Evolution of linear cosmological perturbations and its observational implications in Galileon-type modified gravity

TL;DR

This work develops a full linear perturbation theory for Galileon-type modified gravity, revealing that perturbations can closely resemble $\Lambda$CDM only under finely tuned initial conditions; otherwise, a super-horizon growing mode indicates potential instability. The authors show that, despite a similar background expansion, perturbations predict an enhanced weak-lensing signal and a characteristic anticorrelation between the ISW effect and large-scale structure, with the magnitude depending on the Brans-Dicke parameter $\omega$. These signatures provide a practical way to distinguish Galileon gravity from $\Lambda$CDM using CMB-LSS cross-correlations and lensing surveys. The results underscore that background mimicry does not guarantee perturbative equivalence, highlighting observational tests as a critical probe of Galileon cosmology, and point to future work on higher-order interactions and non-linear effects.

Abstract

A scalar-tensor theory of gravity can be made not only to account for the current cosmic acceleration, but also to satisfy solar-system and laboratory constraints, by introducing a non-linear derivative interaction for the scalar field. Such an additional scalar degree of freedom is called "Galileon". The basic idea is inspired by the DGP braneworld, but one can construct a ghost-free model that admits a self-accelerating solution. We perform a fully relativistic analysis of linear perturbations in Galileon cosmology. Although the Galileon model can mimic the background evolution of standard $Λ$CDM cosmology, the behavior of perturbation is quite different. It is shown that there exists a super-horizon growing mode in the metric and Galileon perturbations at early times, suggesting that the background is unstable. A fine-tuning of the initial condition for the Galileon fluctuation is thus required in order to promote a desirable evolution of perturbations at early times. Assuming the safe initial condition, we then compute the late-time evolution of perturbations and discuss observational implications in Galileon cosmology. In particular, we find anticorrelations in the cross-correlation of the integrated Sachs-Wolfe effect and large scale structure, similar to the normal branch of the DGP model.

Figures (11)

• Figure 1: Dimensionless physical distance for different $\omega$.
• Figure 2: Linear growth factor for different $k$. The initial condition for the numerical calculation is $\Omega_i=1$, $\dot\Omega_i=0$, and $\varphi_i=0=\dot\varphi_i$. The plotted value is divided by the initial value of the growth factor. The parameters are given by $\omega=-50$ and $\Omega_{{\rm m}0}=0.3$. Results obtained from the quasi-static approximation and in the $\Lambda$CDM model are also shown.
• Figure 3: Evolution of the potential $\Omega$ for different $k$. The same parameters as in Fig. \ref{['fig:D50.eps']} are used.
• Figure 4: Evolution of the Galileon fluctuation $\varphi$ for different $k$. The same parameters as in Fig. \ref{['fig:D50.eps']} are used.
• Figure 5: Same as Fig. \ref{['fig:D50.eps']}, but with $\omega =-5000$.