Matter perturbations in Galileon cosmology

Abstract

We study the evolution of matter density perturbations in Galileon cosmology where the late-time cosmic acceleration can be realized by a field kinetic energy. We obtain full perturbation equations at linear order in the presence of five covariant Lagrangians ${\mathcal{L}}_{i}$ ($i=1,\ensuremath{\cdots},5$) satisfying the Galileon symmetry ${\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}\ensuremath{\rightarrow}{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}+{b}_{\ensuremath{\mu}}$ in the flat space-time. The equations for a matter perturbation as well as an effective gravitational potential are derived under a quasistatic approximation on subhorizon scales. This approximation can reproduce full numerical solutions with high accuracy for the wavelengths relevant to large-scale structures. For the model parameters constrained by the background expansion history of the Universe, the growth rate of matter perturbations is larger than that in the $\ensuremath{\Lambda}$-cold dark matter model, with the growth index $\ensuremath{\gamma}$ today typically smaller than 0.4. We also find that, even on very large scales associated with the integrated-Sachs-Wolfe effect in cosmic microwave background temperature anisotropies, the effective gravitational potential exhibits a temporal growth during the transition from the matter era to the epoch of cosmic acceleration. These properties are useful to distinguish the Galileon model from the $\ensuremath{\Lambda}$-cold dark matter model in future high-precision observations.