Considerations from particle physics can have a major impact on much of the preceding discussion. In fact, the predictions of the amplitudes of the largest scale structures observed in the Universe, the dipole and quadrupole anisotropies of the cosmic microwave background radiation, may depend sensitively on the most microscopic scales of the ultimate theory of elementary particles. This apparently paradoxical situation is not really so surprising, given that our theory of large-scale structure depends on the specified initial conditions at an epoch when causally connected regions encompassed only a small number of elementary particles.

A recent development in cosmology has centered on the application of
grand unified theories (GUTs) of the strong, weak and electromagnetic
interactions to the very early Universe. Indeed, the extreme energies
attained as
*t*
0 provide one of the few environments for
studying the
implications of GUTs. One of the few fundamental numbers needed to
characterize the Friedmann cosmological model is the dimensionless
entropy per baryon, equal to 2.5 ×
10^{10}(_{b} *h*^{2} / 0.01)
for photons and
three neutrino flavours. Perhaps the most spectacular success of GUTs
has been to provide a natural explanation (at least in order of
magnitude) for this number in terms of baryon-non-conserving processes
that occur in these theories (see
Weinberg, 1982,
for a recent
review). While the entropy-per-comoving-volume remains approximately
constant, the baryon number, an excess of particles over
antiparticles, which is initially zero, is generated as the symmetry
of the grand unified era is broken soon after the Planck time. Since a
universal baryon number is generated, any pre-existing isothermal
perturbations, which are equivalent to baryon number or specific
entropy variations, cannot survive the baryosynthesis era in the
standard model. Only adiabatic perturbations should be present to form
galaxies, according to this result.

There is at least one noteworthy means of resurrecting isothermal
fluctuations. Spatial variations in the expansion rate on scales
larger than the horizon during baryosynthesis will give rise to
entropy fluctuations
(Bond, Kolb and Silk,
1982;
Barrow and Turner, 1981).
To understand how this arises, consider first the role of the
X-bosons, which unify the electromagnetic, weak, and strong
interactions, and consequently mediate proton decay. Only because the
baryon non-conserving reactions go out of equilibrium as the Universe
expands does baryon number build up, *X*-bosons being
destroyed more often than they are created. Reactions like
*X*
*qq* dominate over
*X*
by an amount that depends on how much CP violation there is in
*X*-decay. This is a free parameter, although measurements
for the kaon system indicate a value
~ 3 ×
10^{-3} for the fractional amount of CP
violation. As the temperature drops to
*kT* << *mX* ~ 10^{15} GeV, both the
baryon formation and destruction rates become small relative to the
expansion rate, and a net baryon number is frozen out. For a uniformly
expanding Friedmann cosmological model, the only free parameter is a
value of order 10^{-6} is required in order to attain the
observed entropy per baryon
(Kolb and Wolfram, 1980;
Fry, Olive and Turner,
1980).

Now consider the fate of energy density inhomogeneities, which can
be decomposed into two independent linear fluctuation modes
corresponding to constant and decaying curvature perturbations. While
any primordial entropy fluctuations are "cooked" away, the growing
mode of primordial adiabatic can in principle perturb the expansion
rate at baryosynthesis, except that its effect must be small at this
epoch in order to avoid resulting in unacceptably large energy density
inhomogeneities in the very early Universe. The decaying curvature
mode can lead to a potentially large perturbation of the expansion
rate as
*t*
0, provided that the amplitude of the growing
mode is initially suppressed. This could happen naturally if one
required at, say, the Planck epoch that there was equipartition of
energy between the modes
(Kompaneets, Lukash and
Nvikov, 1982).

There is an additional type of fluctuation that can have a dramatic
effect on baryosynthesis, namely spatial variations in the expansion
rate due to shear or vorticity perturbations. Shear inhomogeneity
includes a decaying mode that could have been large near the Planck time,
*t*_{pl} ~ (8
*Gh*_{p} / *c*^{5})^{1/2} ~
10^{-43} s. One might conjecture that at this
epoch, the threshold of cosmology, all possible decaying modes were
present, only asymptotically resulting in a nearly uniform Friedmann
cosmology. Provided the grand unification era is sufficiently close to
the Planek era at
*kT* ~ 10^{19} GeV, and supersymmetric unified theories
indeed advocate a grand unification energy,
*mX* ~ 10^{17} GeV, the decaying
modes should still be significant at baryosynthesis. For example, if
collisionless particles dominate the energy density, the decaying shear
mode =
_{initial}(*mX* /
*m*_{Planck})^{1/2} ~
0.1_{initial} at this epoch, where
is the
ratio of shear to expansion rates. Analysis of the effect of shear on
baryosynthesis shows that the isothermal fluctuation theory of galaxy
formation is still viable if
_{initial}
is present on comoving scales well above 10^{6}
*M*_{}.
Moreover, the initial shear will have rapidly decayed, and
be completely negligible even by the epoch of nucleosynthesis. One can
also imagine a universe which initially is dominated by inhomogeneous
shear with (*m*_{Planck}) >> 1; in this case
_{B} /
_{B} ~
/
. One potential
source of difficulty in these models is that decaying curvature modes are
coupled to growing modes at any transition from a relativistic
collisionless to a collisional particle dominated universe
(Vishniac, 1982).