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

Understand

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 $\omega \rightarrow \infty$.
• Current small-scale astrophysical constraints $\omega \gtrsim 10^5$ are much tighter than large-scale cosmological constraints $\omega \gtrsim 10^3$, 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.