Implementing spectra response function approaches for fast calculation of power spectra and bispectra

TL;DR

This paper introduces a fast computational scheme for predicting cosmological power spectra and bispectra using a Taylor expansion approach, significantly reducing computation time for parameter inference in large-scale structure studies.

Contribution

The authors develop a Taylor expansion-based method within regularized perturbation theory to efficiently compute spectra, enabling rapid cosmological parameter estimation.

Findings

Achieves spectrum predictions within minutes for arbitrary parameters.

Reduces computational cost of 2-loop and 1-loop perturbation calculations.

Suitable for MCMC analyses in cosmology.

Abstract

Perturbation theory of large-scale structures of the Universe at next-to-leading order and next-to-next-to-leading order provides us with predictions of cosmological statistics at sub-percent level in the mildly non-linear regime. Its use to infer cosmological parameters from spectroscopic surveys, however, is hampered by the computational cost of making predictions for a large number of parameters. In order to reduce the running time of the codes, we present a fast scheme in the context of the regularized perturbation theory approach and applied it to power spectra at 2-loop level and bispectra at 1-loop level, including the impact of binning. This method utilizes a Taylor expansion of the power spectrum as a functional of the linear power spectrum around fiducial points at which costly direct evaluation of perturbative diagrams is performed and tabulated. The computation of the predicted spectra for arbitrary cosmological parameters then requires only one-dimensional integrals that can be done within a few minutes. It makes this method suitable for Markov chain Monte-Carlo analyses for cosmological parameter inference.