Structure formation in the universe: comparison of some observations and models

Abstract

Recent cosmological observations like the detection of large scale streaming motion, APM and QOOT surveys, detection of temperature anisotropy in the microwave background radiation (MBR) etc., impose severe constraints on models for structure formation. The theoretical background for these models and the restrictions arising from the observations are reviewed. In particular, the COBE satellite results for the temperature fluctuation (ΔT/T)_rms = (1.1 ± 0.2) × 10^-5 and (ΔT/T)_Q = (0.48 ± 0.15) × 10^-5 are consistent with a scale-invariant spectrum, of density perturbations σ(R)=(R₀/R)² at large scales with R₀ ⋍ (23.9 ± 2.1) h^-1 Mpc. This is consistent with APM data and large scale streaming velocity measurements (both of which require σ (50 h^-1≃Mpc) ⋍ 0.2) provided the scale- invariant spectrum is extrapolated from 3000 h^-1 Mpc to 50h-1 Mpc. Comparing the shape of σ(R) at R≲60 h^-1 Mpc, determined from galaxy surveys (RAS, CfA, and APM), with the COBE result, we find that a relatively rapid bend in σ (R) around R ≈ (40 - 60) h^-1 Mpc is needed. The fact that COBE results match with galaxy survey results at 50 h^-1Mpc suggests that biasing is not significant at R≳(50h^-1Mpc. On the other hand a CDM spectrum, normalized to the COBE value, will overshoot galaxy survey results at small scales. Such a spectrum can be consistent with observations only if the biasing varies with scale and b < 1 at small scales. The implications of this result are discussed.