Cosmology in a model with Lagrange multiplier, and Gauss-Bonnet and non-minimal kinetic couplings

A scalar-tensor model with Gauss-Bonnet and non-minimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is deviced for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with the most accurate values of the observational indices.