Nonlinear Evolution of Very Small Scale Cosmological Baryon Perturbations at Recombination

The evolution of baryon density perturbations on very small scales isinvestigated. In particular, the nonlinear growth induced by the radiation dragforce from the shear velocity field on larger scales during the recombinationepoch, which is originally proposed by Shaviv in 1998, is studied in detail. Itis found that inclusion of the diffusion term which Shaviv neglected in hisanalysis results in rather mild growth whose growth rate is $\ll 100$ insteadof enormous amplification $\sim 10^4$ of Shaviv's original claim since thediffusion suppresses the growth. The growth factor strongly depends on theamplitude of the large scale velocity field. The nonlinear growth mechanism isapplied to density perturbations of general adiabatic cold dark matter (CDM)models. In these models, it has been found in the previous works that thebaryon density perturbations are not completely erased by diffusion damping ifthere exists gravitational potential of CDM. With employing the perturbed rateequation which is derived in this paper, the nonlinear evolution of baryondensity perturbations is investigated. It is found that: (1) The nonlineargrowth is larger for smaller scales. This mechanism only affects theperturbations whose scales are smaller than $\sim 10^2M_\odot$, which arecoincident with the stellar scales. (2) The maximum growth factors of baryondensity fluctuations for various COBE normalized CDM models are typically lessthan factor 10 for $3-\sigma$ large scale velocity peaks. (3) The growth factordepends on $\Omega_{\rm b}$.Comment: 24 pages, 9 figures, submitted to Ap