  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.
