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

Abstract

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 $0.5lzl2$, $2lzl4$, and $3.5lzl6.5$. 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 $\ensuremath{\sigma}({m}_{\ensuremath{\nu},\mathrm{tot}})=0.059$, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as $\ensuremath{\sigma}({m}_{\ensuremath{\nu},\mathrm{tot}})$ 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, $\ensuremath{\sigma}({n}_{s})=(3.8,3.7,3.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\ensuremath{\sigma}({\ensuremath{\alpha}}_{s})=(5.9,5.7,2.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at ${k}_{0}=0.05\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, 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 ${\ensuremath{\alpha}}_{s}$ 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, ${\ensuremath{\alpha}}_{s}=\ensuremath{-}(0.8\char21{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.