Small Scale Cosmological Perturbations:
An Analytic Approach:
Through analytic techniques verified 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 CMB,
baryons, cold dark matter (CDM), 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 diffusion scale.
Decoupling of the photons at last scattering and
of the baryons at the end of the Compton drag epoch, freezes the
diffusion-damped acoustic oscillations into
the CMB and matter power spectra at different 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 effect,
compete with CDM fluctuations in the present matter power spectrum.
We present new exact analytic solutions for the
cold dark matter fluctuations 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.
Astrophys. J. 471 542 (1996)