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 $\Lambda$. 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.

17 pages, comments are welcome

References in corpus (31)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• The Effective Field Theory of Inflation
• The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
• The trouble with $H_0$
• Effective Field Theory for Inflation
• Teleparallel Gravity: From Theory to Cosmology
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Construction of cosmologically viable f(G) gravity models
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Modified Gravity and Cosmology: An Update by the CANTATA Network
• Growth factor in f(T) gravity
• The Pantheon+ Analysis: SuperCal-Fragilistic Cross Calibration, Retrained SALT2 Light Curve Model, and Calibration Systematic Uncertainty
• Dark energy from modified gravity with Lagrange multipliers
• Stability of the flat FLRW metric in $f(T)$ gravity
• Metric-Affine Gravity as an Effective Field Theory
• Quasinormal modes of black holes in f(T) gravity
• The effective field theory of inflation/dark energy and the Horndeski theory
• Effective Field Theory for the Perturbations of a Slowly Rotating Black Hole
• Effective Field Theory of Black Hole Perturbations with Timelike Scalar Profile: Formulation
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Cosmic evolution in f(T) gravity theory
• N-body simulations, halo mass functions, and halo density profile in $f(T)$ gravity
• Quantum fields in teleparallel gravity: renormalization at one-loop
• Chiral primordial gravitational waves in extended theories of Scalar-Tensor gravity

Cited by in corpus (10)

• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology
• Cosmic Growth in $f(T)$ Teleparallel Gravity
• Growth of structures using redshift space distortion in $f(T)$ Cosmology
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Myrzakulov Gravity in Vielbein Formalism: A Study in Weitzenböck Spacetime
• Einstein-Gauss-Bonnet-Myrzakulov Gravity from $R+F(T,G)$: Numerical Insights and Torsion-Gauss-Bonnet Dynamics in Weitzenböck Spacetime
• Big Bang Nucleosynthesis constraints on $f(T,L_m)$ gravity
• White Dwarf Envelops and Temperature Corrections in Exponential $f(T)$ Gravity
• Growth factor in teleparallel Gauss-Bonnet gravity