Cosmological perturbations in modified teleparallel gravity models

Abstract

Cosmological perturbations are considered in f (T ) and in scalar-torsion f (ϕ)T teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.1 One may remind that rather than something "extra" or "alternative", the tetrad is necessary to couple matter to gravitation. Only currently, a new preprint claims to consistently supersede the tetrad by a more minimal structure, which may shed new light on the singularity resolution and, surprisingly, the nature of dark matter [4].2 Unfortunately, with a typo (missing prime for the extra perturbation in the space-space field equation) inherited in [22].

Higgs inflation and teleparallel gravity

“…So if there is no matter apart from ϕ, there are no scalar metric perturbations. This result has previously been discussed in [109,120,124]. If other matter is included, the combination (3.26) remains zero regardless of the form of the matter action S (m) .…”

Photon sphere and perihelion shift in weak f(T) gravity

“…An important opportunity, our here presented approach offers, is to investigate the connection between the vanishing of the first order contributions of teleparallel corrections around Minkowski spacetime and the non-vanishing of the corrections around Schwarzschild geometry, with the degrees of freedom of f (T ) gravity. The latter being debated in the literature [32][33][34]. Here we considered static perturbations, in the future non-static spherically and axially symmetric gravitational waves from weak power law f (T ) gravity will be investigated and complement the gravitational wave analysis of f (T ) gravity around Minkowski and FLRW geometry [32,35,36] and also at astrophysical level with compact binary coalescences [37].…”

“…The latter being debated in the literature [32][33][34]. Here we considered static perturbations, in the future non-static spherically and axially symmetric gravitational waves from weak power law f (T ) gravity will be investigated and complement the gravitational wave analysis of f (T ) gravity around Minkowski and FLRW geometry [32,35,36] and also at astrophysical level with compact binary coalescences [37]. This paper is a first step towards a complete phenomenological catalogue of observables, which shall be derived in weak power law f (T )-gravity to systematically check its consistency with observations.…”

“…To relate the influence of a teleparallel modification of general relativity to observables we study the motion of test particles in the background solution defined by the metric coefficients (31) and (32). We explicitly derive the photon sphere around the black hole and the perihelion shift of nearly circular orbits.…”

Parametrized post-Newtonian limit of general teleparallel gravity theories

“…A large class of modified teleparallel gravity theories is obtained by assuming a gravitational Lagrangian of the form f (T ) [6,7], where T is the torsion scalar appearing in the TEGR action [2]. Various phenomenological and theoretical aspects of these theories have been investigated, including their cosmological dynamics [8,9] and perturbations [10], gravitational waves [11][12][13][14] and degrees of freedom from a Hamiltonian analysis [15][16][17][18][19]. The rich phenomenology and generality of this class of gravity theories hence invite for further investigations of the class of a whole, studying further phenomenological aspects.…”