CTP Seminar
In the talk, we reconsider the dynamical systems approach to analyze inflationary universe in the Jordan frame models of scalar field nonminimally coupled to curvature, torsion, or nonmetricity. The adopted set of variables allows us to clearly distinguish between different asymptotic states in the phase space, including the kinetic and inflationary regimes. Inflation is realized as a heteroclinic trajectory originating either at infinity from a nonhyperbolic asymptotic de Sitter point or from a regular saddle de Sitter point. We also present a comprehensive picture of possible initial conditions leading to sufficient inflationary expansion and show their extent on the phase diagrams. In addition we comment on the correct slow roll conditions applicable in the Jordan frame and show how they approximate the leading inflationary “attractor solution”. 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. We conclude with remarks on how to construct a teleparallel analogue of Higgs inflation.