Constraints on the shape of the density spectrum from COBE and galaxy surveys

Abstract

Many popular models for galaxy formation are based on power spectra which behave as P(k) = Ak for small k and flatten at large k. The resulting mass fluctuation can be constrained by galaxy surveys up to R about 60/h Mpc. Recent COBE results, however, constrain the dark matter spectrum at very large scales and are consistent with a scale-invariant density spectrum σ_DM(R). The extrapolated COBE results matches galaxy survey results at 50/h Mpc, suggesting that biasing is not significant at R greater than about 50/h Mpc. On the other hand, a CDM spectrum normalized to the COBE value overshoots galaxy survey results at small scales. Comparing the shape of sigma(R) at R less than about 60/h Mpc with the COBE results, it is found that relatively rapid bend in σ(R) around R 40-60/h Mpc is needed. It is shown that simple models describing this bend are severely constrained.