Global portraits of nonminimal teleparallel inflation

TL;DR

This paper analyzes the global phase space of inflationary models in teleparallel gravity with a nonminimally coupled scalar field, revealing how different couplings affect inflationary dynamics and viability.

Contribution

It introduces a heuristic method to identify fixed points in nonminimally coupled teleparallel inflation models and compares their phase portraits to scalar-curvature models.

Findings

Inflation occurs only at small nonminimal coupling for quadratic models.

Quartic potential models are generally not viable for inflation in this framework.

The phase portraits differ qualitatively from scalar-curvature counterparts.

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.