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

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 ω serve as a benchmark for testing GR, which is recovered in the limit ω → ∞. Current small-scale astrophysical constraints ω ≳ 10 5 are much tighter than large-scale cosmological constraints ω ≳ 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 BD . By comparing the boost B = P BD / P GR 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 /√ G eff ( a = 0) and σ 8 , where G eff is the (effective) gravitational strength. Our prediction is 1% accurate for ω ≥ 100, z ≤ 3, and k ≤ 1 h /Mpc; and 2% up to k ≤ 5 h /Mpc. It also holds for G BD that do not match Newton’s constant today, so one can study GR with different gravitational constants G GR by sending ω → ∞. We provide a code that computes B with the linear Einstein-Boltzmann solver HI_CLASS and multiplies it by the nonlinear P GR from E UCLID E MULATOR 2 to predict P BD .