[Paper Review] Difficulties in reconciling non-negligible differences between the local and cosmological values of the gravitational coupling in extended Brans-Dicke theories

Adrià Gómez Valent, Prajwal Hassan Puttasiddappa|arXiv (Cornell University)|May 31, 2021

Cosmology and Gravitation Theories66 references4 citations

TL;DR

This paper investigates whether extended Brans-Dicke theories with screening mechanisms can reconcile the observed 4–9% higher effective gravitational coupling in cosmology with the locally measured Newtonian value. Despite exploring various screening mechanisms, the study finds they can only produce negligible deviations—insufficient to explain the observed tension in $H_0$ and $\sigma_8$ without violating Solar System constraints.

ABSTRACT

Recent studies by Sola Peracaula, Gomez-Valent, de Cruz Perez and Moreno-Pulido (2019,2020) have pointed out the intriguing possibility that Brans-Dicke cosmology with constant vacuum energy density (BD-$\Lambda$CDM) may be able to alleviate the $H_0$ and $\sigma_8$ tensions that are found in the framework of the concordance cosmological model (GR-$\Lambda$CDM). The fitting analyses presented in these works indicate a preference for values of the effective gravitational coupling appearing in the Friedmann equation, $G$, about $4-9\%$ larger than Newton's constant (as measured on Earth), and mildy evolving with the expansion of the universe. The signal reaches the $\sim 3.5\sigma$ c.l. when the prior on $H_0$ from SH0ES and the angular diameter distances to strong gravitationally lensed quasars measured by H0LICOW are considered, and the $\sim 3\sigma$ c.l. when only the former is included. Thus, the improvement in the description of the cosmological datasets relies on the existence of a mechanism capable of screening the modified gravity effects at those scales where deviations from standard General Relativity (GR) are highly constrained, as in the Solar System. In this paper we explore several extensions of BD-$\Lambda$CDM that can leave the cosmological evolution basically unaltered at the background and linear perturbations level, while being able to screen the Brans-Dicke effects inside the regions of interest, leading to standard GR. We search for weak-field solutions around spherical static massive objects with no internal pressure and show that, unfortunately, these mechanisms can only explain very tiny departures of the effective cosmological gravitational coupling from the one measured locally. This might hinder the ability of BD-$\Lambda$CDM to alleviate the cosmological tensions.

Motivation & Objective

• To assess whether extended Brans-Dicke theories can resolve the $H_0$ and $\sigma_8$ tensions observed in the $\Lambda$CDM model.
• To investigate if screening mechanisms can suppress modified gravity effects in the Solar System while allowing enhanced gravitational coupling in cosmological contexts.
• To determine whether weak-field solutions around static, non-pressurized objects can reproduce the required cosmological deviations without violating local gravity constraints.
• To evaluate the viability of BD-$\Lambda$CDM as a solution to cosmological tensions under realistic screening scenarios.

Proposed method

• Derivation of weak-field solutions for spherically symmetric, static, non-pressurized massive objects in extended Brans-Dicke theories.
• Application of screening mechanisms that suppress deviations from General Relativity in high-density environments like the Solar System.
• Analysis of the effective gravitational coupling in the weak-field limit to compare cosmological values with local measurements.
• Use of the trace-free condition in the field equations to ensure consistency with the background evolution of BD-$\Lambda$CDM.
• Comparison of predicted gravitational potentials with observational constraints from Solar System tests.
• Numerical evaluation of the resulting deviations from Newton's constant in the weak-field regime.

Experimental results

Research questions

• RQ1 Can extended Brans-Dicke theories with screening mechanisms produce a cosmological gravitational coupling 4–9% larger than Newton's constant?
• RQ2 To what extent can screening mechanisms suppress deviations from General Relativity in the Solar System while preserving cosmological modifications?
• RQ3 What are the maximum possible deviations of the effective gravitational coupling from Newton's constant in weak-field, static, spherically symmetric solutions?
• RQ4 How do the constraints from local gravity experiments limit the viability of BD-$\Lambda$CDM in resolving cosmological tensions?
• RQ5 Can the observed $\sim 3.5\sigma$ preference for enhanced $G$ in cosmological data be reconciled with local measurements?

Key findings

• The screening mechanisms explored in the paper can only produce deviations of the effective gravitational coupling from Newton's constant that are too small to account for the 4–9% enhancement observed in cosmological data.
• Weak-field solutions around static, non-pressurized objects yield negligible departures from standard gravity, falling short of the required cosmological signal.
• The maximum allowed deviation in the weak-field regime is insufficient to reconcile the $H_0$ and $\sigma_8$ tensions without violating Solar System constraints.
• Even with favorable priors from SH0ES and H0LICOW, the screening mechanisms fail to generate the needed enhancement in $G$ at cosmological scales.
• The results suggest that BD-$\Lambda$CDM may not be viable as a solution to the cosmological tensions unless new physics beyond the considered screening mechanisms is introduced.