Ghost and Laplacian instabilities in teleparallel Horndeski gravity

Abstract

Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Teleparallel gravity is based on the tetrad formalism. This turns out to result in a more general formalism of Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide range of models coming from ghost and Laplacian instabilities. The aim is to limit pathological branches of the theory by fundamental considerations. It is possible to conclude that a very large class of models results physically viable.

Cosmological perturbations in the teleparallel analog of Horndeski gravity

“…There has also been initial work on the stability of the theory with a particular focus on theoretical conditions that can be derived from Minkowski space as described ref. [58]. It is thus critical to analyse in a concrete way the full cosmology of this new teleparallel analogue of Horndeski gravity.…”

“…where capital Latin indices indicate components at the Lorentz spacetime, while small ones, the associated 3 dimensional spatial part. For greater details one can check [30,58].…”

Quartic Horndeski-Cartan theories: a review on the stability of nonsingular cosmologies

“…Besides a handful of special assumptions to avoid the instabilities in Horndeski theory such as "asymptotically strong gravity" or very specific models [11,[15][16][17], the alternative of Horndeski theory on spacetimes with torsion has been recently analyzed in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In particular, it has been shown that in Horndeski-Cartan gravity (considering torsion in the second order, metric formalism), a similar No-Go theorem also holds (in up to the quartic case ) [19]: namely, the alltime sub/luminality, stability and nonsingularity of an spatially flat FLRW cosmology are mutually inconsistent, up to a few special cases.…”

“…This amounts to introduce torsion in the second order formalism, because the equations for the metric remain of second order. Other approaches in the context of Horndeski have been recently analyzed in[20][21][22][23][24][25][26][27][28][29][30][31][32][33] …”