IAS/SNS-AST-95/42, CfPA-TH-95-18, UTAP-212 SMALL SCALE COSMOLOGICAL PERTURBATIONS: AN ANALYTIC APPROACH y

Through analytic techniques veri ed by numerical calculations, we establish general relations between the matter and cosmic microwave background (CMB) power spectra and their dependence on cosmological parameters on small scales. Fluctuations in the cosmic microwave background (CMB), baryons, cold dark matter, and neutrinos receive a boost at horizon crossing. Baryon drag on the photons causes alternating acoustic peak heights in the CMB and is uncovered in its bare form under the photon di usion scale. Decoupling of the photons at last scattering and of the baryons at the end of the Compton drag epoch, freezes the di usion-damped acoustic oscillations into the CMB and matter power spectra at di erent scales. We determine the dependence of the respective acoustic amplitudes and damping lengths on fundamental cosmological parameters. The baryonic oscillations, enhanced by the velocity overshoot e ect, compete with CDM uctuations in the present matter power spectrum. We present new exact analytic solutions for the cold dark matter uctuations in the presence of a growth-inhibiting radiation and baryon background. Combined with the acoustic contributions and baryonic infall into CDM potential wells, this provides a highly accurate analytic form of the small-scale transfer function in the general case.