From Theory to Forecast: Neutrino Mass Effects on Mode-Coupling Kernels and Their Observational Implications

TL;DR

This paper develops analytical models for matter and tracer power spectra including neutrino effects, uses simulations to test parameter estimation, and finds that bispectrum data can significantly improve constraints on neutrino mass.

Contribution

It introduces an analytical expression for 1-loop power spectra with neutrino effects and demonstrates the benefit of bispectrum inclusion for parameter constraints.

Findings

Neutrino signature kernels yield similar parameter estimates as standard perturbation theory.

Including bispectrum reduces uncertainties on key cosmological parameters by about 20%.

Models accurately fit the Quijote simulation data for upcoming surveys.

Abstract

We present an analytical expression that gives both the matter and tracer (halo or galaxy) power spectrum with 1-loop corrections that include the neutrino effects on the mode coupling kernels. We use the FFTLog algorithm to accelerate calculating the higher-order corrections to the power spectrum. We then use our power spectrum and bispectrum models to pursue two main goals. First, we examine the impact of neutrino mass on cosmological parameter estimation from both the power spectrum and bispectrum in real space. We create 1-loop power spectrum and bispectrum templates in real-space and fit to the \texttt{Quijote} simulation suite, including the cross-covariance between the power spectrum and the bispectrum. We show the neutrino signature kernels estimate the same cosmological parameters as the model with the SPT (Standard Perturbation Theory) kernels, even for DESI Year 5 volume, except for the galaxy bias parameters inferred from the bispectrum. Second, we investigate to what extent the bispectrum can improve parameter constraints. We perform a Fisher forecast using the power spectrum, the tree-level bispectrum, and a joint analysis that includes the cross-covariance between them. We show that including the bispectrum can substantially reduce the error bars on key parameters. For the neutrino mass in particular, the uncertainty is reduced by $\sim 20\%$