General effective field theory of teleparallel gravity

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 Λ. 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 Λ and thus it is not guaranteed that they could be measured in future experiments and observations.

The effective field theory approach to the strong coupling issue in f(T) gravity

“…Additionally, T (0) is used to represent the torsion scalar at the background level with the value T (0) = 6H 2 (not to be confused with the zero-th component of the contracted torsion tensor T 0 ). Hence the EFT action at leading order is found to be [49,53]…”

“…Furthermore, note that in the EFT approach f (T ) gravity can be regarded as a low-energy effective theory. It is possible that the strong coupling problem can be eliminated if other operators are introduced in the EFT action beyond the scale M [53].…”

“…Subsequently, one may construct a general framework which includes both f (R) and f (T ) gravity, namely f (T, B) theory [10,11]. A lot of effort has been devoted to the investigation of the theoretical properties and observational implications of these theories , while it was shown that one can apply to them an effective field theory (EFT) approach, modifying and extending the original curvature-based EFT framework [49][50][51][52][53].…”