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 $0.2h{\mathrm{Mpc}}^{-1}$ 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 $0.18h{\mathrm{Mpc}}^{-1}$ at two-loop order, compared to $0.1h{\mathrm{Mpc}}^{-1}$ at one-loop. We also investigate the role of higher-derivative corrections.

Comments: 24 pages, 11 figures; updated bibliography