Cosmology with high-redshift galaxy survey: Neutrino mass and inflation

High-z galaxy redshift surveys open up exciting possibilities for precision determinations of neutrino masses and inflationary models. The high-z surveys are more useful for cosmology than low-z ones owing to much weaker nonlinearities in matter clustering, redshift-space distortion, and galaxy bias, which allows us to use the galaxy power spectrum down to the smaller spatial scales that are inaccessible by low-z surveys. We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum. To illustrate capabilities of high-z surveys for constraining neutrino masses and the primordial power spectrum, we compare three future redshift surveys covering 300 square degrees at 0.5 < z < 2, 2 < z < 4, and 3.5 < z < 6.5. We find that, combined with the cosmic microwave background data expected from the Planck satellite, these surveys allow precision determination of the total neutrino mass with the projected errors of sigma(m(nu,tot))=0.059, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as sigma(m(nu,tot)) is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments, by up to a factor of 4 for the highest redshift survey. The accuracies of constraining the tilt and running index of the primordial power spectrum, sigma(n(s))=(3.8,3.7,3.0)x10(-3) and sigma(alpha(s))=(5.9,5.7,2.4)x10(-3) at k(0)=0.05 Mpc(-1), respectively, are smaller than the current uncertainties by more than an order of magnitude, which will allow us to discriminate between candidate inflationary models. In particular, the error on alpha(s) from the future highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling, alpha(s)=-(0.8-1.2)x10(-3).