The two-loop power spectrum in redshift space

Abstract

We present the matter power spectrum in redshift space including two-loop corrections. We follow a strictly perturbative approach incorporating all non-linearities entering both via the redshift-space mapping and within real space up to the required (fifth) order, complemented by suitable effective field theory (EFT) corrections. This approach can a priori be viable up to scales of order 0.2h Mpc-1 beyond which power suppression related to the finger-of-God effect becomes non-perturbatively strong. We extend a simplified treatment of EFT corrections at two-loop order from real to redshift space, making sure that the leading UV-sensitivity of both the single-hard and double-hard limit of the two-loop contributions to the power spectrum is accounted for, and featuring two free parameters for each multipole. Taking also infrared-resummation into account, we calibrate with and compare to Quijote N-body simulations for the monopole and quadrupole at redshifts z = 0 and z = 0.5. We find agreement within sample variance (at percent-level) up to 0.18h Mpc-1 at two-loop order, compared to 0.1h Mpc-1 at one-loop. We also investigate the role of higher-derivative corrections.