Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity

Abstract

We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General Relativity . In this way, we extend the results that were already found for $F(T)$ gravity in previous works. Furthermore, our calculations reveal the importance of considering a second post-Newtonian (2PN) order approximation or a parametrized post-Newtonian cosmology (PPNC) framework where additional perturbative modes coming from general modifications of Teleparallel Gravity could lead to new observable imprints.

References in corpus (43)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Confrontation between General Relativity and Experiment
• f(R) theories
• Extended Theories of Gravity
• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM
• Cosmological Tests of Modified Gravity
• The teleparallel equivalent of general relativity
• Measurements of the Hubble Constant: Tensions in Perspective
• f(T) Gravity and local Lorentz invariance
• The covariant formulation of f(T) gravity
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Torsion Gravity: a Reappraisal
• Gravitational Energy-Momentum Density in Teleparallel Gravity
• $O(d,d)$-Covariant String Cosmology
• Weak-Field Spherically Symmetric Solutions in $f(T)$ gravity
• Solar System tests in $f(T)$ gravity
• Post-Newtonian limit of generalized symmetric teleparallel gravity
• $f(T)$ gravity: effects on astronomical observation and Solar System experiments and upper-bounds
• Spin Connection and Renormalization of Teleparallel Action
• Photon sphere and perihelion shift in weak $f(T)$ gravity
• Constraining f(T) gravity in the Solar System
• Solar System Tests in Modified Teleparallel Gravity
• Gauge Structure of Teleparallel Gravity
• The Spherically Symmetric Vacuum in Covariant $F(T)=T+\frac{\alpha }{2}{T}^2+\mathcal{O}(T^{\gamma })$ Gravity Theory
• Parameterized Post-Newtonian Cosmology
• Noether Symmetries and Quantum Cosmology in Extended Teleparallel Gravity
• Parameterized post-Newtonian limit of general teleparallel gravity theories
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Modified teleparallel gravity with higher-derivative torsion terms
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking
• Slow-roll inflation in generalized scalar-torsion gravity
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• Post-Newtonian limit of generalized scalar-torsion theories of gravity
• Gravitational Waves in Higher Order Teleparallel Gravity
• Growth of matter overdensities in non-minimal torsion-matter coupling theories
• Violation of causality in $f(T)$ gravity
• Light bending in $f(T)$ gravity
• Inflation and Primordial Fluctuations in $F(T)$ Gravity's Rainbow
• Parameterized second post-Newtonian framework with conservation Laws

Cited by in corpus (2)

• Teleparallel Gravity: From Theory to Cosmology
• Revisiting $f(R)$ gravity's rainbow: Inflation and primordial fluctuations