The dark sector of the Universe as a scalar field in Horndeski Gravity

Abstract

In the present work, we study a subclass of Horndeski gravity characterized by a non-minimal derivative coupling between a scalar field and the Einstein tensor, as a possible alternative to alleviate the observational tension associated with estimates of the Hubble constant $H_{0}$. Two scenarios within a flat FRW spacetime were considered. In the first case, the scalar field mimics cold dark matter, whereas in the second case, it acts as dark energy. We derive the dynamical equations and perform a statistical analysis using observational data of $H(z)$, obtaining constraints for the cosmological parameters. The results indicate that the model can effectively fit the cosmic expansion rate at late epochs, providing values of $H_{0}$ that are more compatible with local measurements. These results suggest that the non-minimal coupling sector in the Horndeski context constitutes a viable and promising approach to alleviate the $H_{0}$ tension and investigate scenarios beyond the standard cosmological model.

Figures (7)

• Figure 1: In the left panel, we present the evolution of the Hubble parameter as a function of redshift, confronted with observational data of $H(z)$. In the right panel, we have the evolution of the normalization $H(z)/(1+z)$. In both graphs, we show the confidence bands of $1\sigma$ and $2\sigma$ results for $\phi$ as dark matter.
• Figure 2: Posterior distribution of the model parameters $\alpha$ and $\beta$ and the background quantities $h$, $\Omega_m$ and $\Omega_{\Lambda}$. Here, for a better display of the graph, we use $h=H_{0}/100$. For each parameter, we have the respective contour plots with confidence regions $1\sigma$ and $2 \sigma$ of the MCMC sampling, for individual CC data (blue regions) and for combined CC$+$BAO$+$SH$0$ES data (green regions).
• Figure 3: In the left panel we have the evolution of the Hubble parameter as a function of redshift, compared with observational data of $H(z)$. In the panel on the right, we have the evolution of the normalization $H(z)/(1+z)$. In both graphs, we show the confidence bands of $1\sigma$ and $2\sigma$ with $\phi$ as dark energy.
• Figure 4: Posterior distribution of the model parameters $\alpha$ and $\eta$ together with the background quantities $h$ and $\Omega_m$, again we have that $h=H_{0}/100$. For each parameter, we have its respective contour plot with 1$\sigma$ and 2$\sigma$ confidence regions from the MCMC sampling, for individual CC (blue regions) and BAO (green regions) data, and also for combined CC$+$BAO$+$SH$0$ES data (black edges).
• Figure 5: In Fig. \ref{['grafcS']}, we show the evolution of the squared propagation speed of scalar perturbations, $c_S^2$, as a function of redshift $z$. In Fig. \ref{['grafQS']}, we present the evolution of the kinetic energy parameter associated with scalar perturbations, $Q_S$, also as a function of redshift $z$. In both cases we have the contribution of the scalar field as dark matter (dotted blue lines) and the scalar field as dark energy (dashed black lines)