Early and late time cosmology: the $f(R)$ gravity perspective

TL;DR

This paper reviews $f(R)$ gravity as an alternative to $\\Lambda$CDM, exploring its cosmological implications, model selection via Noether symmetries, and potential to resolve cosmic tensions and energy issues.

Contribution

It provides a comprehensive overview of $f(R)$ gravity models, focusing on their cosmological applications and criteria for viability, including Noether symmetries and energy conditions.

Findings

Identified viable $f(R)$ models using Noether symmetries.

Analyzed the evolution of models from matter domination to present.

Discussed the potential of $f(R)$ gravity to address cosmic tensions.

Abstract

Discrepancies between observations at early and late cosmic epochs, and the vacuum energy problem associated with the interpretation of cosmological constant, are questioning the $\Lambda$CDM model. Motivated by these conceptual and observational facts, extensions of Einstein's gravity are recently intensively considered in view of curing unsolved issues suffered by General Relativity at ultraviolet and infrared scales. Here, we provide a short overview of some aspects of $f(R)$ gravity, focusing, in particular, on cosmological applications. Specifically, Noether symmetries are adopted as a criterion to select viable models and investigate the corresponding dynamics. We thus find solutions to the cosmological field equations, analyzing the behaviour of selected models from the matter-dominated to the present epoch. Moreover, constraints coming from energy conditions and the so-called swampland criteria are also considered. In particular, we qualitatively discuss the possibility of $f(R)$ gravity to account for fixing cosmic tensions.