Cosmology in the Next Millennium: Combining MAP and SDSS Data to Constrain Inflationary Models
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_S^2(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_S^2(k) and the cosmological parameters by combining the data from the 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. If we assume that the cosmological parameters are known a priori, the primordial power spectrum in 20 steps in log k to k\leq 0.5hMpc^{-1} can be determined to \sim 10% accuracy for k\sim 0.01hMpc^{-1}, and to \sim 1% accuracy for $k\sim 0.1hMpc^{-1}. The uncertainty in the primordial power spectrum increases by less than a factor of 2 if we solve simultaneously for h, \Lambda, \Omega_b, \tau_{ri}, and the effective bias between the matter density field and the galaxy redshift density field b_{eff}. Thus, combining the MAP and SDSS data allows the independent measurement of important cosmological parameters, and a model-independent measurement of the primordial power spectrum, giving us valuable information on physics in the early Universe, and providing clues to the correct inflationary model.(abridged)Keywords
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