Cosmic expansion and growth histories in Galileon scalar-tensor models of dark energy

TL;DR

This work analyzes Galileon scalar-tensor cosmologies with a non-linear derivative interaction that screens the scalar force via the Vainshtein mechanism. The authors show that the background expansion is largely indistinguishable from $\Lambda$CDM, while the growth of density perturbations carries a distinctive signature: the asymptotic growth index is $\gamma_\infty = 9/16$ and the present value is around $\gamma \approx 0.4$, signaling enhanced structure formation relative to GR. The fate of the universe depends on the parameter $\alpha$, with $\alpha<0$ leading to a big rip and $\alpha>0$ producing transient phantom-like behavior before settling. These results provide analytic and numerical benchmarks for distinguishing Galileon gravity from standard dark energy and other modified gravity scenarios through growth-history observations.

Abstract

We study models of late-time cosmic acceleration in terms of scalar-tensor theories generalized to include a certain class of non-linear derivative interaction of the scalar field. The non-linear effect suppress the scalar-mediated force at short distances to pass solar-system tests of gravity. It is found that the expansion history until today is almost indistinguishable from that of the $Λ$CDM model or some (phantom) dark energy models, but the fate of the universe depends clearly on the model parameter. The growth index of matter density perturbations is computed to show that its past asymptotic value is given by 9/16, while the value today is as small as 0.4.

Figures (5)

• Figure 1: Dimensionless physical distance for $\omega=-500$ and various $\alpha$.
• Figure 2: Effective equation of state $w_{\rm eff}$ as a function of $z$ for $\omega=-500$ and various $\alpha$.
• Figure 3: $\gamma$ as a function of $z$ for $\alpha=4$ and $\alpha=-1$. The parameters are given by $\omega=-500$ and $\Omega_{{\rm m}0}=0.3$.
• Figure 4: $\gamma$ as a function of $z$ for $\alpha=1$ and various $\omega$. The parameters are given by $\Omega_{{\rm m}0}=0.3$.
• Figure 5: The sound speed squared (defined in the Appendix) as a function of $z$. The sound speed squared is positive, and can be temporarily greater than 1.