Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations

Abstract: We perform for the first time a joint analysis of the monopole and quadrupoles for power spectrum, bispectrum and integrated trispectrum (i-trispectrum) from the redshift space matter field in N-body simulations. With a full Markov Chain Monte Carlo exploration of the posterior distribution, we quantify the constraints on cosmological parameters for an object density of $n_\mathrm{p}=5\times10^{-4} (h\,\mathrm{Mpc}^{-1})^{3}$, redshift $z=0.5$, and a covariance corresponding to a survey volume of $V_\mathrm{survey} =25\,(h^{-1}\mathrm{Gpc})^3$, a set up which is representative of forthcoming galaxy redshift surveys. We demonstrate the complementarity of the bispectrum and i-trispectrum in constraining key cosmological parameters. In particular, compared to the state-of-the-art power spectrum (monopole plus quadrupole) and bispectrum (monopole) analyses, we find 1D $68\%$ credible regions smaller by a factor of $(72\%,78\%,72\%,47\%,46\%)$ for the parameters $(f,\sigma_8,f_\mathrm{nl},\alpha_\parallel,\alpha_\perp)$ respectively. This work motivates the additional effort necessary to include the redshift-space anisotropic signal of higher-order statistics in the analysis and interpretation of ongoing and future galaxy surveys.