Exact solutions for scalar field cosmology in f(R) gravity

TL;DR

This paper derives exact solutions in scalar field cosmology within f(R) gravity without specifying the f(R) form, analyzing the universe's evolution and comparing it to the standard Lambda-CDM model.

Contribution

It provides a method to find exact solutions in scalar field f(R) gravity without fixing the f(R) function, including solutions applicable to the current universe epoch.

Findings

Derived exact solutions for scalar field cosmology in f(R) gravity.

Compared scale factor evolution with Lambda-CDM, impacting universe age estimates.

Presented solutions for special and general cases with initial conditions.

Abstract

We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that acceleration of the scalar curvature is negligible. We first present solutions for special cases and then the general solution. Using initial conditions which represent the universe at the present epoch, we evaluated the constants of integration. This allows for the comparison of the scale factor in the new solutions with that of the $\Lambda CDM$ solution, thereby affecting the age of the universe in $f(R)$ gravity.