http://arxiv.org/abs/2004.05049
We investigate whether the $4.4\sigma$ tension on $H_0$ between SH${0}$ES 2019 and Planck 2018 can be alleviated by a variation of Newton’s constant $G_N$ between the early and the late Universe. This changes the expansion rate before recombination, similarly to the addition of $\Delta N{\rm eff}$ extra relativistic degrees of freedom . We implement a varying $G_N$ in a scalar-tensor theory of gravity, with a non-minimal coupling of the form $(M^2+\beta \phi^2)R$. If the scalar $\phi$ starts in the radiation era at an initial value $\phi_I \approx 0.3 \, M_{Pl}$ and with $\beta\approx-0.8$, a dynamical transition occurs naturally around the epoch of matter-radiation equality and the field evolves towards zero at late times. As a consequence the $H_0$ tension between SH${0}$ES (2019) and Planck 2018+BAO decreases, as in $\Delta N{\rm eff}$ models. However, mostly due to late-time constraints from Post-Newtonian (PN) local gravity, the tension is reduced only to 3.5$\sigma$ level. When including also the SH${0}$ES data in the fit, the varying $G_N$ model has $H_0=69.2{-0.75}^{+0.62}$ and an improvement of $\Delta\chi^2=-3.6$ compared to $\Lambda$CDM, at the cost of 2 extra parameters. This corresponds to a decrease of $7_{-6}^{+3}$ percent in the value of $G_N$ from the radiation era to the present time. For comparison, we update the fit of the $\Delta N_{\rm eff}$ model to the same dataset. We find that the $\Delta N_{\rm eff}$ model performs better than the simplest varying $G_N$ scenario, with $H_0=70_{-0.95}^{+0.93}$ and $\Delta\chi^2=-5.5$. The $\Lambda$CDM limit of the $\Delta N_{\rm eff}$ model is disfavored at slightly more than 2$\sigma$, since $\Delta N_{\rm eff}=0.316_{-0.15}^{+0.15}$.
G. Ballesteros, A. Notari and F. Rompineve
Mon, 13 Apr 20
25/35
Comments: 18 pages, 5 figures
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