First and second order cosmological perturbations in light mass Galileon models

In this paper, we investigate the first and second order cosmological perturbations in the light mass Galileon (LMG) scenario. LMG action includes cubic Galileon term along with the standard kinetic term and a potential which is added phenomenologically to achieve late time acceleration. The scalar field is nonminimally coupled to matter in the Einstein frame. Integral solutions of growing and decaying modes are obtained. The effect of the conformal coupling constant ($\beta$), at the perturbation level, has been studied. In this regard, we have studied linear power spectrum and bispectrum. Though different values of $\beta$ has different effects on power spectrum on reduced bispectrum the effect is not significant. It has been found that the redshift-space distortions (RSD) data can be very useful to constrain $\beta$. In this study we consider potentials which can lead to tracker behavior of the scalar field.