New inflationary exact solution from Lie symmetries

Abstract

For the inflaton field, we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral indices for the density perturbations [Formula: see text] and the scalar-to-tensor ratio [Formula: see text] are related as [Formula: see text]. Function [Formula: see text] is classified according to the admitted Lie symmetries for the master equation. The possible admitted Lie symmetries form the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] Lie algebras. The new inflationary solution is recovered by the Lie symmetries of the [Formula: see text] algebra. Scalar field potential is derived explicitly, while we compare the resulting spectral indices with the observations.