# Constraining An Exact Brans-Dicke gravity theory with Recent Observations

## TL;DR

This paper derives an exact solution for Brans-Dicke gravity with a cosmological constant and uses recent observational data to constrain its parameters, finding results consistent with general relativity.

## Contribution

It introduces a new parameter, the scalar field density, in Brans-Dicke theory and constrains it using multiple cosmological observations, comparing with the standard model.

## Key findings

- No significant deviation from general relativity.
- Constraint on scalar field density: $oxed{oxed{ extOmega_{ extphi}=0.010^{+0.021}_{-0.012}}}$.
- Bounds on the variation of gravitational constant: $1.150 imes 10^{-13} yr^{-1} < rac{ extdot G}{G} < 1.198 imes 10^{-13} yr^{-1}$.

## Abstract

In this paper first we study Brans-Dicke equations with the cosmological constant to find an exact solution in the spatially flat Robertson-Walker metric. Then we use Observational Hubble data, the baryon acoustic oscillation distance ratio data as well as cosmic microwave background data from Planck to constrain parameters of the obtained Brans-Dicke model. To compare our results and find out the amount of deviation from general relativity, we also constrain concordance cosmological model using the same data. In our theoretical model the Brans-Dicke coupling constant is replaced by a , say new, parameter namely \textgravedbl scalar field density $\Omega_{\phi}$\textacutedbl. Therefore, as $\Omega_{\phi}\to 0$ which is equivalent to $\omega\to \infty$ general relativity is recovered. In general, we found no significant deviation from general relativity. Our estimations show $\Omega_{\phi}=0.010^{+0.021}_{-0.012}$ which is equivalent to $\omega>1560$ at $95\%$ confidence level. We also obtained constraint the rate of change of gravitational constant, $\dot{G}/G$, at present time as $1.150\times 10^{-13}yr^{-1}<\dot{G}/G<1.198\times 10^{-13}yr^{-1}$ (at $1\sigma$ error). The total variation of gravitational constant, since the epoch of recombination, is also constrained as $-0.0084<\delta G/G<-0.0082$ at $68\%$ confidence level.