Dynamical aspects of asymmetric Eddington gravity with scalar fields

TL;DR

This paper extends Eddington gravity by including antisymmetric Ricci components and scalar fields, revealing new dynamical features and potential implications for theories involving scalar fields.

Contribution

It introduces a novel formulation of Eddington gravity with antisymmetric Ricci parts and scalar couplings, leading to a richer dynamical structure.

Findings

The metric acquires an additional antisymmetric component.

The second curvature affects connection dynamics and scalar field evolution.

New dynamical features emerge from the extended action.

Abstract

In Eddington gravity, the action principle involves only the symmetric parts of the connection and the Ricci tensor, with a metric that emerges proportionally to the latter. Here, we relax this symmetric character, prolong the action with the antisymmetric parts of the Ricci term, and allow for various couplings with scalar fields. We propose two possible invariant actions formed by distinct combinations of the independent Ricci tensors and show that the generated metric must involve an additional antisymmetric part due to the relaxation of the symmetrization property. The comprehensive study shows that the second curvature influences the dynamics of the connection, hence its solution in terms of the metric, and the evolution of the scalar fields. These new dynamical features are expected to stand viable and to have interesting implications in domains where scalar fields are indispensable.