The role of energy conditions in $f(R)$ cosmology

TL;DR

This paper explores how energy conditions influence cosmological evolution in $f(R)$ gravity, examining their role in acceleration, singularities, and frame transformations.

Contribution

It provides a classification of cosmological solutions and equations of state based on energy conditions in $f(R)$ gravity, including effects of conformal transformations.

Findings

Energy conditions relate to acceleration and singularities in $f(R)$ cosmology.

Frame transformations can qualitatively change energy conditions.

Cosmological solutions can be classified by energy conditions.

Abstract

Energy conditions can play an important role in defining the cosmological evolution. Specifically acceleration/deceleration of cosmic fluid, as well as the emergence of Big Rip singularities, can be related to the constraints imposed by the energy conditions. Here we discuss this issue for $f(R)$ gravity considering also conformal transformations. Cosmological solutions and equations of state can be classified according to energy conditions. The qualitative change of some energy conditions for transformations from the Jordan frame to the Einstein frame is also observed.