Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term

Abstract

Within this work, we propose a new generalised quintom dark energy model in the teleparallel alternative of general relativity theory, by considering a non-minimal coupling between the scalar fields of a quintom model with the scalar torsion component T and the boundary term B. In the teleparallel alternative of general relativity theory, the boundary term represents the divergence of the torsion vector, B = 2∇µT µ , and is related to the Ricci scalar R and the torsion scalar T , by the fundamental relation: R = −T + B. We have investigated the dynamical properties of the present quintom scenario in the teleparallel alternative of general relativity theory by performing a dynamical system analysis in the case of decomposable exponential potentials. The study analysed the structure of the phase space, revealing the fundamental dynamical effects of the scalar torsion and boundary couplings in the case of a more general quintom scenario. Additionally, a numerical approach to the model is presented to analyse the cosmological evolution of the system.

Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

“…Still, there is a long route for understanding the possible astrophysical effects of modified Teleparallel theories of gravity. It might be interesting to follow a similar approach done in this paper for other Teleparallel theories, such as scalar-tensor theories [66][67][68][69][70][70][71][72][73][74][75], non-local theories [76] or theories with non-minimally couplings between matter and gravity [77]. These works will be done in forthcoming studies.…”

Generalized tachyonic teleparallel cosmology

“…In the teleparallel setting, scalar fields have been investigated to a moderate degree, with various extensions having been investigated in the cosmological context [23][24][25][26][27][28]. Furthermore, the effects of the boundary couplings in scalar tensor theories have been discussed in various papers [25,[29][30][31][32][33][34][35][36][37][38][39][40][41]. A recent review on various studies related to dynamical analysis in different cosmological constructions can be found in [42].…”

Scalar-torsion theories of gravity. III. Analogue of scalar-tensor gravity and conformal invariants

“…First, note that the matter action functional in the Jordan frame action (43) agrees with the action functional we used in the definition (12) of the matter action; this is the reason for using the notation involving the superscript J. Further, we see that S J m depends only on the Jordan frame tetrad and matter fields, and carries no additional, explicit dependence on the scalar field besides the implicit dependence through the definition (40). This is the most important advantage and typical reason for using the Jordan frame, since also the resulting matter field equations ̟ J I = 0 are expressed in terms of the Jordan frame tetrad and matter fields only, without further dependence on the scalar field.…”

“…Note that in contrast to the algebraic conditions (40) and (49) for the Jordan and Einstein frame transformations we obtain a differential equation, which fixes γ D only up to an additive constant. Hence, also the corresponding debraiding tetrad θ D a = e γ D (φ) θ a is determined only up to a constant factor.…”