The matter power spectrum in redshift space using effective field theory

Abstract

The use of Eulerian 'standard perturbation theory' to describe mass assembly in the early universe has traditionally been limited to modes with k $\lesssim$ 0.1 h/Mpc at z = 0. At larger k the SPT power spectrum deviates from measurements made using N-body simulations. Recently, there has been progress in extending the reach of perturbation theory to larger k using ideas borrowed from effective field theory. We revisit the computation of the redshift-space matter power spectrum within this framework, including for the first time the full one-loop time dependence. We use a resummation scheme proposed by Vlah et al. to account for damping of baryonic acoustic oscillations due to large-scale random motions and show that this has a significant effect on the multipole power spectra. We renormalize by comparison to a suite of custom N-body simulations matching the MultiDark MDR1 cosmology. At z = 0 and for scales k $\lesssim$ 0.4 h/Mpc we find that the EFT furnishes a description of the real-space power spectrum up to $\sim$2%, for the $\ell$ = 0 mode up to $\sim$5%, and for the $\ell$ = 2, 4 modes up to $\sim$25%. We argue that, in the MDR1 cosmology, positivity of the $\ell$ = 0 mode gives a firm upper limit of k $\approx$ 0.75 h/Mpc for the validity of the one-loop EFT prediction in redshift space using only the lowest-order counterterm. We show that replacing the one-loop growth factors by their Einstein-de Sitter counterparts is a good approximation for the $\ell$ = 0 mode, but can induce deviations as large as 2% for the $\ell$ = 2, 4 modes. An accompanying software bundle, distributed under open source licenses, includes Mathematica notebooks describing the calculation, together with parallel pipelines capable of computing both the necessary one-loop SPT integrals and the effective field theory counterterms.