Enhancing BOSS bispectrum cosmological constraints with maximal compression

Abstract

We apply two compression methods to the galaxy power spectrum monopole/quadrupole and
\nbispectrum monopole measurements from the Baryon Oscillation Spectroscopic Survey DR12
\nCMASS sample. Both methods reduce the dimension of the original data vector to the number
\nof cosmological parameters considered, using the Karhunen–Loeve (KL) algorithm with an `
\nanalytic covariance model. In the first case, we infer the posterior through Markov chain
\nMonte Carlo (MCMC) sampling from the likelihood of the compressed data vector (MC–
\nKL). The second, faster option, works by first Gaussianizing and then orthogonalizing the
\nparameter space before the compression; in this option (G-PCA) we only need to run a lowresolution preliminary MCMC sample for the Gaussianization to compute our posterior. Both
\ncompression methods accurately reproduce the posterior distributions obtained by standard
\nMCMC sampling on the CMASS data set for a k-space range of 0.03–0.12 h Mpc−1
\n. The
\ncompression enables us to increase the number of bispectrum measurements by a factor of ∼23
\nover the standard binning (from 116 to 2734 triangle bins used), which is otherwise limited by
\nthe number of mock catalogues available. This reduces the 68 per cent credible intervals for the
\nparameters (b1, b2, f, σ8) by (−24.8 per cent, −52.8 per cent, −26.4 per cent, −21 per cent),
\nrespectively. Using these methods for future redshift surveys such as DESI, Euclid, and PFS
\nwill drastically reduce the number of simulations needed to compute accurate covariance
\nmatrices and will facilitate tighter constraints on cosmological parameters.