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

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 ofn_p = 5 × 10^-4 (h Mpc^-1)³, redshift z = 0.5, and a covariance corresponding to a survey volume of V_survey = 25 (h^-1Gpc)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,σ₈,f_nl,α_∥,α_⊥) 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.