Brans-Dicke gravity with a cosmological constant smoothes out $Λ$CDM tensions

TL;DR

The paper tests Brans-Dicke gravity with a cosmological constant (BD-ΛCDM) against modern cosmological data to see if a slowly evolving gravitational coupling can alleviate ΛCDM tensions. By formulating BD in both the fundamental and GR frames and incorporating linear perturbations, the authors fit BD-ΛCDM to Planck 2015 likelihood data plus diverse large-scale structure and distance measurements. They find that BD-ΛCDM provides a better fit than ΛCDM, yields a mild quintessence-like effective EoS near today, and significantly reduces the H0 tension while keeping σ8 in a compatible range. The work demonstrates that an evolving G(t) in BD gravity can reconcile key observables without introducing new exotic components, and it makes concrete predictions for the late-time behavior of the universe and the gravitational coupling.

Abstract

We analyze Brans-Dicke gravity with a cosmological constant, $Λ$, and cold dark matter (BD-$Λ$CDM for short) in the light of the latest cosmological observations on distant supernovae, Hubble rate measurements at different redshifts, baryonic acoustic oscillations, large scale structure formation data, gravitational weak-lensing and the cosmic microwave background under full Planck 2015 CMB likelihood. Our analysis includes both the background and perturbations equations. We find that BD-$Λ$CDM is observationally favored as compared to the concordance $Λ$CDM model, which is traditionally defined within General Relativity (GR). In particular, some well-known persisting tensions of the $Λ$CDM with the data, such as the excess in the mass fluctuation amplitude $σ_8$ and specially the acute $H_0$-tension with the local measurements, essentially disappear in this context. Furthermore, viewed from the GR standpoint, BD-$Λ$CDM cosmology mimics quintessence at $\gtrsim3σ$ c.l. near our time.

Figures (2)

• Figure 1: Triangular matrix containing some relevant combinations of two-dimensional marginalized distributions for fitting parameters of the BD model (at $1\sigma$, $2\sigma$ and $3\sigma$ c.l.), together with the corresponding one-dimensional marginalized likelihoods for each parameter. $H_0$ is expressed in km/s/Mpc. We present the contours for the data sets DS1 (in purple) and DS2 (in red) (cf. Table 1 for the numerical fitting results).
• Figure 2: The effective EoS parameter for the BD model and its corresponding $1\sigma$ bands as a function of the redshift, Eq. (\ref{['BDEoS']}). We plot the results derived under both, dataset DS1 (in purple) and DS2 (in red), in the redshift range $z<10^6$. In black we plot the EoS parameter of the vacuum energy density, i.e. $w_\Lambda =-1$ . During the matter and radiation-dominated eras the EoS of BD-$\Lambda$CDM tracks the dominant component of the universe. This is no longer true at low redshift near our time. We zoom in the region $z<1$ to better appreciate the existing deviation of the EoS parameter from $-1$. With the error bars at $1\sigma$, $2\sigma$ and $3\sigma$ the results are the following: $w_{eff}(0) = -0.961^{+0.012+0.023+0.033}_{-0.011-0.023-0.034}$ for the DS1 scenario, and $w_{eff}(0) = -0.951^{+0.012+0.026+0.041}_{-0.013-0.026-0.039}$ for the DS2 one. These results point to an effective quintessence signal at $\gtrsim3\sigma$ c.l. in both cases.