The effective field theory approach of teleparallel gravity, f(T) gravity and beyond

Abstract

We develop the effective field theory approach to torsional modified gravities, a formalism that allows for the systematic investigation of the background and perturbation levels separately. Starting from the usual effective field theory approach to curvature-based gravity, we suitably generalize it at the background level by including terms of the contracted torsion tensor, and at the perturbation level by including pure torsion perturbative terms and mixed perturbative terms of torsion and curvature. Having constructed the effective field theory action of general torsional modified gravity, amongst others we focus on f (T ) gravity and we perform a cosmological application. We investigate the scalar perturbations up to second order, and we derive the expressions of the Newtonian constant and the post Newtonian parameter γ. Finally, we apply this procedure to two specific and viable f (T ) models, namely the power-law and the exponential ones, introducing a new parameter that quantifies the deviation from general relativity and depends on the model parameters. Since this parameter can be expressed in terms of the scalar perturbation mode, a precise measurement of its evolution could be used as an alternative way to impose constraints on f (T ) gravity and break possible degeneracies between different f (T ) models.

Growth of matter overdensities in non-minimal torsion-matter coupling theories

“…These are the so-called f (T ) gravity theories whose cosmological dynamics has been studied both at background level [44,45,46,62], as well at perturbations level in Ref. [59,60,74]. The above action can also be generalized by including a non-minimal coupling between torsion and matter in the following way [79,80]…”

“…Clearly, when f 2 (T ) = 1, Eq. (9) reduces to the field equations of f (T ) gravity [74]. On the other hand, GR is recovered when f 1 (T ) = T and f 2 (T ) = 1 [40].…”

“…Let us consider a perturbed tetrad field whose sector of scalar perturbations is written as [59,60,74]…”

“…In comparison with f (R), whose field equations are of fourth-order, the f (T ) gravity has the advantage that its dynamics is given by second-order differential equations [46]. This remarkable characteristic, added to the fact that f (T ) gravity allow us to explain the currently observed accelerated expansion of the Universe, has given rise to a fair number of papers on these gravity theories, in which several features of f (T ) gravity have been examined, including observational solar system constraints [47,48,49], cosmological constraints [50,51,52,53,54], dynamical behavior [55], cosmological perturbations [56,57,58,59,60,61,62,63,64], spherically symmetric solutions [65,66,67], the existence of relativistic stars [68], cosmographic constraints [69], energy conditions bounds [70], homogeneous Gödel-type solutions [71,72] and gravitational waves (GWs) constraints [73,74]. For an excellent review on f (T ) gravity see Ref.…”

Tensor stability in Born-Infeld determinantal gravity

“…The property of tensor perturbations has been widely analyzed in torsional theories, such as f (T ), f (T, B), f (T, T G ) and extended symmetric teleparallel gravities, see for instance [23][24][25][26][27][28][29]. In this work, we investigate the evolution of transverse-traceless (TT) tensor perturbation in early high energy regime of the spatially flat Friedmann-Robertson-Walker (FRW) cosmology in Born-Infeld determinantal gravity.…”