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A simple prediction of the nonlinear matter power spectrum in Brans-Dicke gravity from linear theory
Herman Sletmoen, Hans A. Winther
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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≳10⁵ are much tighter than large-scale cosmological constraints ω≳10³, 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 H₀ / √([b]G_(eff)(a=0)) and σ₈, 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 EuclidEmulator2 to predict P_(BD).
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