A larger value for $H_0$ by an evolving gravitational constant

TL;DR

This work investigates a massless scalar σ with a non-minimal coupling to gravity to address the H0 tension without invoking complex late-time dynamics. The approach yields early-time radiation-like effects (especially for ξ<0) and, depending on the dataset, modest increases in H0 relative to ΛCDM, with larger gains attainable if the effective number of relativistic species N_eff is allowed to vary. The analysis demonstrates compatibility with Solar System tests and BBN, while showing that the model can achieve competitive Δχ^2 improvements, offering a simpler alternative to some Early Dark Energy scenarios. Overall, the study highlights scalar-tensor constructions as viable, testable modifications to reconcile local and CMB-inferred expansion histories.

Abstract

We provide further evidence that a massless cosmological scalar field with a non-minimal coupling to the Ricci curvature of the type $M^2_{\rm pl}(1+ξσ^n/M_{\rm pl}^n) $ alleviates the existing tension between local measurements of the Hubble constant and its inference from CMB anisotropies and baryonic acoustic oscillations data in presence of a cosmological constant. In these models, the expansion history is modified compared to $Λ$CDM at early time, mimicking a change in the effective number of relativistic species, and gravity weakens after matter-radiation equality. Compared to $Λ$CDM, a quadratic ($n=2$) coupling increases the Hubble constant when {\em Planck} 2018 (alone or in combination with BAO and SH0ES) measurements data are used in the analysis. Negative values of the coupling, for which the scalar field decreases, seem favored and consistency with Solar System can be naturally achieved for a large portion of the parameter space without the need of any screening mechanism. We show that our results are robust to the choice of $n$, also presenting the analysis for $n=4$.

Figures (4)

• Figure 1: We plot the evolution of the energy injection $\Omega_i\coloneqq\rho_i/\rho_c$ [Top], the scalar field [Center] and the deviation from 1 of the effective (solid lines) and cosmological (dot-dashed lines) Newton constant [Bottom] for the models with $n=2,\,\xi<0$ (purple lines), $n=4,\,\xi<0$ (magenta lines), $n=2,\,\xi>0$ (red lines) and $n=4,\,\xi>0$ (brown lines), together with the EDE model of Ref. Agrawal:2019lmo (orange lines) and the $\Lambda$CDM+$N_\textup{eff}$ model (cyan lines). In order to compare the evolution of our model to the aforementioned ones, we set the cosmological parameters to the bestfit values in Table 3 of Ref. Agrawal:2019lmo and set $\xi=-1/6$. In the cases with $\xi>0$, we change the values of the initial conditions on the scalar field and the coupling $\xi$ as in the plot legends.
• Figure 2: Constraints on main and derived parameters of the CC model with $n=2$ and $\xi=-1/6$ from Planck 2018 data (P18), P18 in combination with BAO and SH0ES measurements and P18 in combination with BAO and a combined prior which takes into account all the late time measurements. Parameters on the bottom axis are our sampled MCMC parameters with flat priors, and parameters on the left axis are derived parameters (with $H_0$ in [km s$^{-1}$Mpc$^{-1}$]). Constraints for the $\Lambda$CDM model obtained with P18 data are also shown for a comparison. Contours contain 68% and 95% of the probability.
• Figure 3: Constraints on main and derived parameters of the model with $n=2$ and $\xi$ as a main parameter from Planck 2018 data (P18), P18 in combination with BAO and SH0ES measurements and P18 in combination with BAO and a combined prior which takes into account all the late time measurements. Parameters on the bottom axis are our sampled MCMC parameters with flat priors, and parameters on the left axis are derived parameters (with $H_0$ in [km s$^{-1}$Mpc$^{-1}$]). Constraints for the $\Lambda$CDM model obtained with P18 data are also shown for a comparison. Contours contain 68% and 95% of the probability.
• Figure 4: Constraints on some of the main and derived parameters of the CC and $n=2$ model with the addition of $N_\textup{eff}$ from P18 in combination with BAO and a combined prior which takes into account all the late time measurements. Parameters on the bottom axis are our sampled MCMC parameters with flat priors, and parameters on the left axis are derived parameters (with $H_0$ in [km s$^{-1}$Mpc$^{-1}$]). Contours contain 68% and 95% of the probability.