Eddington gravity with matter: An emergent perspective

TL;DR

This paper presents an action principle within Eddington gravity that incorporates matter, reproduces Einstein's equations, and supports the view of gravity as an emergent phenomenon, with implications for the cosmological constant and extensions to torsion and higher-order gravity.

Contribution

It introduces a novel action principle in Eddington gravity that naturally includes matter and yields Einstein's equations, supporting the emergent gravity paradigm.

Findings

Derivation of Einstein's equations from the new action principle.

The cosmological constant appears as an integration constant.

Extension of the framework to include torsion and Lanczos-Lovelock gravity.

Abstract

We describe an action principle, within the framework of the Eddington gravity, which incorporates the matter fields in a simple manner. Interestingly, the gravitational field equations derived from this action is identical to the Einstein's equations, in contrast with the earlier attempts in the literature. The cosmological constant arises as an integration constant in this approach. In fact, the derivation of the field equations demands the existence of a non-zero cosmological constant, thereby providing the raison d'\^{e}tre for a non-zero cosmological constant, implied by the current observations. Several features of our approach strongly support the paradigm that gravity is an emergent phenomenon and, in this perspective, our action principle could have a possible origin in the microstructure of the spacetime. We also discuss several extensions of the action principle, including the one which can incorporate torsion in the spacetime. We also show that an Eddington-like action can be constructed to obtain the field equations of the Lanczos-Lovelock gravity.