A simple prediction of the nonlinear matter power spectrum in Brans–Dicke gravity from linear theory

Abstract

Brans-Dicke (BD), one of the first proposed scalar-tensor theories of gravity, effectively makes the gravitational constant of general relativity (GR) time-dependent. Constraints on the BD parameter omega serve as a benchmark for testing GR, which is recovered in the limit $ Current small-scale astrophysical constraints $ 10^5$ are much tighter than large-scale cosmological constraints $ 10^3$, but the two decouple if the true theory of gravity features screening. On the largest cosmological scales, BD approximates the most general second-order scalar-tensor (Horndeski) theory, so constraints here have wider implications. These constraints will improve with upcoming large-scale structure and cosmic microwave background surveys. To constrain BD with weak gravitational lensing, one needs its nonlinear matter power spectrum $P_ By comparing the boost $B = P_ from linear theory and nonlinear $N$-body simulations, we show that the nonlinear boost can simply be predicted from linear theory if the BD and GR universes are parameterized in a way that makes their early cosmological evolution and quasilinear power today similar. In particular, they need the same $H_0 / b G_ eff (a=0) $ and $ where eff $ is the (effective) gravitational strength. Our prediction is $1<!PCT!>$ accurate for $ 100$, $z 3$, and $k 1\,h/ Mpc $; and $2<!PCT!>$ up to $k 5\,h/ Mpc $. It also holds for $G_ that do not match Newton's constant today, so one can study GR with different gravitational constants $G_ by sending $ We provide a code that computes $B$ with the linear Einstein-Boltzmann solver and multiplies it by the nonlinear $P_ from to predict $P_