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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.


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