Modified Gravity and Cosmology: An Update by the CANTATA Network

TL;DR

This review summarizes recent advances in modified gravity theories and their cosmological implications, emphasizing theoretical consistency, observational tests, and future research directions within the context of the CANTATA network.

Contribution

It provides a comprehensive overview of the latest developments in extended gravity theories, assessing their viability against observational data and highlighting open problems and future research avenues.

Findings

Identification of viable modified gravity models consistent with observations

Analysis of theoretical consistency and observational constraints on extended theories

Outline of future directions in gravity and cosmology research

Abstract

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''.