Modified gravity a la Galileon: Late time cosmic acceleration and observational constraints

TL;DR

This work investigates late-time cosmic acceleration through fourth-order Galileon gravity, deriving the cosmological dynamics and demonstrating a single stable self-accelerating de Sitter phase with $\dot{\pi}>0$. It combines an autonomous-system analysis with observational constraints from SN Ia, BAO, and CMB data, finding a tight bound $\beta<0.02$ (in certain parameter choices) and revealing degeneracies among $ (c_2,\tilde{c}_3,\tilde{c}_4) $ that limit discrimination from $\Lambda$CDM. A perturbation analysis shows the subhorizon approximation fails and the growth of structure is strongly scale-dependent via $G_{\rm eff}$, with GR-like behavior during matter domination but problematic late-time behavior for some parameter choices. The results point to the need for additional terms or potentials (e.g., a fifth Galileon term $c_5$ or chameleon-like mechanisms) to alleviate pathologies and possibly reconcile the model with observations while preserving a viable de Sitter attractor.

Abstract

In this paper we examine the cosmological consequences of fourth order Galileon gravity. We carry out detailed investigations of the underlying dynamics and demonstrate the stability of one de Sitter phase. The stable de Sitter phase contains a Galileon field $π$ which is an increasing function of time (\dotπ>0). Using the required suppression of the fifth force, supernovae, BAO and CMB data, we constrain parameters of the model. We find that the $π$ matter coupling parameter $β$ is constrained to small numerical values such that $β$<0.02. We also show that the parameters of the third and fourth order in the action (c_3,c_4) are not independent and with reasonable assumptions, we obtain constraints on them. We investigate the growth history of the model and find that the sub-horizon approximation is not allowed for this model. We demonstrate strong scale dependence of linear perturbations in the fourth order Galileon gravity.

Figures (6)

• Figure 1: Top Panel: The projected phase space in the plane $(x,y)$ in Poincaré coordinates for $\beta=0.1$, $c_2=1$, $\tilde{c}_3=15$, $\tilde{c}_4=4$. The circles represent critical points. The initial conditions are chosen in the subspace $(x,y)\in \mathbb{R}_+^2$. Bottom Panel: The evolution of $\Omega$ as a function of $\log (1+z)$.
• Figure 2: Top Panel: The projected phase space in the plane $(x,y)$ in Poincaré coordinates for $\beta=0.7$, $c_2=1$, $\tilde{c}_3=15$, $\tilde{c}_4=4$. The circles represent critical points. The initial conditions are chosen in the subspace $(x,y)\in \mathbb{R}_-^2$. Bottom Panel: The evolution of $\Omega$ as a function of $\log (1+z)$.
• Figure 3: Top Panel: Contour plots at 1$\sigma$, 2$\sigma$ and 3$\sigma$ for $c_2=\beta$. Middle Panel: Contour plots at 1$\sigma$, 2$\sigma$ and 3$\sigma$ for $c_2=1$. Bottom Panel:Contour plots at 1$\sigma$, 2$\sigma$ and 3$\sigma$ for $\beta=0.01$.
• Figure 4: $G_{\rm eff}$ versus the redshift $\log(1+z)$ for $\beta=0.01$, $c_2=1$, $\tilde{c}_3=15$ and $\tilde{c}_4=4$.
• Figure 5: $\gamma$ versus $\log(1+z)$ for $\beta=0.01$, $c_2=1$, $\tilde{c}_3=15$ and $\tilde{c}_4=4$.