the vicinity of the
singularity at (0,0) and (t_{W},s_{W})
is sufficiently great that R_{o}-->0 as t_{o}-->t_{W},
with (0,0) and (t_{W},s_{W})
rotationally equivalent.

Depending on the position of our local comoving spherical shell (t

(4.4)
z = l_{o}/l_{e}
- 1 .

Obviously
the SCM interpretation of z does not fit the CCM scenario. According
to the SCM the universe did not only initiate at a single point but at
a single time. Unfortunately, the continuous cosmogony of the CCM thoroughly
confuses the issue. Within our co-moving spherical shell all celestial
bodies originated at the same time, regardless of their red shift relative
to the observer. Disregarding non-Hubble drift, the observed spectral
shift z reveals essentially circumferential motion of bodies orthogonal
to the radial motion of our comoving spherical shell. Observed very high
spectral shifts could indicate either bodies at great distance from us
- but still within our co-moving shell - where the component of radial
motion becomes important, or bodies outside our co-moving shell.
The latter case introduces even more confusion inasmuch as the age of the
bodies become important: some would be younger and others older.
That extensive starbirth observed (Barger)
in high-redshift galaxies is consistant with the CCM inasmuch as these
galaxies may be members of comoving spheres subsequent to our comoving
sphere, and consequently of an earlier age.

The singularity is the state of the CCM universe at local t

According to the CCM the singularity
is a volume V_{s}=0 radiator through which no information whatsoever
can transit. Accordingly only photons without wavelength (l=0)
can possibly pass through such a singularity without carrying information.
This latter condition will be the basis of the following discussion, although
employing the SCM formalism where applicable.

According to the CCM the radiation
emitted by the singularity at t=0 has an infinite frequency n=oo
with an infinite density D_{s}=oo and therefore infinite temperature
T=oo. Beyond V_{s}=0
of course T immediately falls as the radiation expands into the surrounding
transparent volume V_{P} presumably with T
oct^{-}^{1/2} and T ocV^{-}^{1/3}.
Hence the CCM singularity is decidedly not the single quantum state as
conceived by Lemaître. The CCM singularity condition
immediately precludes fermions transiting the singularity inasmuch
as matter possesses information in the form of mass, charge and spin.
Ostensibly bosons would also be precluded because mesons have mass.

The CCM singularity is encased within an opaque sphere spewing out matter and energy at a surface temperature of roughly T=3600 K. Using the SCM formalism this fireball has a diameter of roughly three parsecs and our comoving portion of the universe will have emerged roughly 10

.

.

In accordance with the SCM after an
elapsed time t

This is a crucial juncture because at temperatures T>10

Another approach is of course a
Grand Unification of the gravitational interactions with the electrostrong,
electroweak and electromagnetic interactions. Although the electroweak
and electromagnetic interactions have finally been unified, the real stumbling
block is the formulation of the electrostrong and electromagnetic interactions
in a geometric framework, as are gravitational interactions. Such
a framework would involve some kind of non-spatial but space-like dimensions.
These would have to be quite small (<<10^{-18}
m) because nothing of the sort have been observed.

An alternative approach would be the formulation of a non-geometric theory of gravitational interactions wherein the interactions would be mediated by tensor particles with even-integral spin. Such particles must have zero-mass and they are still as imaginary as non-spatial dimensions. A further alternative is that perhaps no such integration of non-gravitational and gravitational fields is possible: we are indeed dealing with apples and oranges.

Hence at T>10^{19}
GeV there is no satisfactory model to describe the processes operating,
a temperature above which mass particles in any event could not be distinguished
from one another. *A plausible way to resolve this dilemma
is to assume that matter does not exist above the Planck Temperature. *This
is a reasonable assumption considering that the electron radius is presumed
to be on the order of 10^{-17 }m, enormous
compared to the Planck radius r_{Pl}=10^{-34}
m.

According to the CCM a monochromatic
flux radiates outwardly from the singularity, striking the Planck interface
at Tª10^{20}
GeV, and constitutes the driving force for the ejection process.
The radiation pressure imposed on the Planck imterface is roughly 10^{77}
J/m^{2}, which is equivalent to some 10^{33}
solar masses per unit area.

This monochromatic flux striking
the Planck interface is either absorbed or reflected back. Simulanteously
energy radiates inwardly from the Planck interface at Tª10^{19}
GeV. Hence, as shown in Figure 6, the singularity is centered in
a steady-state cavity of radiation:

1) emitted from
the singularity g_{1},

2) emitted from
the Planck interface g_{2},
:

3) reflected
from the Planck interface g_{3},
and

4) absorbed
at the Planck interface g_{4.}

Hence within the cavity n_{g3}+n_{g}_{4}=n_{g}_{1}+n_{g}_{2}+n_{g}_{3}.

.

.

Because a temperature gradient exists
between the singularity and the Planck Interface black-body conditions
are not achieved.

The spacetime geodesics are essentially time invarient with K=+1 in the CCM rather than expanding as in the SCM with most likely K<0. Because the local mass-density of the universe is greatest at the singularity the greatest curvature occurs about the singularity. This does not imply however that most of the mass of the CCM universe resides in the vicinity of the singularity. Obviously matter ejected from the singularity at (0,0) must have an initial velocity sufficient to overcome the gravitational attraction of the singularity, as must antimatter, in order to reach the cusp at (t

Let us now consider particle synthesis under CCM conditions as an on-going process rather than a past happening and consider the means by which the present universe survived despite B=0 and L=0.

**5 SYNTHESIS**

According to CCM fermions appears at T<10

Our principle concern however is the lepton production of electron particles e and

(5.1a)
2g --> e + __e__

Hence the monochromatic flux radiating
from the singularity is scattered by the intercepted lepton production
shell when T<10^{19} GeV, as shown in Figure
3b. Accordingly, the universe becomes opaque with radiation scattering
within a shell of inner radius r=10^{-34}
m, with matter produced by reaction (5.1a) and annihilation by reverse
reaction (5.1b), both reactions operating simultaneously.

(5.1b)
e + __e__ --> 2g
.

Consequently the radiation expanding
beyond r=10^{-34} m gradually assumes a blackbody
energy distribution in thermal equilibrium with the essentially equilibrated
leptons permanently existing within this CCM region whose inner boundary
is the Planck Interface. That such a thermalizing process could occur
has been affirmed by Hawking
and Ellis.

Although such interactions
cannot be considered as truly equilibrium processes because there is a
co-moving flow of particles outwards from r=10^{-34} m under the
influence of radiation pressure, nevertheless this region of spacetime
divergence can be considered one of steady-state or pseudo-equilibrium
processes. As such the radiation will gradually approach thermalization
with increasing distance from the interface, with the result that the particles
react in a soup of near-blackbody radiation beyond the Planck interface.
As such leptons and radiation are effectively coupled in essentially thermal
equilibrium.

From classical particle collision
theory the formation rate of lepton pairs e__e__ per unit volume V according
to equation (5a) is k_{f}^{2}g
and the annihilation rate according to equation (5b) is k_{r}e__e__
then the overall lepton pair production rate R is

(5.2a)
R = k_{f}2g -
k_{r}e__e__

where g
indicates number of photons. The reaction rate constants k_{f}
and k_{r} can be equated at equilibrium where R_{eq}=0
and therefore k_{f}2g_{eq}=R_{r}e_{eq}__e___{eq}
where 2g_{eq }and e_{eq}__e___{eq}
are the equilibrium number of photon and lepton pairs per unit volume V.
Hence

(5.2b)
R = k_{f} [2g
- 2g_{eq}(e__e__/e_{eq}__e___{eq})]
.

and accordingly when e+__e__<e_{eq}+__e___{eq}
reaction (5a) predominates (R>0) and when e+__e__>e_{eq}+__e___{eq}
reaction (5b) predominates (R<0).

The number of particles in equilibrium
at unit volume V can be represented by (e_{eq}+__e___{eq})/2g_{eq}
which is simply k_{f}/k_{r} from particle collision theory.
According to Steigman
the unit volume V is proportional to

(5.3)
V µ mc^{2}/kT
.

As long at V<1 thermal equilibrium
is maintained (e__e__=e_{eq}__e___{eq})
and with decreasing temperature (e_{eq}__e___{eq})/g
decreases with decreasing rate of reaction (5a). At some critical
temperature at which V>1 equilibrium is broken and the number of lepton
pairs, specifically e and __e__ becomes essentially fixed, with e__e__<<g.
Because CCM lepton number L=0 inasmuch as no information can pass through
the singularity and therefore e = __e__, primordial leptons are so effectively
annihilated by reaction (5.1b) that only an insignificant relic could possibly
survive beyond this freeze-out temperature. Likewise for quarks:
after freeze-out q = __q__ and pair annihilation would be essentially
complete. Hence
the observed universe could not have evolved, ostensibly a CCM problem
shared with the SCM.

At temperatures on the order of T=1 GeV the quark-hadron transition occurs with the formation of neutrons n and protons p in a specific ratio. However these particles can interact, changing the ratio of neutrons to protons with decreasing temperature (T<1 GeV) by reversible processes involving neutrino n

(5.4a)
n + n_{e}
<--> p + e

or

(5.4b)
n + __e__ <--> p
+ __n___{e}
.

These reactions are assumed to proceed by an ordinary reversible first-order mechanism:

(5.5)
R = k_{f} c_{n}
- k_{r} c_{p}

where R is the neutron reaction
rate, c_{n} is
the neutron fraction and c_{p}
the proton fraction present: c_{n}+c_{p}=1.
From equation (5.5) at equilibrium R=0 and consequently k_{r}/k_{f}=c_{n}
/c_{p} .

According to Weinberg the ratio of the rate constants takes the form

(5.6)
k_{r}/k_{f} = e^{-Q/kT}

where Q is the energy difference between electrons and neutrinos. Combining equations (9) and (10) yields

(5.7a)
c_{n}=
1/[1+e^{-Q/kT}]

From equation (5.7a) at the quark-hadron
transition (T=1 GeV) c_{n}=0.38.
However the temperature is decreasing with expansion and at roughly T=20
MeV thermal equilibrium is broken, with c_{n}=0.16.
The number fraction of protons c_{p}
and neutrons c_{n}
are subsequently fixed except for the crucial b-decay
of the neutrons according to c_{n
}oc
t/t_{n} where t_{n}
is the neutron half-life.

Obviously the relative numbers of
neutrons and protons present at nucleosynthesis is crucial to the relative
quantities of the nucleides formed, and consequently to the measured value
of t_{n}, which
is known only to ±3%. However, as far as anyone can surmise,
the chemical potentials of particles are identical to that of their equivalent
antiparticles, and consequently an equivalent process to (5.4a) and (5.4b)
is simultaneously occurring between antiprotons and antineutrons, resulting
in

(5.7b)
__ ^{c}_{n}__
= 1/[1+e

for

(5.8a)
__n__ + __n___{e}
<--> __p__ + e .

Because equivalent particle-antiparticle
chemical potentials are identical obviously Q=__Q__. Moreover,
because proton-neutron interacts also involve antiparticles [equation (8b)]
obviously antiproton-antineutron interacts can involve equivalent particles.

(5.8b)
__p__ + __n___{e}
<--> __n__ + e
.

The only problem with this scenario is that it presupposes an original L=0 and B=0 and moreover that both dL=0 and dB=0. These conditions are generally considered contradictory. That is, the SCM harbors a contradiction, ostensibly shared by the CCM. Under the SCM B=0 and therefore from 1 GeV to 20 MeV equal numbers of baryons and antibaryons are coupled to radiation and are equally reactive because chemical potentials are identical. Consequently the baryons should share the same fate as the leptons: mutual annihilation.

(5.9)
B + __B__ -->
2g

With B=0 the result would be a cold matter-free universe after decoupling. The general observation that a matter-containing universe supposedly exists ostensibly argues against this eventuality.

Seeking means of circumventing this SCM eventuality that a matter-containing universe cannot exist constitutes a full-time effort on the part of a slew of cosmologists: to demonstrate that baryon symmetry-violation is either an initial condition or arises from suppression of the antiquark-->antihadron transition, and thereby in either case eliminating any relevancy to processes (5.8a) and (5.8b).

Accordingly, in regard to
this question of baryons symmetry violation, let us consider:

1. the requirement for baryon symmetry violation,

2. the empirical evidence for baryon symmetry violations, and

3. the mechanisms proposed for baryon symmetry violations.

1. Need for Baryon Symmetry Violation:

a) Annihilation processes after freeze out at T=20 MeV are so efficient

that reaction (13) would deplete
the universe of necessary baryons

were in fact n_{B}/ng=n_{B}/ng.

b) Statistical fluctuations leading to clustering that might circumvent
reaction (5.9) are too small to achieve any kind of significant B and __B__
isolation before freeze out. Our galaxy (and presumably the
universe) contains roughly n_{B}/ng
=10^{-10}. Statistical fluctuations
might achieve locally n_{B}/ng
=10^{-40} but could not possibly attain
parity: n_{B}/ng
=
n_{B}/ng
= 10^{-10}.

2. Evidence for Baryon Symmetry
Violations:

a) Asteroids comprising anti-matter have not been observed. Their
interaction with the solar-wind would have permitted their detection
as they would constitute a very luminous source of g-radiation.

b) Cosmic rays are generally of extra-solar origin, particularly above
100 MeV, with the most abundant antimatter comprising antiprotons
and antihelium nuclei; however their relative abundance in cosmic rays
is only __p__/p = 10^{-4} and __He__/He
= 10^{-5}.

c) Even the number of antimatter particles found in cosmic rays could have
originated by collisions, such as p+__p__=3p+__p__, rather than from
an extra-solar source.

d) Gases between matter and antimatter galactic clusters should
produce g-radiation. Such radiation has
not been detected.

3. Mechanisms for Baryon Symmetry
Violations:

a) Initially B>0 in the primordial universe.

b) Initially B=0 wherein processes are conjectured that produce greater
numbers of baryons compared to antibaryons n_{B}/ng
<n_{B}/ng
;
the mutual annihilation of all but the excess resulting in a residuum of
baryons and virtual disappearance of antibaryons.

Let us now consider the implications of the two mechanisms proposed, neither of which arise from the SCM formalism.

Mechanism (a) is purely arbitrary,
and although it solves the baryon assymmetry problem, it places an *a
priori* condition on the singularity without further describing or defining
the nature of the singularity. This mechanism is probably not amenable
to empirical verification.

Mechanism (b) introduces baryon assymmetry as a integral part of baryosynthesis. This is the realm of the Grand Unification Theories (GUT), of which there are a sufficient number to satisfy any condition or eventuality; variations of which are often contradictory.

A horizon problem is confronted with the GUT, but can be circumvented by modifying the SCM by introducing the inflationary period already discussed which is accompanied by a drastic temperature decrease below the SCM prediction, followed by an abrupt rebound. During this period the horizon expands to encompass the entire universe, a condition which persists to the present epoch, contrary to the classical SCM.

Accordingly the early universe is causally connected. The essentially unlimited horizon permits baryosynthesis to occur in all portions of the universe involving supermassive bosons under conditions of sufficiently high temperature that the electroweak and electromagnetic fields become unified. The collision and decay of these bosons violate B symmetry, shifting B towards a matter-dominated universe. Because the universe is causally connected such matter domination is global.

For example Kuzmin
propose that anomalous baryon and lepton symmetry violating processes can
be effective at T=200 GeV: the electroweak phase transition, and as a result
|B+L| >0 and |B-L| =0. However, these processes require that initially
|B-L|<0, thus illustrating the flaw in grand unification schemes.
Charge and Parity (CP) violation must be somehow *a priori* prescribed,
and hence the assymmetry that results from such models is an intrinsic
outcome of the assymmetry that enters the models. Worse,
no means are provided to create the initial |B-L|*0, although the original
assymmetry required would amount to only B/__B__~10^{9}/(10^{9}+1)
to result in a present universe of essentially pure matter.
That is, regardless of how miniscule the original B/__B__ assymmetry
it still must be accounted for. This is imperative because without
such an a priori assumption B=0 and therefore n_{B}/ng
=
n_{B}/ng~10^{-18}.
In contrast observations ostensibly indicate instead n_{B}/ng~10^{-10}
with n_{B}/ng =0,
a significant difference.

Although it is argued that
both boson and antiboson decay violate CP, they must do so with a subtle
difference sufficient to break B symmetry to obtain the observed n_{B}/ng,
while suppressing any processes leading towards an equivalent n_{B}/ng
.
Not surprisingly, at presently not a single GUT model has been experimentally
and unambiguously confirmed to the degree that a definitive mechanism of
spontaneous symmetry breaking can even be conditionally accepted, let alone
precluding all others candidates. In fact as simpler GUT models fail,
for example by the requirement for proton instability, more complex GUT
models must be proposed. Nevertheless, there is a continuing and
almost frantic effort to break baryon symmetry and the driving force
was best summed up by Sakharov
more than a quarter of a century ago:

*"The theory of the expanding
Universe, which presupposes a superdense initial state of matter, apparently
excludes the possibility of macroscopic separation of matter from antimatter;
it must therefore be assumed that there are no antimatter bodies in nature,
i.e., the Universe is asymmetrical with respect to the number of particles
and antiparticles."*

Of course the culprit in all
these machinations is the observed existence of antimatter, the nonexistance
of which would have greatly simplified cosmology but greatly complicated
particle physics. At present all experimentally observable processes
assumed to be involve in the synthesis of leptons and baryons conserve
B and L respectively. Likewise CP is conserved in all observable
processes that might contribute to symmetry breaking, although CP violation
is a condition for baryon symmetry-breaking in all of the GUT mechanisms
proposed. Consequently all early-universe symmetry-breaking scenarios
must provide a means to restore the presently observed experimental symmetry,
and this is conveniently provided by a break-down in grand unification
at T = 10^{14} GeV. Moreover, if in
fact the universe is asymmetrical with respect to B and L, then the relationship
between the non-zero values of B and L must be considered. Obviously
charge conservation puts a restriction on any flights of fancy. Consequently
the proviso that |B-L| = 0 is generally accepted, often arbitrarily, as
a requirement of certain grand unification theories to obtain the observed
n_{B}/ng.

It is apparent that there
are as many problems as solutions involved in the effort to break baryon
symmetry to conform with Sakharov's conclusion that *"the Universe is
asymmetrical with respect to the number of particles and antiparticles."*
However, this conclusion arises from an unwarranted assumption that the
lack of a suitable alternative mechanism *"apparently excludes the possibility
of macroscopic separation of matter from antimatter".*

Let us now examine the possibility of a suitable alternative mechanism that improves the possibility of macroscopic separation of matter from antimatter. Such an assumption first requires that the universe be highly anisotropic on a scale much greater than previously imagined. Fortunately quantitative observational analyses indicate that galaxies are not even remotely distributed uniformly: that there are in general regions of supercluster chains separated from other clusters by astronomical voids, and these observations are not restricted to any particular quadrant.

Because any definitive experimental confirmation of symmetry-breaking models is absent, the only evidence for an asymmetrical universe are those observations discussed in section Evidence for Baryon Symmetry violations. For the purpose of critiquing this evidence it will be assumed for the sake of argument that the universal baryon number, lepton number and charge number are symmetrical and accordingly the vast voids observed between galactic super-cluster structures separate matter portions of the universe from antimatter portions. The evidence for L and B symmetry violations will be reconsidered in terms of this conservation assumption.

a) That asteroids comprising anti-matter have not been observed would be expected. Even if asteroids were of extra-galactic origin, they would still in all probability have originated within our local cluster. The minuscule possibility that anti-matter asteroids, having reached our particular galaxy within our local cluster from a galaxy within an antimatter cluster, would survive our local cluster matter-field to approach our local star and be observable during some pass-by period is too small to be reasonably considered.

b) Conceding that cosmic rays are generally of extra-solar origin, particularly above 100 MeV, and even conceding that they might originate from very distance galactic clusters, the probability that any antimatter particles would survive reaching our galaxy after traversing millions of parsecs through our local cluster matter-field is too small to be reasonably considered.

c) The
embarrassingly high concentration of antiparticles in cosmic rays
probably have a local origin such as p + p --> 3p + __p__, rather than
from an extra-solar source. Conversely, cosmic rays originating
from antimatter galaxies would similarly have a significant matter
particle content: __p__ + __p__ --> 3__p__ + p.

d) Although the dust and gases between matter and antimatter galactic super-clusters would produce g-radiation, the dust and gas particles in these vast regions would have been largely annihilated prior to and after decoupling. No doubt such regions still are producing g-radiation from dust and gases swept in since then, but at an intensity too small to be detected at such distances.

It is evident that the
*observations
used to defend baryon assymmetry are unconvincing, and in fact could be
used equally well to defend baryon symmetry*, particularly Argument
(c). Nevertheless we must still confront Sakharov's concern: thermal
equilibrium between baryons and antibaryons before decoupling would result
in baryon annihilation, and rather than an observed baryon content of
n_{B}/n_{g}Ý=
10^{-10} we would have an inconceivable
n_{B}/ng <10^{-18}.
Accordingly, means must be found that promote matter-antimatter segregation
before decoupling.

Returning now to the CCM, it is
evident that baryon number, lepton number and charge number all carry information,
and inasmuch as information cannot transit the zero-volume singularity,
it follows that B=0, L=0 and C=0 are necessary conditions for the CCM at
local time t=0. Hence during the later period of thermal equilibrium
both n_{B}=n_{B}
and n_{L}=n_{L},
a condition which persists to the present epoch according to the CCM, wherein
n_{B}/ng = n_{B}/ng
ª 10^{-10}. How to resolve this
delemma is both a SCM and CCM problem.

We know that in themselves
statistical fluctuations that might circumvent reaction (5.9) are too small
to achieve any kind of significant B and __B__ clustering before freeze
out. In terms of nucleation theory, the clusters cannot grow
to a critical size beyond which the volume free energy of a cluster exceeds
its surface free energy, promoting further growth. Rather the clusters
tend to collapse. To remedy this situation it will be necessary
to reexamine the gravity interactions that exist between matter and antimatter.

**6 INTERACTIONS**

This section is the most speculative portion of this discourse and consequently the most controversial. Although the assumed potentials are not central to the CCM, these potentials go a long way in explaining the large scale structure of our co-moving portion of the universe, and their verification is discussed. According to the weak equivalence principle for both matter and antimatter inertial mass m

(6.1)
m_{I} = m_{G}
and __m___{I} = __m___{G}
.

Consequently the gravitational potential
V^^(r) between two matter particles m_{1}
and m_{2} and the potential V__^^__(r)
between two otherwise identical antimatter particles __m___{1}
and __m___{2} at displacement distance
r are identical:

(6.2)
V^^(r) = V__^^__(r) .

Consistent with, but outside
general relativity, the force between the particles m_{1}
and m_{2} is assumed to be mediated by a tensor
particle with even-integral spin, for which the gravitational potentials
V^^(r) and V__^^__(r) can each only be attractive. Using the Yukawa
form of the potential between particles __m___{1}
and __m___{2} the tensor particle is a
spin-two boson.

Using this formalism there is ostensibly
only three possible outcomes, and these have been considered by investigators
concerning the gravitational potential V^__^__(r) between a matter particle
m and an antimatter particle __m__. The most obvious is of course
equivalence

(6.3a)
V^__^__(r) = V^^(r) = V__^^__(r)
.

Less obvious is a potential greater than equivalent matter and antimatter potentials arising from quantum gravitational considerations

(6.3b)
V^__^__(r) > V^^(r) = V__^^__(r)

but a distinct possibility being seriously contemplated.

A repulsion possibility that has been considered and generally found wanting, if for no other reason than antigravity presumably violates energy conservation according to Morrison, although a not too convincing argument.

There is however another possibility hitherto not considered, namely that matter and antimatter cause opposing perturbations in spacetime curvature.

Although the proposed potential form is speculative, ironically it is the concept presented most amenable to verification. It is assumed that

mass can only be quantitatively described as a complex number: a matter part and an anti-matter part. However there is no preferential viewpoint. In our local co-moving portion of the universe naturally we would designate matter rather than anti-matter as the real part of the complex description. In terms of the conventional Newtonian potential between two particles therefore

V(r) = G[(m_{1}+im_{1})(m_{2}+im_{2})]/r^{2}

the conventional Newtonian potential relating matter-matter interactions is a special case of a general potential relating matter-matter, antimatter-antimatter and matter-antimatter interactions. Essentially consistent with the usual Newtonian formalism the universal gravitational potential V(r) will be expanded to comprise the sum of three terms where V^^(r) is our usual matter-matter potential

(6.4)
V(r) = V^^(r) + V__^^__(r) + V^__^__(r)
,

V__^^__(r) is the usual
antimatter-antimatter potential, and V^__^__(r) is a Newtonian mixing
term equal to 2G(m__m__)/r^{2}.

For matter-matter
interactions __m__=0 and consequently the second and third terms of
potential (6.4) vanish. Accordingly potential (6.4) takes the expected
form

(6.5a)
V(r) = G(mm)/r^{2}

For antimatter-antimatter interactions m=0 and consequently the first and third terms of potential (6.4) vanish. Accordingly potential (6.4) takes the expected form

(6.5b)
V(r) = G(__mm__)/r^{2}

However for matter-antimatter interactions all the terms of potential (6.4) are operative and consequently on combining terms potential (6.4) takes the form

(6.5c)
V(r) = G(m+__m__)^{2}/r^{2}

The implications
of equation (6.5c) is discussed in the *Verification Section.* Nieto
& Bonner discuss the validity of alternative potentials.

According to
equation (6.5c) there will exist between a matter (m>0) particle and an
equivalent antimatter particle (__m__<0) a potential null point [V(r)=0]
as shown in FigureÝ6.1a.

.

.

.

This view is consistant with
the gravitational force being mediated by a spin-two tensor particle with
the force always attractive. A possible interpretation of this approach
is that there exists an .

.

.

Hence there exists an

Consider the SCM universe after the quark-hadron transition (T=1 GeV) but before decoupling (T=1 eV) in accordance with equation (6.5). Immediatly after transition the universe is homogeneous and its mass density is largely baryonic. To effect any kind of clustering that would lead to the segregation of particles from antiparticles requires fluctuations in the isotropic universe. Essentially, only by clustering can particles be separated from antiparticles, or otherwise particle-antiparticle annihilation will keep n

The conclusion that discrete
B and __B__ clustering cannot occur before decoupling is an outcome
of the Jeans construction. Only clusters with a mass M greater than
a critical Jeans mass M_{J} will nucleate and thereafter accrete
additional matter and grow. Accordingly

(6.6)
M_{J} = p
d_{J} [n_{s}(p/Gd_{J})^{1/2}]^{3}

where d_{J} is the critical
cluster density and n_{s} is the speed
of sound within the uniform medium from which clustering occurs.
Because the speed of sound approaches the speed of light before decoupling
(T=1 eV) the Jean mass M_{J} encompasses a significant portion
of the mass of the primordial universe. This mass is so great that
M cannot possibly attain M_{J} before decoupling. Only
after decoupling however, when the speed of sound decreases some 10^{5}
fold would clustering be possible, which according to the SCM gives rise
to the galaxies. By then however it is too late to save the universe
or the SCM.

This SCM scenario is predicated
on the assumption however that the universe is still homogeneous after
the quark-hadron transition, and consequently fluctuations required to
nucleate clusters have wavelengths far too small compared to that required
for M>M_{J}. Hence the SCM universe will not survive
the quark-hadron transition and by necessity the assumption of B>0 is made,
an excrescence fastened to the SCM to save the model.Although statistical
fluctuations that might circumvent the Jeans limitations are too small
to achieve any kind of discrete B and __B__ clustering before decoupling,
this is not the case under conditions of equation (6.5).

Although the effect of V^__^__(r)=0
will be inconsequential at high temperatures, presumably before the quark-hadron
transition, nevertheless, such a system cannot be homogeneous: discrete
particle and antiparticle clustering must occur with matter continuously
accreting and dispersing from such clusters. Although such clusters
would be unstable at a sufficiently high temperature, nevertheless *the
CCM universe is inherently inhomogeneous,* conditions under which the
Jeans fluctuation criteria is unnecessary. Clustering occurs by virtue
of V^^(r)=V__^^__(r)>0 as would be expected but also V^__^__(r)=0,
not fluctuations in a homogeneous medium.

Accordingly a critical temperature
T_{c} must be defined wherein the rates of matter dissipation and
matter accretion equilibrate at a cluster mass M_{c}<M_{J}.
Therefore at T>T_{c} clusters are unstable, with matter dispersion
exceeding accretion so that cluster masses cannot increase to their critical
value M_{c}. Only when T<T_{c} are clusters stable
with M>M_{c}. Thereafter matter accretion exceeds dispersion
and clusters grow, as shown in Figure 6.2.

From baryonic symmetry considerations
the practical range of values of T_{c} have a definite limit.
Baryonic clustering can only occur after the quark-hadron transition (T_{c}<1
GeV) and must have occurred by virtue of V^__^__(r)=0 before decoupling
(T_{c}>1 eV), or otherwise there would be essentially nothing to
decouple with baryonic symmetry. However the T_{c} temperature
range must be further limited. Inhomogenization must initiate before
nucleosynthesis (T>20 MeV) otherwise all of the components required for
nucleosynthesis would not have collected in discrete B and __B__ clusters.
Hence T_{c} must lie in the range 1000 MeV>T_{c}>20 MeV.

Unlike the SCM scenario wherein decoupling is a global event at Tª1 eV, according to the CCM scenario at freeze-out the matter and antimatter particles that were dispersed between the clusters effectively annihilate, thereby eliminating photon coupling between clusters.

Figure 6.2. Cluster
accretion at Critical Temperature

.

Interestingly, a small fraction of quarks could conceivably survive quark-hadron transition as such quarks could only be annihiliated by an equivalent antiquark, and separations would be too great for collisions. Such primordial quarks might form a stable bond with hadrons at T<200 MeV (Satz). Alternatively heavy hadrons might form from up, down and residual strange quarks rather than from up and down quarks alone as in ordinary baryons (DeRujula).

Obvious any extremely massive
particles and antiparticles surviving the quark-hadron transition would
strongly promote clustering, inasmuch as under such circumstances V^^(r)=V__^^__(r)>>0
while invarient V^__^__(r)=0. Accordingly, such
primordial particles would act as powerful nucleating agents, promoting
M-->M_{c}.

The matter and antimatter clusters formed after freeze-out but before nucleosynthesis (T>20 MeV) are subject to non-Hubble drift. Matter-matter clusters drifting into contact will agglomerate, as will antimatter-antimatter clusters. In contrast matter and antimatter clusters drifting together will rebound under radiation pressure arisng from peripheral particle annihilation at points of contact. (This scenario is similar in some degree to that of Alfven as a means of segregating matter and antimatter particles.) Hence large volumes of space will be cleared of clusters by agglomeration of contacting like-clusters and rebounding of contacting unlike-clusters. Consequently separation of matter and antimatter clusters into separate groups of clusters will proceed simultaneously with agglomeration under gravitational attraction to superclusters as shown in Figure 6.2. The result will be a structured region inhabited by these superclusters before nucleosynthesis.

With rotation these superclusters will evolve into disc-like proto-galaxies after decoupling (Tª1 eV). Hence structure develops early in the CCM universe despite B=0, with matter and antimatter forming essentially interwoven but separate universes.

As the temperature cools through T=20 MeV nucleosynthesis initiates and the cluster accretion rate increases markedly inasmuch as the enhanced gravitational potential of the nuclear clusters will sweep any surrounding matter or antimatter towards their respective clusters, with the concentration of matter and antimatter relative to radiation progressively increasing: n

As in the case of the SCM with decreasing
temperature nucleosynthesis rapidly progresses with the formation of ^{1}H^{+},
^{2}D^{+},
^{3}He^{++},
^{4}He^{++}
and ^{7}Li^{+++} within matter clusters and equivalent
^{1}__H__^{-},
^{2}__D__^{-},
^{3}__He__^{=},
^{4}__He__^{=}
and ^{7}__Li__ within antimatter clusters.
With n_{B}/n_{g}
=10^{-10} the nuclear ratios ^{2}D^{+}/^{1}H^{+}=^{3}He^{++}/^{1}H^{+}=10^{-5}
and ^{4}He^{++}/^{1}H^{+}=^{7}Li^{+++}/^{1}H^{+}=10^{-10}
would be expected. Because the CCM scenario and the SCM are
identical as far as physical processes are concerned __n___{B}/n_{g}
=10^{-10} will lead to an equivalent ratio of antinuclei: ^{2}__D__^{-}/^{1}__H__^{-}=^{3}__He__^{=}/^{1}H^{+}=10^{-5}
and ^{4}__He__^{=}/^{1}__H__^{-}=^{7}__Li__^{*}/^{1}__H__^{-}=10^{-10}.

As T-->1 eV decoupling will progress but only within clusters inasmuch as intercluster particles will have been largely annihilated at freeze-out. Hence intracluster space will become progressively transparent as the clusters become increasingly isolated.

Disregarding the cosmological constant, the expansion rate can be represented as

(6.7)
H = [CD + (aR)^{-2}]^{1/2}

where H is the Hubble's constant, D is the mass density,
a is the expansion parameter, R is the radius of curvature and C is a constant.
At an earlier epoch the mass density term (1st term) predominated in determining
the expansion rate but at present the curvature term (2nd term) predominates.
What is remarkable is that there is such a fine balance between the expansion
kinetic energy (KE) dependent on a and the potential energy (PE) dependent
on D. If the KE of expansion predominated then the universe would freely
expand without matter gathering into galaxies. In contrast if the
PE of expansion predominated matter would gather rapidly, with the universe
finally collapsing before galaxies could form. Rather the KE and
the PE are so finely balance that neither eventuality occurred, a fortunate
coincidence first discerned by Dicke
and accordingly termed the *Dicke Coincidence.* This coincidence
is so central to the SCM that it guides much of the cosmological interpretation
of astronomical obsrvations.

Often however the requirement for such coincidences result in doubts in the model that require such a natural coincidence and the seeking of alternative models. Consider the five following conditions in relation to expansion energy: PE<<KE, PE<KE, PE~KE, PE>KE and PE>>KE. Only the middle condition would allow the SCM universe to evolve into the observed universe. However any of these energy imbalances could characterize the successive comoving spherical shells of the CCM universe. The matter within some shells could rapidly collapse preventing galaxy formation while the matter of other shells would fully disappate, likewise preventing galaxy formation. For others collapse would be a slow steady process, as would dissipation for others, depending on KE-PE imbalance.

Galaxy formation from rotating proto-galactic clusters would be highly dependent on cluster mass M

If Mcl<Mcl_{min} centrifugal acceleration of
the clustered gases and dust formed after nuleosynthesis would dissipate
into interstellar gas and dust clouds, although extra-galactic star formation
need not be precluded.

If Mcl>Mcl_{max }gravitational contraction will
overcome centrifugal dissipation, resulting in unconstrained contraction.
The result would be a rapidly-rotating galactic black hole significantly
more massive than a stellar black hole. Because the CCM universe
is not evolving in the strictest sense, although our local co-moving portion
of that universe is certainly doing so, these galactic black holes would
be analogous to the contraction singularity at t_{W},s_{W},
essentially a *Secondary Singularity.* Presuming thusly, the
galactic black hole would have associated with it a galactic *white hole*
analogous to the expansion sigularity at 0,0: another
secondary singularity. For mass and energy balance these singularities
must be contemporaneous, and could be considered a single entity.

.

.

Of course there has been much speculation
about black holes leading to other universes but such speculation has always
been made within the context of the SCM universe wherein the spacetime
geodesics are temporal. In terms of the CCM universe however the
spacetime geodesics are largely invarient and fold in on themselves, providing
ample opportunities for tunneling from one portion of the universe to another
portion. Matter spewing forth from galactic white holes might constitute
the core of later galaxies, a most interesting speculation.
Consistent with the SCM model the Cosmic Background Radiation (CBR) of the CCM model would have a local temperature of roughly 2.7 K characteristic of our co-moving spherical region. However, depending on the coordinates of our local region t,s in relation to the maximum radial extent of the universe at t

6.7 DT_{CBR}/T_{CBR}µ(DD/D)^{3}

Consequently any gradient DT_{CBR}would
hardly be perceivable, if at all.

Although the CBR is characteristic of thermalized radiation it is far smoother than would have been expected, considering the required inhomogenity for structure formation in the early universe would have disturbed the CBR spectral distribution (Peebles). However according to the CCM fireball radiation is an ongoing concern and hence disturbances in the spectral distribution of energy radiating from the fireball will integrate over time, smoothing the spectral distribution.

According to the SCM the observed red shift in the spectrum of distant galaxies is indicative of the cosmological expansion of the entire universe rather than a Doppler effect in a static universe. In contrast, according to the CCM the observed red shift is indicative of the cosmological expansion of only our co-moving portion of the universe, but only if t,s<t

**7 CCM CONCERNS**

With all of the matter of the CCM universe distributed essentially as it had been and as it will always be, but with sufficient mass density in the vicinity of the sigularity to force closure. Obviously matter ejected from the singularity at (0,0) must have an initial velocity sufficient to overcome the gravitational attraction of the singularity, as must antimatter, in order to reach the cusp at (t

Because the CCM spherical shell bound by the planck temperature (T=10

By providing for nucleosynthesis within distinct matter and antimatter clusters baryon, lepton and charge symmetry can be maintained without mutual annihilation of matter. This CCM view is of course far closer to the SCM than are the inflationary models.

Because clustering occurred before decoupling, galactic clusters and other large scale structures are a natural outcome of the CCM. Genesis is an ongoing concern and hence disturbances in the spectral distribution of energy radiating from the fireball will integrate over time, smoothing the spectral distribution.

Homogeneity

On the scale of the Hubble length the universe is essentially homogeneous and isotropic. According to the CCM this observation would be expected. Although each comoving sphereical shell might in itself be highly heterogeneous and anisotropic, on viewing the universe through successive shells the universe would appear both homogeneous and isotropic. as is observed. Viewing through a limited number of shells however should reveal the intrinsic heterogeniety of our local portion of the universe, as also is observed. Evidently, the inhomogeneity of each shell must affect the matter ditribution in successive shells or large scale structure could not form.

8 VERIFICATION

Certain claims are made herein concerning the CCM, namely that:

1) a temporal singularity exists with zero-volume and infinite temperature;

2) no information whatsoever can pass through the temporal singularity;

3) matter cannot exist at temperatures higher than the Planck temperature;

4) there is sufficient mass in the vicinity of the singularity to effect closure.

5) no gravitational potential exists between equivalent matter and antimatter particles;

6) large scale structure forms before nucleosynthesis; and

7) the baryon number, lepton number, and charge number of the universe are each absolutely zero.

The spacetime geodesics are essentially time invarient with K=+1 in the CCM rather than expanding as in the SCM with most likely K<0. Because the local mass-density of the universe is greatest at the singularity the greatest curvature occurs about the singularity. This does not imply however that most of the mass of the CCM universe resides in the vicinity of the singularity.

The failure of any of the tabulated claims will of course compromise the CCM model, but evidence of that failure must be empirical. The only condition amenable to an empirical test at present is conditionÝ(4). According to Nieto & Goldman such an experiment is not only possible, but practical, albeit with much difficulty. Such experiments are being prepared at CERN (Nieto).

Time-of-flight determinations were conducted by Fairbanks to compare the gravitational deceleration of electrons and positrons in a vertical drift tube. The results were inconclusive because stray electric and magnetics fields interact with the positron charge as predicted by Schiff & Barnhill, although attempts were made to reduce stray fields to <10

Again using a vertical time-of-flight procedure, described by Holtzscheiter. Antiprotons will be cooled to a few degrees Kelvin and collected. The deceleration of antiprotons escaping up the drift tube will be measured and compared with the deceleration of protons. Stray fields unfortunately had the same debilitating effect as on the lepton experiment.

Neutrons have been found by McReynolds to be affected by a gravitational field in the expected manner without being hampered by stray fields. Antineutrons would solve the stray field problem but they are difficult to collect and thermalize (Brando, Fainberg, Kalogeropoulos, Michael & Tzanakos). Antihydrogen would be an ideal particle to examine but is difficult to manufacture although experiments are planned at CERN to commence in the next two years. Horizonal trajectory tests may also be considered and would perhaps be superior to vertical drift experiments as a wider range of initial particle accelerations can be tolerated.

In 1957 Fairbanks
made the observation that *"Nothing is known about the gravitational
acceleration of antimatter"*. His assessment still stands.

9 DISCUSSION

According to the CCM the universe is in a permanent state of unending genesis, with a cosmogony being meaningful only for a specified comoving portion of the universe. Our portion the universe had evolved from a local t

Following spacetime divergence, the galaxies move towards convergence. The processes that gave birth to the structure of the universe are then reversed, with the eventual annihilation of matter and antimatter; the resultant energy merging at the singularity as T=oo radiation . Evidently this process requires that baryon number, lepton number and charge number be zero because no information whatsoever can pass through the singularity at T=oo.

10 SUMMARY

A Continuum Cosmological Model is presented that in large measure is consistant with the mechanics of the Standard Cosmological Model. However, according to the Continuum Cosmological Model

According to the SCM the universe is no older than our clocks indicate. No matter how far out we gaze, the age of the universe is no older than our present age. According to CCM however, our clocks merely measure the age of our co-moving portion of the universe. Other portions are either older or younger, depending on their timeframe in the CCM Universe.