Scalar-tensor theories of gravity, neutrino physics, and the $H_0$ tension

TL;DR

This paper tests whether simple non-minimally coupled scalar-tensor theories of gravity can alleviate the H0 tension by modifying the early-time expansion via a Ricci-coupled scalar. Using Planck 2018 data plus BAO and, in some cases, the SH0ES H0 prior, the authors constrain two representative models (induced gravity and conformal coupling) and explore degeneracies with the neutrino sector, including N_eff and m_nu. They find tighter bounds on the coupling parameters than previous work, and while H0 can be raised relative to ΛCDM, the alleviation of the tension is limited and sensitive to neutrino physics and external H0 priors. Overall, the study demonstrates robust, gravity-driven increases in H0 that partially mitigate, but do not fully resolve, the Planck-local H0 discrepancy, highlighting persistent model- and data-dependent degeneracies with neutrino parameters.

Abstract

We use $Planck$ 2018 data to constrain the simplest models of scalar-tensor theories characterized by a coupling to the Ricci scalar of the type $F(σ) R$ with $F(σ) = N_{pl}^2 + ξσ^2$. We update our results with previous $Planck$ and BAO data releases obtaining the tightest constraints to date on the coupling parameters, that is $ξ< 5.5 \times 10^{-4}$ for $N_{pl}=0$ (induced gravity or equivalently extended Jordan-Brans-Dicke) and $(N_{pl} \sqrt{8 πG})-1 < 1.8 \times 10^{-5}$ for $ξ= -1/6$ (conformal coupling), both at 95% CL. Because of a modified expansion history after radiation-matter equality compared to the $Λ$CDM model, all these dynamical models accommodate a higher value for $H_0$ and therefore alleviate the tension between $Planck$/BAO and distance-ladder measurement from SNe Ia data from $4.4σ$ at best to $2.3σ$. We show that all these results are robust to changes in the neutrino physics. In comparison to the $Λ$CDM model, partial degeneracies between neutrino physics and the coupling to the Ricci scalar allow for smaller values $N_{\rm eff} \sim 2.8$, $1σ$ lower compared to the standard $N_{\rm eff} = 3.046$, and relax the upper limit on the neutrino mass up to 40%.

Figures (12)

• Figure 1: Left panel: marginalized joint 68% and 95% CL regions 2D parameter space using current versus previous releases of Planck data and BOSS BAO data from Umilta:2015ctaBallardini:2016cvy. Right panel: marginalized joint 68% and 95% CL regions 2D parameter space using P18 (gray) in combination with BAO (blue) and BAO + R19 (red) for the IG model.
• Figure 2: Left panel: marginalized joint 68% and 95% CL regions 2D parameter space using P18 (P15) data in combination BAO in blue (red). Right panel: marginalized joint 68% and 95% CL regions 2D parameter space using P18 (gray) in combination with BAO (blue) and BAO + R19 (red) for the CC model.
• Figure 3: Left panel: marginalized joint 68% and 95% CL regions 2D parameter space $H_0-\xi$ using P18 + BAO data for IG with $V(\sigma) = \lambda F(\sigma)^2/4$ (red) and $V(\sigma) = \Lambda$ (blue). Right panel: marginalized joint 68% and 95% CL regions 2D parameter space $H_0-N_{pl}$ using P18 + BAO data for CC with $V(\sigma) = \lambda F(\sigma)^2/4$ (red) and $V(\sigma) = \Lambda$ (blue).
• Figure 4: Differences with respect to the $\Lambda$CDM with ($N_{\rm eff} = 3.046$) with IG (top panels) for $\xi = 0.0008,\,0.0016$ (solid, dashed) and $N_{\rm eff} = 2.846,\,3.046,\,3.246$ (red, green, blue), and CC (bottom panels) for $N_{pl} = 1.00003,\,1.00004$ M$_{pl}$ (solid, dashed) and $N_{\rm eff} = 2.846,\,3.046,\,3.246$ (red, green, blue). $D_\ell \equiv \ell(\ell+1)C_\ell/(2\pi)$ are the band-power angular power spectra.
• Figure 5: Marginalized joint 68% and 95% CL regions 2D parameter space using the P18 (gray) in combination with BAO (blue) and BAO + R19 (red) for the IG+$N_{\rm eff}$ model. In the central panel, we include the $H_0-N_{\rm eff}$ contours for the $\Lambda$CDM in green. In the right panel, we include the $H_0-\xi$ contours for the IG with $N_{\rm eff} = 3.046$ in green.