Neutrino Mass, Dark Energy, and the Linear Growth Factor

TL;DR

This paper investigates how neutrino mass and dark energy influence cosmological observations, providing new formulas for the growth factor and power spectrum that account for their complex interplay.

Contribution

It introduces a revised fitting formula for the growth factor and modifies existing power spectrum approximations to better include effects of massive neutrinos.

Findings

Suppression of matter power spectrum depends on neutrino and total mass densities independently.

Provides a new fitting formula for the growth factor in flat universes with massive neutrinos.

Revises the Eisenstein & Hu power spectrum approximation to include neutrino effects.

Abstract

We study the degeneracies between neutrino mass and dark energy as they manifest themselves in cosmological observations. In contradiction to a popular formula in the literature, the suppression of the matter power spectrum caused by massive neutrinos is not just a function of the ratio of neutrino to total mass densities f_nu=Omega_nu/Omega_m, but also each of the densities independently. We also present a fitting formula for the logarithmic growth factor of perturbations in a flat universe, f(z, k;f_nu,w,Omega_DE)= (1-A(k)*Omega_DE*f_nu+B(k)*f_nu^2-C(k)*f_nu^3)*Omega_m(z)^alpha, where alpha depends on the dark energy equation of state parameter w. We then discuss cosmological probes where the f factor directly appears: peculiar velocities, redshift distortion and the Intergrated Sachs-Wolfe effect. We also modify the approximation of Eisenstein & Hu (1999) for the power spectrum of fluctuations in the presence of massive neutrinos and provide a revised code (http://www.star.ucl.ac.uk/~lahav/nu_matter_power.f)