Linear perturbations in Galileon gravity models

TL;DR

We study linear perturbations in Galileon gravity to quantify deviations from standard cosmology. We derive fully covariant, gauge-invariant perturbation equations using two independent methods and solve them with a modified version of CAMB to predict the CMB, weak lensing, and matter power spectra. The results show background expansion deviations shift CMB acoustic peak positions and drive the Weyl potential $\phi$ to evolve, enhancing the ISW signal, while the Galileon field clusters and boosts the linear growth of density perturbations with rich parameter dependence. Some Galileon models are already disfavored by current data, and future galaxy clustering, ISW, and lensing measurements will place strong constraints on the theory.

Abstract

We study the cosmology of Galileon modified gravity models in the linear perturbation regime. We derive the fully covariant and gauge invariant perturbed field equations using two different methods, which give consistent results, and solve them using a modified version of the {\tt CAMB} code. We find that, in addition to modifying the background expansion history and therefore shifting the positions of the acoustic peaks in the cosmic microwave background (CMB) power spectrum, the Galileon field can cluster strongly from early times, and causes the Weyl gravitational potential to grow, rather than decay, at late times. This leaves clear signatures in the low-$l$ CMB power spectrum through the modified integrated Sachs-Wolfe effect, strongly enhances the linear growth of matter density perturbations and makes distinctive predictions for other cosmological signals such as weak lensing and the power spectrum of density fluctuations. The quasi-static approximation is shown to work quite well from small to the near-horizon scales. We demonstrate that Galileon models display a rich phenomenology due to the large parameter space and the sensitive dependence of the model predictions on the Galileon parameters. Our results show that some Galileon models are already ruled out by present data and that future higher significance galaxy clustering, ISW and lensing measurements will place strong constraints on Galileon gravity.

Figures (8)

• Figure 1: (Color online) Evolution of the ratio of the Hubble expansion rates of the Galileon and $\Lambda$CDM models, $H / H_{\Lambda CDM}$ ($H = \theta/3$), and of the Galileon field equation of state parameter $w$. The evolutions are shown for the four models of Table \ref{['Models']} for different initial conditions. In the Galileon 1, Galileon 2 and Galileon 3 panels, on the left-hand side from top to bottom and on the right-hand side from right to left, the lines correspond, respectively, to $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-4},10^{-5},10^{-6},10^{-7},10^{-8}\}$. The same for the Galileon 4 panels but for $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-4},10^{-5},5\times10^{-6}\}$.
• Figure 2: (Color online) CMB temperature power spectra for the Galileon 3 model with two different initial conditions and for $\Lambda$CDM (dashed black), together with the WMAP 7-year (squares) Komatsu:2010fb and ACT (circles) Dunkley:2010ge data. From top to bottom, at $l = 500$, the Galileon lines (solid) correspond to $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-4}, 10^{-5}\}$, respectively.
• Figure 3: (Color online) CMB power spectra for the four Galileon models for different initial conditions and $\Lambda$CDM, together with the WMAP 7-year data (squares) Komatsu:2010fb and ACT (circles) Dunkley:2010ge data. In the Galileon 1 and Galileon 3 panels, from top to bottom, at $l = 10$, the lines correspond, respectively, to $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-4}(\rm{not\ visible}),10^{-5},10^{-6}\}, \Lambda\rm{CDM}$. The same for the Galileon 2 and Galileon 4 panels, but for $l = 2$ and for $\rho_{\varphi, i}/\rho_{m,i} = 10^{-4}(\rm{not\ visible}), \Lambda\rm{CDM}, \rho_{\varphi, i}/\rho_{m,i} = \{*10^{-6}, 10^{-5},5\times10^{-6}, 10^{-6}\}$, and $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-4}(\rm{not\ visible}),10^{-5},5\times10^{-6}\}, \Lambda\rm{CDM}$, respectively.
• Figure 4: (Color online) Time evolution of the Weyl gravitational potential $\phi$ for the four Galileon models and $\Lambda$CDM (dashed) for $k = \{1.0,\ 0.1,\ 0.01\ {\rm and}\ 0.001\} \ \rm{hMpc}^{-1}$. All the models have the initial condition $\rho_{\varphi, i}/\rho_{m,i} = 10^{-5}$. At $a = 0.1$, for the $k = \{1.0,0.1,0.01\} \ \rm{hMpc}^{-1}$ panels, and at $a = 0.4$ for the $k = 0.001 \ \rm{hMpc}^{-1}$ panel, from top to bottom the lines correspond, respectively, to $\Lambda$CDM, Galileon 1, Galileon 3, Galileon 2 and Galileon 4.
• Figure 5: (Color online) Angular power spectrum of the weak lensing potential $\psi$ for the four Galileon models with different initial conditions and $\Lambda$CDM (dashed). In the Galileon 1, Galileon 2 and Galileon 3 panels, from top to bottom, the lines correspond, respectively, to $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-5},10^{-6},10^{-7}\}$ and $\Lambda$CDM (the two smallest initial conditions are nearly indistinguishable in the Galileon 1 and Galileon 3 panels). The same for the Galileon 4 panel but for $\rho_{\varphi, i}/\rho_{m,i} = \{10^{-5},5\times10^{-6}\}$ and $\Lambda$CDM.