Constraints on Cosmological Parameters from the Lyα Forest Power Spectrum andCOBEDMR

John Phillips,Max Pettini,Neal Katz,Lars Hernquist,David H Weinberg,Rupert A C Croft

doi:10.1086/322369

Abstract

We combine COBE DMR measurements of cosmic microwave background (CMB) anisotropy with a recent measurement of the mass power spectrum at redshift z = 2.5 from Lyα forest data to derive constraints on cosmological parameters and test the inflationary cold dark matter (CDM) scenario of structure formation. By treating the inflationary spectral index n as a free parameter, we are able to find successful fits to the COBE and Lyα forest constraints in Ωm = 1 models with and without massive neutrinos and in low-Ωm models with and without a cosmological constant. Within each class of model, the combination of COBE and the Lyα forest P(k) constrains a parameter combination of the form ΩmhαnβΩ, with different indices for each case. This new constraint breaks some of the degeneracies in cosmological parameter determinations from other measurements of large-scale structure and CMB anisotropy. The Lyα forest P(k) provides the first measurement of the slope of the linear mass power spectrum on ~Mpc scales, ν = -2.25 ± 0.18, and it confirms a basic prediction of the inflationary CDM scenario: an approximately scale invariant spectrum of primeval fluctuations (n ≈ 1) modulated by a transfer function that bends P(k) toward kn-4 on small scales. Considering additional observational data, we find that COBE-normalized, Ωm = 1 models that match the Lyα forest P(k) do not match the observed masses of rich galaxy clusters, and that low-Ωm models with a cosmological constant provide the best overall fit to the available data, even without the direct evidence for cosmic acceleration from Type Ia supernovae. With our fiducial parameter choices, the flat, low-Ωm models that match COBE and the Lyα forest P(k) also match recent measurements of small-scale CMB anisotropy. Modest improvements in the Lyα forest P(k) measurement could greatly restrict the allowable region of parameter space for CDM models, constrain the contribution of tensor fluctuations to CMB anisotropy, and achieve a more stringent test of the current consensus model of structure formation.

Highlights

Cosmological models based on cold dark matter (CDM) and simple versions of inÑation have had considerable success in accounting for the origin of cosmic structure
We focus our attention on several other constraints that can be cast into a form that complements our results from ° 3 : the mass function of galaxy clusters, the mass power spectrum inferred from galaxy peculiar velocities, the shape parameter of the galaxy power spectrum, and a constraint on n from cosmic microwave background (CMB) anisotropy data
The TCDM, OCDM, and CHDM models are clearly ruled out, and while we have not attempted to adjust their parameters within the constraints allowed by equations (7) and (8), it appears unlikely that any such adjustment would allow these models to Ðt the current CMB data

Summary

INTRODUCTION

Cosmological models based on cold dark matter (CDM) and simple versions of inÑation have had considerable success in accounting for the origin of cosmic structure. In this class of models, the primordial density Ñuctuations are Gaussian distributed, and the shape of their power spectrum is determined by a small number of physical parameters that describe the inÑationary Ñuctuations themselves and the material contents of the universe. We combine the COBE normalization with a recent measurement of the matter power spectrum by Croft et al (1999b, hereafter CWPHK) to test the inÑation ] CDM scenario and constrain its physical.

PARAMETER SPACE FOR CDM MODELS

COMBINING WITH OTHER CONSTRAINTS

Findings

CONCLUSIONS