Cosmological constraints on post-Newtonian parameters in effectively massless scalar-tensor theories of gravity

TL;DR

This work extends scalar-tensor cosmology beyond the extended Jordan–Brans–Dicke framework by analyzing a nonminimally coupled, effectively massless scalar with $F(\sigma)=N_{pl}^2+\xi\sigma^2$ and $V(\sigma)\propto F(\sigma)^2$. By solving background and linear perturbations and confronting Planck 2015 plus BAO data, the authors derive constraints on the coupling $\xi$ and the normalization $N_{pl}$, quantify the time variation of the effective gravitational constant, and extract bounds on the post-Newtonian parameters $\gamma_{PN}$ and $\beta_{PN}$. They find no statistically significant deviation from General Relativity, with tight 95% CL limits such as $0.995<\gamma_{PN}<1$ and $0.99987<\beta_{PN}<1$ for $\xi>0$, and $0.997<\gamma_{PN}<1$, $1<\beta_{PN}<1.000011$ for $\xi<0$, while the conformal coupling $\xi=-1/6$ yields constraints comparable to Solar System tests. The analysis also indicates a higher inferred $H_0$ relative to $\Lambda$CDM, partially alleviating the tension with local $H_0$ measurements, and highlights the potential of CMB polarization data to tighten these cosmological tests of gravity.

Abstract

We study the cosmological constraints on the variation of the Newton's constant and on post-Newtonian parameters for simple models of scalar-tensor theory of gravity beyond the extended Jordan-Brans-Dicke theory. We restrict ourselves to an effectively massless scalar field with a potential $V \propto F^2$, where $F(σ)=N_{pl}^2+ξσ^2$ is the coupling to the Ricci scalar considered. We derive the theoretical predictions for cosmic microwave background (CMB) anisotropies and matter power spectra by requiring that the effective gravitational strength at present is compatible with the one measured in a Cavendish-like experiment and by assuming adiabatic initial condition for scalar fluctuations. When comparing these models with $Planck$ 2015 and a compilation of baryonic acoustic oscilation (BAO) data, all these models accomodate a marginalized value for $H_0$ higher than in $Λ$CDM. We find no evidence for a statistically significant deviation from Einstein's general relativity. We find $ξ< 0.064$ ($|ξ| < 0.011$) at 95 % CL for $ξ> 0$ (for $ξ< 0$, $ξ\ne -1/6$). In terms of post-Newtonian parameters, we find $0.995 < γ_{\rm PN} < 1$ and $0.99987 < β_{\rm PN} < 1$ ($0.997 < γ_{\rm PN} < 1$ and $1 < β_{\rm PN} < 1.000011$) for $ξ>0$ (for $ξ< 0$). For the particular case of the conformal coupling, i.e. $ξ=-1/6$, we find constraints on the post-Newtonian parameters of similar precision to those within the Solar System.

Figures (24)

• Figure 1: Top panel: relative evolution of $\sigma$ for different values of $\xi$. Bottom panel: evolution of $\sigma$ for different values of $N_{pl}$ for the CC case, i.e. $\xi=-1/6$.
• Figure 2: Evolution of $w_{\rm DE}$ for different values of $N_{pl}$ and $\xi$. We plot the effective parameter of state for DE for $\xi>0$ in the upper panel, $\xi<0$ in the central panel, and the CC case $\xi=-1/6$ in the bottom panel.
• Figure 3: Evolution of the density parameters $\Omega_i$: radiation in yellow, matter in blue, and effective DE in red. We plot $\tilde{N}_{pl}=1$ ($\tilde{N}_{pl}=0.9$) for $\xi = 10^{-2},\,10^{-3}$ in the top (bottom) panel.
• Figure 4: Evolution of the density parameters $\Omega_i$: radiation in yellow, matter in blue, and effective DE in red. We plot $\tilde{N}_{pl}=1.01$ ($\tilde{N}_{pl}=1.1$) for $\xi = -10^{-2},\,-10^{-3}$ in the top (bottom) panel.
• Figure 5: Evolution of the density parameters $\Omega_i$: radiation in yellow, matter in blue, and effective DE in red. We plot the CC case $\xi = -1/6$ for $\Delta\tilde{N}_{pl}=10^{-3},\,10^{-4},\,10^{-5}$.