Nonlinear evolution of very small scale cosmological baryon perturbations at recombination

The evolution of baryon density perturbations on very small scales is investigated. In particular, the nonlinear growth induced by the radiation drag force from the shear velocity field on larger scales during the recombination epoch, originally proposed by Shaviv in 1998, is studied in detail. We find that inclusion of the diffusion term, which Shaviv neglected in his analysis, results in rather mild growth with growth factor ≪ 100, instead of the enormous amplification, ∼ 10⁴, of Shaviv's original claim, since the diffusion suppresses the growth. The growth factor strongly depends on the amplitude of the large-scale velocity field. The nonlinear growth mechanism is applied to density perturbations of general adiabatic cold dark matter (CDM) models. For these models, it has been found in previous works that the baryon density perturbations are not completely erased by diffusion damping if there are gravitational potential perturbations from the CDM component. Employing the perturbed rate equation derived in this paper, the nonlinear evolution of baryon density perturbations is investigated. We find that: (1) The nonlinear growth is larger for smaller scales. This mechanism only affects perturbations whose scales are smaller than ∼10₂ M⊙, comparable to stellar scales. (2) The maximum growth factors of baryon density fluctuations for various COBE-normalized CDM models are typically less than a factor of 10 for 3 σ large-scale velocity peaks. (3) The growth factor depends on Ωb.