Cosmology in the Next Millennium: Combining Microwave Anisotropy Probe and Sloan Digital Sky Survey Data to Constrain Inflationary Models

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Abstract
The existence of primordial adiabatic Gaussian random-phase density fluctuations is a generic prediction of inflation. The properties of these fluctuations are completely specified by their power spectrum, A(k). The basic cosmological parameters and the primordial power spectrum together completely specify predictions for the cosmic microwave background radiation anisotropy and large-scale structure. Here we show how we can strongly constrain both A(k) and the cosmological parameters by combining data from the Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow A(k) to be a free function, and thus probe features in the primordial power spectrum on all scales. If we assume that the cosmological parameters are known a priori and that galaxy bias is linear and scale-independent, and if we neglect nonlinear redshift distortions, the primordial power spectrum in 20 steps in log k to k≤0.5 h Mpc-1 can be determined to ~16% accuracy for k~0.01 h Mpc-1, and to ~1% accuracy for k~0.1 h Mpc-1. The uncertainty in the primordial power spectrum increases by a factor of up to 3 on small scales if we solve simultaneously for the dimensionless Hubble constant h, the cosmological constant Λ, the baryon fraction Ωb, the reionization optical depth τri, and the effective bias between the matter density field and the redshift-space galaxy density field beff. Alternately, if we restrict A(k) to be a power law, we find that inclusion of the SDSS data breaks the degeneracy between the amplitude of the power spectrum and the optical depth inherent in the MAP data, significantly reduces the uncertainties in the determination of the matter density and the cosmological constant, and allows a determination of the galaxy bias parameter. Thus, combining the MAP and SDSS data allows the independent measurement of important cosmological parameters, and a measurement of the primordial power spectrum independent of inflationary models, giving us valuable information on physics in the early universe, and providing clues to the correct inflationary model.

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