Cosmology in the Next Millennium: Combining MAP and SDSS Data to Constrain In ationary Models

The existence of primordial adiabatic Gaussian random-phase density uctuations is a generic prediction of innation. The properties of these uctuations are completely speciied by their power spectrum A 2 S (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 2 S (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 2 S (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 0:5hMpc ?1 can be determined to 10% accuracy for k 0:01hMpc ?1 , and to 1% accuracy for k 0:1hMpc ?1. The uncertainty in the primordial power spectrum increases by less than a factor of 2 if we solve simultaneously for the dimensionless Hubble constant h, the cosmological constant , the baryon fraction b , the reionization optical depth ri , and eeective bias between the matter density eld and the galaxy redshift density eld b ee. Alternately, if we restrict A 2 S (k) to be a power law, we nd 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, 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 model-independent measurement of the primordial power spectrum, giving us valuable information on physics in the early Universe, and providing clues to the correct innationary model.