Redshift-space distortions in massive neutrino and evolving dark energy cosmologies

Large-scale structure surveys in the coming years will measure the redshift-space power spectrum to unprecedented accuracy, allowing for powerful new tests of the Λ cold dark matter (ΛCDM) picture as well as measurements of particle physics parameters such as the neutrino masses. We extend the time-renormalization-group (RG) perturbative framework to redshift space, computing the power spectrum Pₛ(k,μ) in massive neutrino cosmologies with time-dependent dark energy equations of state $w(z)$. Time-RG is uniquely capable of incorporating scale-dependent growth into the Pₛ(k,μ) computation, which is important for massive neutrinos as well as modified gravity models. Although changes to $w(z)$ and the neutrino mass fraction both affect the late-time scale dependence of the nonlinear power spectrum, we find that the two effects depend differently on the line-of-sight angle μ. Finally, we use the hacc N-body code to quantify errors in the perturbative calculations. For a ΛCDM model at redshift $z=1$, our procedure predicts the monopole (quadrupole) to 1% accuracy up to a wave number 0.19h/Mpc (0.28h/Mpc), compared to 0.08h/Mpc (0.07h/Mpc) for the Kaiser approximation and 0.19h/Mpc (0.16h/Mpc) for the current state-of-the-art perturbation scheme. Our calculation agrees with the simulated redshift-space power spectrum even for neutrino masses above the current bound, and for rapidly evolving dark energy equations of state, |dw/dz|~1. Along with this article, we make our redshift-space time-RG implementation publicly available as the code redtime.