Reconstruction of $F(T)$ gravity in homogeneous backgrounds

Abstract

A technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity has recently been developed by Alexander Y. Kamenshchik, Alessandro Tronconi, and Giovanni Venturi [73]. In this paper, this extended reconstruction method is utilized to investigate the nature of the scalar potentials of the most extended action of F (T ) -gravity context. First, a general formalism is formulated and then it is utilized for considering some well-known special cases including 'Barotropic Fluid', 'Cosmological Constant', and 'Modified Chaplygin Gas'. The analysis of the results is carried out by the use of the B-function method which has recently been suggested by the author [74]. As we know, assuming a proportional relation between the scale factor of the x-direction and the scale factors of y and z directions (i.e. A = B m ) in dealing with LRS Bianchi-I background is prevalent. Pursuant to observational data, the correct physical range of m is extracted. It is demonstrated that, unlike several papers, m is very close to 1. Some interesting discussions about the modified and generalized Chaplygin gases are performed. The ranges of the amounts of free parameters of the various types of Chaplygin gases are corrected according to observational data. It is demonstrated that the generalized Chaplygin gas model namely P = −σ 2 /ρ ν may be developed asUltimately, by combining ref.[73] and the current paper, a general prescription is recommended for the reconstruction of the potentials of alternative theories of gravity (especially F (R) and F (T ) ), and their relevant analysis.

Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether’s approach

“…It has been demonstrated in ref. [80] that according to recent observational data, m is very close to 1. Utilizing this well-known reasonable condition, a = b m , the expansion scalar (21) takes the form…”

“…Based on the recent observational data, in ref. [80], it has been demonstrated that m is very close to one 4 . The case m = 1 is FRW.…”

Raychaudhuri-based reconstruction of anisotropic Einstein-Maxwell equation in 1+3 covariant formalism of $f(R)$-gravity

“…Note that according to (30), the rate of σ and Θ would be equal since ( σ/σ) = ( Θ/Θ) . Pursuant to observational data, it has been demonstrated in [37,42] that…”

“…Cosmological models are investigated via several powerful tools: exact solutions, phase space [25,26], B-function method [27], Noether symmetry approach [28][29][30][31], Beyond Noether symmetry approach (B.N.S.) [32], Noether symmetry approach using CSSS-trick [33], Reconstruction methods [34][35][36][37][38], etc. Recently, a new strategy to the reconstruction of f (R) -gravity models using Raychaudhuri equation has been proposed by Choudhury et al [1].…”

Investigating the physical and geometrical parameters of the cosmological models with anisotropic background

“…This further provides anisotropic relationship between the scale factors. Tajahmad [75] has considered the similar relation to reconstructed the F (T ) gravity. Most recent, Tajahmad [76] has shown that late time accelerated expansion arisen from gauge fields in an anisotropic background.…”