Large- and small-scale constraints on power spectra in Omega = 1 universes

The cold dark matter (CDM) model of structure formation, normalized on large scales, leads to excessive pairwise velocity dispersions on small scales. In an attempt to circumvent this problem, we study three scenarios (all with {OMEGA} = 1) with more large-scale and less small- scale power than the standard CDM model: (1) cold dark matter with significantly reduced small-scale power (inspired by models with an admixture of cold and hot dark matter); (2) cold dark matter with a non- scale-invariant power spectrum; and (3) cold dark matter with coupling of dark matter to a long-range vector field. Despite the reduced small-scale power, when such models are evolved to large amplitude, the velocities on small scales are actually increased over CDM with the same value of σ_8_. This "flip-over," in disagreement with the expectation from linear perturbation theory, arises from the nonlinear coupling of the extra power on large scales with shorter wavelengths. However, the recent COBE DMR results indicate smaller amplitudes for these models, σ_8_~ 0.5-0.7, than for CDM (for which σ_8_~ 1.2). Therefore, when normalized to COBE on large scales, such models do lead to reduced velocities on small scales and they produce fewer halos compared with CDM. However, models with sufficiently low small-scale velocities apparently fail to produce an adequate number of halos.