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 non-linearities 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 ) \times 10 ^ { -3 } and \sigma ( \alpha _ { s } ) = ( 5.9 ,~ { } 5.7 ,~ { } 2.4 ) \times 10 ^ { -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 ) \times 10 ^ { -3 } .