Extended Theories of Gravity

TL;DR

Extended Theories of Gravity aim to address fundamental issues in cosmology and astrophysics by extending General Relativity, incorporating concepts like f(R)-gravity and scalar-tensor theories, to unify phenomena such as Dark Energy, Dark Matter, and Quantum Gravity.

Contribution

This paper reviews the foundational principles, mathematical frameworks, and viability criteria of Extended Theories of Gravity, highlighting their potential to solve key cosmological problems.

Findings

Analysis of f(R)-gravity and scalar-tensor theories in different approaches.

Discussion on the role of torsion and conformal equivalence.

Consideration of observational tests like gravitational waves and neutrino oscillations.

Abstract

Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is aimed to address conceptual and experimental problems recently emerged in Astrophysics, Cosmology and High Energy Physics. In particular, the goal is to encompass, in a self-consistent scheme, problems like Inflation, Dark Energy, Dark Matter, Large Scale Structure and, first of all, to give at least an effective description of Quantum Gravity. We review the basic principles that any gravitational theory has to follow. The geometrical interpretation is discussed in a broad perspective in order to highlight the basic assumptions of General Relativity and its possible extensions in the general framework of gauge theories. Principles of such modifications are presented, focusing on specific classes of theories like f (R)-gravity and scalar-tensor gravity in the metric and Palatini approaches. The special role of torsion is also discussed. The conceptual features of these theories are fully explored and attention is payed to the issues of dynamical and conformal equivalence between them considering also the initial value problem. A number of viability criteria are presented considering the post-Newtonian and the post-Minkowskian limits. In particular, we discuss the problems of neutrino oscillations and gravitational waves in Extended Gravity. Finally, future perspectives of Extended Gravity are considered with possibility to go beyond a trial and error approach.