Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Brans-Dicke-like field for co-varying $G$ and $c$: observational constraints

J. Bezerra-Sobrinho, R. R. Cuzinatto, L. G. Medeiros, P. J. Pompeia

Abstract

Ref. [Symmetry 15 (2023) 709] introduced a Brans-Dicke-like framework wherein the scalar field $φ$ is composed of both $G$ and $c$ which, for this reason, co-vary according to $c^{3}/G=\text{constant}$. In this paper, we use observational data to constrain the supposed co-varying $G$ and $c$, under the hypothesis of the validity of the standard Lemaitre formula $1+z\sim a^{-1}$. The datasets include SN Ia, BAO and the value of $θ$ extracted from CMB data. A proxy function is demanded for the varying $c$ since the framework does not provide a closed set of equations for computing the functional form of either $G$ or $c$ uniquely. Accordingly, we choose three separate parameterizations for $c\left(z\right)$ inspired both by desirable properties of the varying speed of light (VSL) and by successful phenomenological models from the literature -- including the one by Gupta (CCC framework in e.g. Ref. [Mon. Not. R. Astron. Soc., 498 (2020) 4481-4491]. When combined with DESI, Pantheon+ data strongly favor a variable speed of light with more than $3σ$ confidence level for all parameterizations considered in this paper, whereas Union2.1 suggests no variation of the speed of light. As we shall demonstrate, this apparent discrepancy is due to a strong correlation that emerges between $H_0$ and VSL.

Brans-Dicke-like field for co-varying $G$ and $c$: observational constraints

Abstract

Ref. [Symmetry 15 (2023) 709] introduced a Brans-Dicke-like framework wherein the scalar field is composed of both and which, for this reason, co-vary according to . In this paper, we use observational data to constrain the supposed co-varying and , under the hypothesis of the validity of the standard Lemaitre formula . The datasets include SN Ia, BAO and the value of extracted from CMB data. A proxy function is demanded for the varying since the framework does not provide a closed set of equations for computing the functional form of either or uniquely. Accordingly, we choose three separate parameterizations for inspired both by desirable properties of the varying speed of light (VSL) and by successful phenomenological models from the literature -- including the one by Gupta (CCC framework in e.g. Ref. [Mon. Not. R. Astron. Soc., 498 (2020) 4481-4491]. When combined with DESI, Pantheon+ data strongly favor a variable speed of light with more than confidence level for all parameterizations considered in this paper, whereas Union2.1 suggests no variation of the speed of light. As we shall demonstrate, this apparent discrepancy is due to a strong correlation that emerges between and VSL.

Paper Structure

This paper contains 17 sections, 93 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background cosmology
  3. Contact with observations: cosmological distances
  4. Proper distance
  5. Luminosity distance
  6. Angular-diameter distance
  7. Distances related to the sound horizon: CMB and BAO
  8. Modelling the varying $c$ (and $G$)
  9. Power-law parameterization
  10. Gupta's parameterization
  11. Continuous parameterization
  12. Constraining the varying $c$ and $G$ cosmology
  13. Datasets
  14. VSL model constraining
  15. Further discussions
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Redshift evolution of the speed of light $c\left(z\right)/c_{0}$ for the power-law parameterization with different values of the power-law index $n$.
  • Figure 2: Redshift evolution of the speed of light $c\left(z\right)/c_{0}$ for the Gupta's parameterization for multiple values of $\beta$ with $\Omega_{m0}=0.3$.
  • Figure 3: Redshift evolution of the speed of light $c\left(z\right)/c_{0}$ for Gupta's parameterization and different values of $\Omega_{m0}$ with (a) $\beta=-0.01$, and (b) with $\beta=0.01$.
  • Figure 4: (a) Redshift evolution of the speed of light $c\left(z\right)/c_{0}$ for the continuous parameterization, multiple values of $\alpha$, with power-law index $n=0.01$ in part (a) and $n=-0.01$ in part (b).
  • Figure 5: [$\Lambda$CDM model] 68% and 95% confidence level posterior distributions and contour plots of the $\Lambda$CDM model for the parameters $\Omega_{m}$, $H_{0}$, $K_{d}$, using the fit to the datasets Pantheon$+$Pantheon+, Union2.1 Union2.1, DESI DESI2025EDE and $\theta_{\ast}$Planck2018VI.
  • ...and 3 more figures