String-Inspired Gravity through Symmetries

We study a string-inspired cosmological model from the symmetries point of view. We start by deducing the form that each physical quantity must take so that the field equations, in the string frame, admit self-similar solutions. In the same way, we formalize the use of power-law solutions (less restrictive than the self-similar ones) by studying the wave equation for the dilaton through the Lie group method. Furthermore, we show how to generate more solutions by using this approach. As examples, we calculate exact solutions to several cosmological models in the four-dimensional NS-NS (Neveu-Schwarz-Neveu-Schwarz) sector of low-energy effective string theory coupled to a dilaton and an axion-like H-field within the string frame background, with FRW and the Bianchi Type II metrics. We also study the existence of Noether symmetries, which allow us to determine the form of the physical quantities in the framework of FRW geometry and to find exact cosmological solutions.