General Effective Field Theory of Teleparallel Gravity

TL;DR

This paper develops the effective field theory for teleparallel gravity, revealing subtle differences from general relativity at high energies due to additional degrees of freedom, with implications for future experimental tests.

Contribution

It constructs the EFT of TEGR including higher-order torsion terms and demonstrates small but fundamental differences from GR at the quantum level.

Findings

EFT of TEGR contains more terms than EFT of GR.

Classical equivalence of GR and TEGR does not extend to their EFTs.

Differences between EFTs are suppressed by a high energy scale.

Abstract

We construct the Effective Field Theory (EFT) of the teleparallel equivalent of general relativity (TEGR). Firstly, we present the necessary field redefinitions of the scalar field and the tetrads. Then we provide all the terms at next-to-leading-order, containing the torsion tensor and its derivatives, and derivatives of the scalar field, accompanied by generic scalar-field-dependent couplings, where all operators are suppressed by a scale $\Lambda$. Removing all redundant terms using the field redefinitions we result to the EFT of TEGR, which includes significantly more terms comparing to the EFT of General Relativity. Finally, we present an application in a cosmological framework. Interestingly enough, although GR and TEGR are completely equivalent at the level of classical equations, we find that their corresponding EFTs possess minor but non-zero differences. Hence, we do verify that at higher energies the excitation and the features of the extra degrees of freedom are slightly different in the two theories, thus making them theoretically distinguishable. Nevertheless, we mention that these differences are suppressed by the heavy mass scale $\Lambda$ and thus it is not guaranteed that they could be measured in future experiments and observations.