Conformal symmetry and accelerating cosmology in teleparallel gravity

Abstract

We discuss conformal issues of pure and extended teleparallel gravity. In particular, we present formulations of conformal transformation in teleparallel gravity. Furthermore, we propose conformal scalar and gauge field theories in teleparallel gravity and study conformal torsion gravity. We explicitly demonstrate that a power-law acceleration (including the $\Lambda$CDM universe) as well as the de Sitter expansion of the universe can be realized in extended teleparallel gravity with a conformal scalar field, and that pure teleparallel gravity with a conformal scalar field can lead to the $\Lambda$CDM model. It is also shown that there can exist the de Sitter solution in conformal torsion gravity.Comment: 13 pages, no figure, version accepted for publication in Physical Review

Teleparallel quintessence with a nonminimal coupling to a boundary term

“…In recent years an alternative formulation has been considered where the coupling occurs between the scalar field and torsion of the form ξTϕ 2 [51][52][53][54][55][56][57][58][59][60][61][62]. This gives rise to different dynamics and interesting phenomenology, for example phantom behavior and dynamical crossing of the phantom barrier.…”

Interacting quintessence in a new scalar-torsion gravity

“…Then its value should somehow increase to account for the late-time accelerated expansion of the universe [60]. Additionally a conformally invariant extension of teleparallel gravity in which derivative of a scalar field nonminimally coupled to the vector torsion can realize a power-law or the de Sitter expansion of the universe and also can give rise to the ΛCDM model as it was shown in [52]. Later we studied the same model using a non-canonical scalar field (tachyon) instead of quintessence in the action [41].…”

“…It is shown in [25] that in the context of teleparallel gravity a scalar field by itself does not feel gravity but its four-derivative (which is a vector field) interacts with the vector part of the torsion. On the other hand, in the framework of teleparallelism, due to the presence of a total derivative in the relation between the curvature scalar and the torsion scalar the essential condition for the torsion scalar T to has its non-minimal coupling to a scalar field in a conformal manner is that a term of the form f (ϕ)∂ µ ϕ V µ has to be assumed in the action [52]. Also, it has been shown in Ref [53] that a Lagrangian which is invariant under the space-time coordinate transformations and conformal transformations and leads to teleparallel Lagrangian in the gauge where the scalar field is restricted to assume a constant value, includes a non-minimal coupling of the form g µν V ν ϕ (∂ µ ϕ).…”

Conformal transformations in modified teleparallel theories of gravity revisited

“…Such a term has also been considered several times, going back to [11], who considered a Brans-Dicke type coupling in the context of Møller's tetradic theory [12]. More recently such a coupling has also been considered in [14,15].…”

“…Now let us look at conformal transformations in the teleparallel framework. Under the conformal transformation (25), it is easy to see that the tetrad and the inverse tetrad must transform as [13,14,25] …”