Constraints on cosmological parameters from the Ly alpha forest power spectrum and COBE DMR

We combine COBE DMR measurements of cosmic microwave background (CMB) aniso tropy with a recent measurement of the mass power spectrum at redshift z = 2.5 from Ly alpha forest data to derive constraints on cosmological paramet ers and test the inflationary cold dark matter (CDM) scenario of structure formation. By treating the inflationary spectral index n as a free paramete r, we are able to find successful fits to the COBE and Ly alpha forest cons traints in Omega (m) = 1 models with and without massive neutrinos and in l ow-Omega (m) models with and without a cosmological constant. Within each c lass of model, the combination of COBE and the Ly alpha forest P(k) constra ins a parameter combination of the form Omega (m)h(alpha)n(beta)Omega (gamm a)(b), with different indices for each case. This new constraint breaks som e of the degeneracies in cosmological parameter determinations from other m easurements of large-scale structure and CMB anisotropy. The Ly alpha fores t P(k) provides the first measurement of the slope of the linear mass power spectrum on similar to Mpc scales, nu -2.25 +/- 0.18, and it confirms a ba sic prediction of the inflationary CDM scenario : an approximately scale in variant spectrum of primeval fluctuations (n approximate to 1) modulated by a transfer function that bends P(k) toward k(n-4) on small scales. Conside ring additional observational data, we find that COBE-normalized, Omega (m) = 1 models that match the Ly alpha forest P(k) do not match the observed m asses of rich galaxy clusters, and that low-Omega (m) models with a cosmolo gical constant provide the best overall fit to the available data, even wit hout the direct evidence for cosmic acceleration from Type Ia supernovae. W ith our fiducial parameter choices, the flat, low-Omega (m) models that mat ch COBE and low the Lya forest P(k) also match recent measurements of small -scale CMB anisotropy. Modest improvements in the Ly alpha forest P(k) meas urement could greatly restrict the allowable region of parameter space for CDM models, constrain the contribution of tensor fluctuations to CMB anisot ropy, and achieve a more stringent test of the current consensus model of s tructure formation.