Modified gravity a la Galileon: Late time cosmic acceleration and observational constraints

In this paper we examine the cosmological consequences of fourth order Galileon gravity. We carry out detailed investigations of the underlying dynamics and demonstrate the stability of one de Sitter phase. The stable de Sitter phase contains a Galileon field $π$ which is an increasing function of time (\dotπ>0). Using the required suppression of the fifth force, supernovae, BAO and CMB data, we constrain parameters of the model. We find that the $π$ matter coupling parameter $β$ is constrained to small numerical values such that $β$<0.02. We also show that the parameters of the third and fourth order in the action (c_3,c_4) are not independent and with reasonable assumptions, we obtain constraints on them. We investigate the growth history of the model and find that the sub-horizon approximation is not allowed for this model. We demonstrate strong scale dependence of linear perturbations in the fourth order Galileon gravity.

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