Einstein-Cartan gravity, matter, and scale-invariant generalization

TL;DR

This paper explores a generalized Einstein-Cartan gravity framework coupled with matter, deriving equivalent metric theories with higher-dimensional operators, and discusses implications for cosmology, inflation, and dark matter.

Contribution

It provides a comprehensive analysis of the most general Einstein-Cartan action with matter, including torsion effects and no-scale scenarios, and outlines potential cosmological applications.

Findings

Derived equivalent metric theories with six-dimensional operators.

Analyzed torsion effects in gravity-matter coupling.

Outlined phenomenological implications for inflation and dark matter.

Abstract

We study gravity coupled to scalar and fermion fields in the Einstein-Cartan framework. We discuss the most general form of the action that contains terms of mass dimension not bigger than four, leaving out only contributions quadratic in curvature. By resolving the theory explicitly for torsion, we arrive at an equivalent metric theory containing additional six-dimensional operators. This lays the groundwork for cosmological studies of the theory. We also perform the same analysis for a no-scale scenario in which the Planck mass is eliminated at the cost of adding an extra scalar degree of freedom. Finally, we outline phenomenological implications of the resulting theories, in particular to inflation and dark matter production.