Decay of baryon inhomogeneities in an expanding universe

Abstract

Baryon inhomogeneities are generated early in the universe. These inhomogeneities affect the phase transition dynamics of subsequent phase transitions, they also affect the nucleosynthesis calculations. We study the decay of the inhomogeneities in the early universe using the diffusion equation in the Friedmann–Lemaître–Robertson–Walker metric. We calculate the interaction cross section of the quarks with the neutrinos, the electrons and the muons and obtain the diffusion coefficients. The diffusion coefficients are temperature dependent. We find that the expansion of the universe causes the inhomogeneities to decay at a faster rate. We find that the baryon inhomogeneities generated at the electroweak epoch have low amplitudes at the time of the quark hadron transition and hence will not affect the phase transition dynamics unless they are generated with a amplitude greater than 10^{5} times the background density. After the quark hadron transition, we include the interaction of the muons with the hadrons till 100 MeV. We find that large density inhomogeneities generated during the quark hadron transition with sizes of the order of 1 km must have amplitudes greater than 10^{5} times the background density to survive upto the nucleosynthesis epoch. This puts constraints on any models that generate these inhomogeneities