Cosmology with Scalar-Euler form Coupling

TL;DR

This paper explores a novel scalar-Euler form coupling in gravity, revealing how torsion influences cosmological evolution and differs from standard models, with potential implications for understanding the universe's dynamics.

Contribution

It introduces a new scalar-Euler form coupling in gravity, demonstrating how torsion affects cosmological evolution beyond standard models.

Findings

Torsion acts as a new source for metric curvature.

The coupling leads to cosmological dynamics different from FRWL models.

Slowly varying scalar fields can still produce significant cosmological effects.

Abstract

A coupling between the spacetime geometry and a scalar field involving the Euler four-form can have important consequences in General Relativity. The coupling is a four-dimensional version of the Jackiw-Teitelboim action, in which a scalar couples to the Euler two-form in two dimensions. In this case the first order formalism, in which the vierbein (or the metric) and the spin connection (or the afine connection) are varied independently, is not equivalent to the second order one, in which the geometry is completely determined by the metric. This is because the torsion postulate (T=0) is not valid and one cannot algebraically solve the spin connection from its own field equation. The direct consequence of this obstruction is that the torsion becomes a new source for the metric curvature, and even if the scalar field is very slowly varying over cosmic scales as to have no observable astronomical efects at the galactic scale, it has important dynamical efects that can give rise to a cosmological evolution radically diferent from the standard FRWL model.