Information content in the redshift-space galaxy power spectrum and bispectrum

Abstract

We present a Fisher information study of the statistical impact of galaxy bias and selection effects on the estimation of key cosmological parameters from galaxy redshift surveys; in particular, the angular diameter distance, Hubble parameter, and linear growth rate at a given redshift, the cold dark matter density, and the tilt and running of the primordial power spectrum. The line-of-sight-dependent selection contributions we include here are known to exist in real galaxy samples. We determine the maximum wavenumber included in the analysis by requiring that the next-order corrections to the galaxy power spectrum or bispectrum, treated here at next-to-leading and leading order, respectively, produce shifts of ≲ 0.25σ on each of the six cosmological parameters. With the galaxy power spectrum alone, selection effects can deteriorate the constraints severely, especially on the linear growth rate. Adding the galaxy bispectrum helps break parameter degeneracies significantly. We find that a joint power spectrum-bispectrum analysis of a Euclid-like survey can still measure the linear growth rate to 10% precision after complete marginalization over selection bias. We also discuss systematic parameter shifts arising from ignoring selection effects and/or other bias parameters, and emphasize that it is necessary to either control selection effects at the percent level or marginalize over them. We obtain similar results for the Roman Space Telescope and HETDEX.