Maximal compression of the redshift space galaxy power spectrum and bispectrum

TL;DR

This paper introduces two efficient data compression methods for redshift space galaxy power spectrum and bispectrum analysis, enabling faster cosmological parameter inference with minimal loss of accuracy for future surveys.

Contribution

It presents two novel compression techniques that significantly reduce data dimensionality and computational time while maintaining accurate posterior distributions for cosmological parameters.

Findings

Both methods recover 68% credible regions within 0.7% and 2% of MCMC results.

Compression reduces data size from ~1000 to 7 parameters, speeding up analysis.

Using combined power spectrum and bispectrum improves parameter constraints over power spectrum alone.

Abstract

We explore two methods of compressing the redshift space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data-vector ( e.g. 1000 elements ) to the number of cosmological parameters considered ( e.g. seven ) using the Karhunen-Lo\`eve algorithm. In the first case, we run MCMC sampling on the compressed data-vector in order to recover the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The second option, approximately 2000 times faster, works by orthogonalising the parameter space through diagonalisation of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, EUCLID and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data-vector, both compression methods on average recover the 68% credible regions to within 0.7% and 2% of those resulting from standard MCMC sampling respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f and the scalar amplitude parameter A_s.