Can Horndeski theory be recast using teleparallel gravity?

Abstract

Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second-order field equations and after the GW170817 it has been severely constrained. Since this theory is very important in modified gravity, it is then worth studying possible similar theories starting from other frameworks. In this paper, we study the analog of Horndeski's theory in the Teleparallel Gravity framework where gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, teleparallel Horndeski contains the standard Horndeski gravity as a subcase and also contains many modified Teleparallel theories considered in the past, such as f (T ) gravity or teleparallel dark energy. Thus, due to the appearance of a new term in the Lagrangian, this theory can explain dark energy without a cosmological constant, may describe a crossing of the phantom barrier, explain inflation and also solve the tension for H0, making it a good candidate for a correct modified theory of gravity.

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.…”

Post-Newtonian limit of generalized scalar-torsion theories of gravity

“…The parameters and the gravitational constant will then depend on the spatial coordinates [27]. One may also consider scalar-torsion theories with more general couplings between the scalar field and the teleparallel geometry, such as the recently proposed teleparallel extension to Horndeski gravity [45] or theories obtained from disformal transformations [46], thus extending previous results on the curvature formulation of Horndeski gravity [47]. Furthermore it is interesting to analyze theories coupled to more than one massive or massless scalar field.…”

Parametrized post-Newtonian limit of general teleparallel gravity theories

“…Our work invites for numerous generalizations and extensions. In particular, one may consider more general theories, for example derived from a general constitutive relation [39], possibly including also parity-odd terms, or coupling to scalar fields [40][41][42][43], up to Horndeski-like teleparallel theories [44,45]. Further, taking inspiration from the socalled trinity of gravity [1], one may consider extensions to the symmetric teleparallel equivalent of gravity [46], and apply the parameterized post-Newtonian formalism to generalized theories based on the symmetric teleparallel geometry [47][48][49][50][51].…”