Generation of isothermal perturbations in the very early universe

If the baryon asymmetry in the universe is produced at a temperature approx.1015 GeV as a result of baryon nonconservation, as predicted in grand unified theories, then perturbations in the baryon density should also be created at this time. Adiabatic perturbations are easily generated by energy density fluctuations. Isothermal (entropy) perturbations can be created as a result of spatial variations in the local expansion rate which can result from spatial inhomogeneities in the cosmological constant, scalar curvature, or shear (and vorticity). We discuss the role of each in turn. We calculate numerically the entropy per baryon created in Bianchi I universe with shear, using model systems based upon the SU(5) grand unified theory. We calculate an effective viscosity in this theory, and use it to show that viscous damping of shear is not sufficiently large to smooth the universe. The shear dissipation after baryon synthesis generates sufficient entropy that we can constrain the magnitude of the decaying mode of shear to values which are negligible by the neutrino decoupling and primordial nucleosynthesis eras. The survival of shear inhomogeneities results in isothermal perturbations being generated. these could be of the magnitude required for the gravitational instability theory of galaxy formation if decaying modes are preferentially selected over growing modes, and galaxy scale shear inhomogeneities exist at very early times