Cosmology in the next millennium: Combining microwave anisotropy probe andSloan Digital Sky Survey data to constrain inflationary models

The existence of primordial adiabatic Gaussian random-phase density fluctua tions is a generic prediction of inflation. The properties of these fluctua tions are completely specified by their power spectrum, A(s)(2)(k). The bas ic cosmological parameters and the primordial power spectrum together compl etely specify predictions for the cosmic microwave background radiation ani sotropy and large-scale structure. Here we show how we can strongly constra in both A(s)(2)(k) and the cosmological parameters by combining data from t he Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow A(s)(2)(k) to be a free function , and thus probe features in the primordial power spectrum on all scales. I f we assume that the cosmological parameters are known a priori and that ga laxy bias is linear and scale-independent, and if we neglect nonlinear reds hift distortions, the primordial power spectrum in 20 steps in Log k to k l ess than or equal to 0.5 h Mpc(-1) can be determined to similar to 16% accu racy for k similar to 0.01 h Mpc(-1), and to similar to 1% accuracy for k s imilar to 0.1 h Mpc(-1). The uncertainty in the primordial power spectrum i ncreases by a factor of up to 3 on small scales if we solve simultaneously for the dimensionless Hubble constant h, the cosmological constant Lambda, the baryon fraction Omega(b), the reionization optical depth tau(ri), and t he effective bias between the matter density field and the redshift-space g alaxy density field b(eff). Alternately, if we restrict A(s)(2)(k) to be a power law, we find that inclusion of the SDSS data breaks the degeneracy be tween the amplitude of the power spectrum and the optical depth inherent: i n the MAP data, significantly reduces the uncertainties in the determinatio n of the matter density and the cosmological constant, and allows a determi nation of the galaxy bias parameter. Thus, combining the MAP and SDSS data allows the independent measurement of important cosmological parameters, an d a measurement of the primordial power spectrum independent of inflationar y models, giving us valuable information on physics in the early universe, and providing clues to the correct inflationary model.