Non-minimal Scalar Effective Cosmology

Abstract

In this work we investigate the most general non-minimally coupled $\mathbb{Z}_2$ symmetric scalar-tensor effective field theory (EFT) of gravity up to dimension six in the operator expansion. The most general action is presented along with its equations of motion both in the covariant form and also in the coordinate form resulting from an FLRW analysis. The pressure and density of the scalar field are found as well as the equation of state parameter and some cosmological parameters. We analyse the background evolution of the scalar field within the framework of the slow-roll approximation and provide a brief discussion of $\mathbb{Z}_2$ symmetry breaking of the scalar field which gives an order of magnitude constraint on one of the coupling constants. To provide a concrete example we choose a couple of potentials for the scalar field and explore the cosmology. Some brief comments on the range of validity of the EFT are also offered as well as the connections between the general model and well-known examples in the literature.