Phenomenological reconstruction of f(T) teleparallel gravity

Abstract

We present a novel reconstruction method of f (T ) teleparallel gravity from phenomenological parametrizations of the deceleration parameter or other alternatives. This can be used as a toolkit to produce viable modified gravity scenarios directly related to cosmological observations. We test two parametrizations of the deceleration parameter considered in recent literatures in addition to one parametrization of the effective (total) equation of state (EoS) of the universe. We use the asymptotic behavior of the matter density parameter as an extra constraint to identify the viable range of the model parameters. One of the tested models shows how tiny modification can produce viable cosmic scenarios quantitatively similar to ΛCDM but qualitatively different whereas the dark energy (DE) sector becomes dynamical and fully explained by modified gravity not by a cosmological constant.

Teleparallel Gravity: From Theory to Cosmology

“…For the ΛCDM cosmology in the presence of dust matter, the Lagrangian reduces to the standard ΛCDM Lagrangian [936,413]. However, it can be generalized for arbitrary perfect fluids with EoS w to give [783]…”

“…An alternative proposal is to reconstruct through a specification of the deceleration parameter q(z). During periods where the matter content is mostly composed of baryonic matter, the reconstructed function is obtained from the relation [413] f…”

“…In particular, the parametrization q(z) = q 0 + q 1 X(z) [413] for constants q 0 , q 1 and for two functional choices of X(z) which determines the cosmological evolution was investigated.…”

“…Lastly, Ref. [413] explores f (T ) reconstruction through the effective fluid EoS w eff for the model w eff = − 1 1+α(1+z) n for some constants α, n [772] which describes an early matter domination and late de Sitter phases. In particular, n = 3 yields the standard ΛCDM cosmology, hence n is expected to deviate slightly from this value.…”

Scalar perturbations in f(T) gravity using the $$1 + 3$$ covariant approach

“…One of the modified gravity theories currently under active exploration is f (T ) gravity [12][13][14][15][16][17][18][19][20], where T represents the torsion scalar. The f (T ) gravitational theory can resolve a number of longstanding issues in general relativity (GR), e.g., to study the primordial nucleosynthesis [21], the static spherically symmetric self-gravitating objects [22,23], observational constraints [24,25], the background and perturbation analysis in the metric formalism [26][27][28][29][30][31], just to mention a few. The study of linear cosmological perturbations in f (T ) gravity theory using the 1 + 3 covariant formalism is the main focus of research in this manuscript.…”