The minimal curvature of the universe in modified gravity and conformal anomaly resolution of the instabilities

TL;DR

This paper explores modified gravity models that produce cosmic acceleration without dark energy, identifying conditions for minimal curvature and showing quantum effects can suppress instabilities, with implications for cosmology.

Contribution

It introduces a class of modified gravity models with minimal curvature and demonstrates how conformal quantum effects can resolve instabilities in these models.

Findings

Models with action increasing as curvature decreases define a universe with minimal curvature.

Quantum effects of conformal fields can suppress instabilities in modified gravity.

Reaching the minimal curvature takes infinite time during cosmic evolution.

Abstract

We discuss the modified gravity which may produce the current cosmic aceleration of the universe and eliminates the need for dark energy. It is shown that such models where the action quickly grows with the decrease of the curvature define the FRW universe with the minimal curvature. It is required the infinite time to reach the minimal curvature during the universe evolution. It is demonstrated that quantum effects of conformal fields may strongly suppress the instabilities discovered in modified gravity. We also briefly speculate on the modification of gravity combined with the presence of the cosmological constant dark energy.