Two-field cosmological α-attractors with Noether symmetry

Abstract

© 2019, The Author(s). We study Noether symmetries in two-field cosmological α-attractors, investigating the case when the scalar manifold is an elementary hyperbolic surface. This encompasses and generalizes the case of the Poincaré disk. We solve the conditions for the existence of a ‘separated’ Noether symmetry and find the form of the scalar potential compatible with such, for any elementary hyperbolic surface. For this class of symmetries, we find that the α-parameter must have a fixed value. Using those Noether symmetries, we also obtain many exact solutions of the equations of motion of these models, which were studied previously with numerical methods