Infrared modified gravity with propagating torsion: Instability of torsionfull de Sitter-like solutions

Abstract

We continue the exploration of the consistency of a modified-gravity theory that generalizes General Relativity by including a dynamical torsion in addition to the dynamical metric. The six-parameter theory we consider was found to be consistent around arbitrary torsionless Einstein backgrounds, in spite of its containing a (notoriously delicate) massive spin-2 excitation. At zero bare cosmological constant, this theory was found to admit a self-accelerating solution whose exponential expansion is sustained by a non-zero torsion background. The scalar-type perturbations of the latter torsionfull self-accelerating solution were recently studied and were found to preserve the number of propagating scalar degrees of freedom, but to exhibit, for some values of the torsion background some exponential instabilities (of a rather mild type). Here, we study the tensor-type and vector-type perturbations of the torsionfull self-accelerating solution, and of its deformation by a non-zero bare cosmological constant. We find strong, "gradient" instabilities in the vector sector. No tuning of the parameters of the theory can kill these instabilities without creating instabilities in the other sectors. Further work is needed to see whether generic torsionfull backgrounds are prone to containing gradient instabilities, or if the instabilities we found are mainly due to the (generalized) self-accelerating nature of the special de Sitter backgrounds we considered.

Spherically symmetric solutions in torsion bigravity

“…Here, we essentially follow the notation of Refs. [21][22][23][24] (which we also used in our previous paper [41]). Latin indices i, j, k, .…”

“…Note that, because of the projections on the frame, the frame components of the F -type curvature depend algebraically on the vierbein e i µ , besides depending on A i jµ and its first derivatives. See Appendix A for more details on the definition of these objects, and for the relation with the notation used in our previous paper [41]. [An explicit form of the general field equations can also be found in the latter reference.…”

“…In this Appendix we recall some of the basic technicalities of the Einstein-Cartan(-Weyl-Sciama-Kibble) formalism (also called Poincaré gauge theory). We generally follow the notation of [21][22][23][24], and of the papers [25,26,[38][39][40][41], except for the notation used for the parameters entering into the action. We use a mostly plus signature and distinguish Lorentz-frame indices (i, j, k, .…”

“…Appendix B: Link with the notation used in [41] In our previous paper Ref. [41] we considered the more general action L = 3 2 α F [e, A, ∂A] + 3 2 α R[e, ∂e, ∂ 2 e] + c 2 (B1)…”

“…In particular, the fact that massive gravity is described in these models by a different Young tableau than the more familiar (symmetric tensor) models completely changes the various issues linked to nonlinear effects, and renders the study of their physical properties a priori interesting. Some of the results of previous work on such models [25,26,[38][39][40][41] has shown them to be remarkably healthy and robust around various backgrounds (though Ref. [41] found the presence of gradient instabilities around the self-accelerating torsionfull cosmological solution found in [38]; but these instabilities might be due to the endemic stability problems of self-accelerating cosmological universes rather than to the theory itself).…”