Constraints on Cosmological Parameters from the Lyman-alpha Forest Power   Spectrum and COBE-DMR
  We combine COBE-DMR measurements of cosmic microwave background anisotropy with a recent measurement of the mass power spectrum at redshift z=2.5 from Lya forest data to derive constraints on cosmological parameters and test the inflation+CDM scenario of structure formation. By treating the inflationary spectral index n as a free parameter, we can find successful fits to the COBE and Lya forest constraints in Omega_m=1 models with and without massive neutrinos and in low-Omega_m models with and without a cosmological constant. Within each class of model, the combination of COBE and the Lya forest P(k) constrains a parameter combination of the form (Omega_m h^a n^b Omega_b^c), with different indices for each case. This new constraint breaks some of the degeneracies in cosmological parameter determinations from other measurements. The Lya forest P(k) provides the first measurement of the slope of the linear mass power spectrum on ~Mpc scales, and it confirms a basic prediction of the inflationary CDM scenario: a nearly scale-invariant spectrum of primeval fluctuations (n~1) that bends towards k^{n-4} on small scales. Considering additional observational data, we find that COBE-normalized, Omega_m=1 models that match the Lya forest P(k) do not match the observed masses of rich galaxy clusters and that a low-Omega_m model with a cosmological constant provides the best overall fit, even without the direct evidence for cosmic acceleration from supernovae. Modest improvements in the Lya 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. 
John Phillips, David H. Weinberg, Rupert A. C. Croft, Lars Hernquist,   Neal Katz and Max Pettini