On f(R) theories in two-dimensional spacetime

TL;DR

This paper explores f(R) gravity theories in two-dimensional spacetime, analyzing their cosmological solutions, inflationary behavior, and quantum properties through the Wheeler-DeWitt equation.

Contribution

It extends the study of f(R) theories to two dimensions, providing exact solutions and quantum analysis, which is a novel approach in lower-dimensional gravity research.

Findings

Derived cosmological solutions in 2D f(R) gravity.

Identified inflationary solutions in the 2D model.

Quantized the model and obtained exact Wheeler-DeWitt solutions.

Abstract

In recent years, theories in which the Einstien-Hilbert lagrangian is replaced by a function f(R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this work 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 obtained.