Global portraits of nonminimal teleparallel inflation

Abstract

We construct the global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed points, including the kinetic and inflationary regimes. The key role in the description of inflation is played by the heteroclinic orbits which run from the asymptotic saddle points to the late time attractor point and are approximated by nonminimal slow roll conditions. To seek the asymptotic fixed points we outline a heuristic method in terms of the "effective potential" and "effective mass", which can be applied for any nonminimally coupled theories. As particular examples we study positive quadratic nonminimal couplings with quadratic and quartic potentials, and note how the portraits differ qualitatively from the known scalar-curvature counterparts. For quadratic models inflation can only occur at small nonminimal coupling to torsion, as for larger coupling the asymptotic de Sitter saddle point disappears from the physical phase space. Teleparallel models with quartic potentials are not viable for inflation at all, since for small nonminimal coupling the asymptotic saddle point exhibits weaker than exponential expansion, and for larger coupling disappears too.

Teleparallel Gravity: From Theory to Cosmology

“…An interesting recent work on the topic is Ref. [629] where inflation is explored through a nonminimally coupled scalar field in f (T ) gravity [440] (see Sec. 5.8) in the same way that previous works have approach the same setting in f ( • R) gravity [267,315].…”

Reconstructing inflation in scalar-torsion $f(T,ϕ)$ gravity

“…These generalized scalar-torsion f (T, φ ) gravity theories can also be seen as the torsion-based analogue of the so-called generalised f (R, φ ) gravity theories [25]. This general action includes f (T ) gravity with scalar field [33,34,35,36], non-minimally coupled scalar-torsion gravity [37,38,39,40,41,42], and its extensions by including a non-linear scalar-torsion coupling [43]. A non-linear coupling between matter and gravity has been first studied in the context of curvature-based models in Refs.…”