Cosmological constraints on Brans-Dicke theory

TL;DR

This paper uses Planck CMB data to place stringent cosmological constraints on Brans-Dicke gravity, a minimal scalar-tensor extension of General Relativity. It analyzes two model classes, restricted (rBD) and unrestricted (uBD), solving the background and perturbation equations with CAMB/CosmoMC, and derives strong lower bounds on the Brans-Dicke parameter $\omega$ ($\omega > 692$ for rBD and $\omega > 890$ for uBD at $99\%$ CL) along with tight limits on the effective gravitational strength $G_{eff}/G$ ($0.981 \le G_{eff}/G_N \le 1.285$ at $99\%$ CL) when Planck data are combined with other CMB measurements. The authors further argue that these constraints extend to the broader Horndeski class of scalar-tensor theories on cosmological scales, thereby placing robust limits on gravity modifications that could drive cosmic acceleration. The work demonstrates that cosmological observations can decisively test gravity theories beyond General Relativity, complementary to Solar System bounds.

Abstract

We report strong cosmological constraints on the Brans-Dicke (BD) theory of gravity using Cosmic Microwave Background data from Planck.We consider two types of models. First, the initial condition of the scalar field is fixed to give the same effective gravitational strength $G_{eff}$ today as the one measured on the Earth, $G_N$. In this case the BD parameter $ω$ is constrained to $ω> 692$ at the $99\%$ confidence level, an order of magnitude improvement over previous constraints.In the second type the initial condition for the scalar is a free parameter leading to a somewhat stronger constraint of $ω> 890$ while $G_{eff}$ is constrained to $0.981 <\frac{G_{eff}}{G_N} <1.285$ at the same confidence level. We argue that these constraints have greater validity than for the BD theory and are valid for any Horndeski theory, the most general second-order scalar-tensor theory, which approximates BD on cosmological scales. In this sense, our constraints place strong limits on possible modifications of gravity that might explain cosmic acceleration.

Figures (1)

• Figure 1: Left: 1D marginalized posterior for $\xi=G_{\mathrm{eff}}/G$. Right: The 1D marginalized posterior of $\ln \omega$ for different BDT models.