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29 March 2024
 
  » arxiv » 1907.3563

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Scalar perturbations in $f(T)$ gravity using the $1+3$ covariant approach
Shambel Sahlu ; Joseph Ntahompagaze ; Amare Abebe ; Alvaro de la Cruz-Dombriz ; David F. Mota ;
Date 8 Jul 2019
AbstractWe investigate the cosmological scalar perturbations of standard matter in the context of extended teleparallel $f(T)$ gravity theories using the 1 + 3 covariant formalism. We review the gravitational field equations of $f(T)$ gravity to introduce therein a gauge-invariant spatial gradient of the torsion fluid and obtain the linear perturbation equations. After performing the usual scalar and harmonic decompositions, we analyze the matter perturbations in the quasi-static approximation for two non-interacting fluids scenarios, namely torsion-dust and mixtures. We consider the $f(T)$ power-law paradigmatic classes of model $f(T) = alpha(-T/T_0)^n$, for both torsion-dust and torsion-radiation scenarios. Under this scope, exact solutions of the matter perturbations are obtained. We examine the growth of the matter density contrast for these mixtures. In a similar manner, we also consider the long- and short-wavelength modes in the torsion-radiation case. We consider different values of n to explore the growth of matter density contrast with red-shift. For the case of n closer to one, our paradigmatic $f(T)$ gravity model is favored with the usual results of general relativity (GR) and general relativity with a cosmological constant ({Lambda}CDM). However, for the case of ngg1 the amplitude of the matter density fluctuation extremely high and unrealistic to compare with GR and {Lambda}CDM results for these non-interacting fluids. Notably, in the torsion-radiation system, the behavior of the growth of matter density contrasts is abandoned and ruled-out for n ll 1 in both wave modes. While our results show a richer set of possibilities that can help to constrain the model parameters using future observational data, they also accommodate currently known features of power spectrum in the large-scale structure in the general relativistic limit.
Source arXiv, 1907.3563
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