On f(R) Theories in Two-Dimensional Spacetime

Abstract

In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function f(R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this paper we carry out an analysis of such theories in two-dimensional spacetime with focus on cosmological implications. Solutions to the cosmological field equations are obtained and their properties are analysed. Inflationary solutions are also obtained and discussed. Quantization is then carried out, the Wheeler-DeWitt equation is set up, and its exact solutions are obtained.