Improving precision and accuracy in cosmology with model-independent spectrum and bispectrum

TL;DR

This paper introduces a model-independent method called FreePower for analyzing large-scale structure data, demonstrating how including bispectrum and symmetry-based kernels significantly improves precision in measuring cosmological parameters with Euclid data.

Contribution

The paper shows that incorporating bispectrum and symmetry-based kernels enhances the accuracy and precision of cosmological measurements in a model-independent framework.

Findings

Improved precision in measuring H(z), D(z), and f(z) with Euclid survey.

Perturbation theory kernels can be constrained at 10-20% level.

Spectrum and bispectrum combination effectively constrains perturbation parameters.

Abstract

A new and promising avenue was recently developed for analyzing large-scale structure data with a model-independent approach, in which the linear power spectrum shape is parametrized with a large number of freely varying wavebands rather than by assuming specific cosmological models. We call this method FreePower. Here we show, using a Fisher matrix approach, that precision of this method for the case of the one-loop power spectrum is greatly improved with the inclusion of the tree-level bispectrum. We also show that accuracy can be similarly improved by employing perturbation theory kernels whose structure is entirely determined by symmetries instead of evolution equations valid in particular models (like in the usual Einstein-deSitter approximation). The main result is that with the Euclid survey one can precisely measure the Hubble function, distance and ($k$-independent) growth rate $f(z)$ in seven redshift bins in the range $z\in [0.6,\, 2.0]$. The typical errors for the lowest $z$bins are around 1\% (for $H$), 0.5--1\% (for $D$), and 1--3\% (for $f$). The use of general perturbation theory allows us, for the first time, to study constraints on the nonlinear kernels of cosmological perturbations, that is, beyond the linear growth factor, showing that they can be probed at the 10--20\% level. We find that the combination of spectrum and bispectrum is particularly effective in constraining the perturbation parameters, both at linear and quadratic order.