First Order Extended Gravity and the Dark Side of the Universe: the General Theory

TL;DR

This paper proposes a new first-order Palatini formalism for gravity, introducing the Dark Metric concept to potentially eliminate the need for Dark Energy and Dark Matter in explaining cosmic phenomena.

Contribution

It introduces a novel mathematical framework for gravity using first-order formalism and the Dark Metric, offering an alternative to dark components in cosmology.

Findings

Dark Metric could replace dark components in cosmological models

New formalism simplifies the mathematical treatment of gravity

Potential to resolve dark matter and dark energy issues

Abstract

General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match it with the today observational data lead to invoke Dark Energy and Dark Matter as the bulk components of the cosmic fluid. Since no final evidence, at fundamental level, exists for such ingredients, it is clear that General Relativity presents shortcomings at infrared scales. On the other hand, the attempts to formulate theories more general than the Einstein one give rise to mathematical difficulties that need workarounds which, in turn, generate problems from the interpretative viewpoint. We present here a completely new approach to the mathematical objects in terms of which a theory of Gravitation may be written in a first-order `a la Palatini formalism, and introduce the concept of Dark Metric which could completely bypass the introduction of disturbing concepts as Dark Energy and Dark Matter.