Global portraits of nonminimal inflation

TL;DR

This paper uses a dynamical systems approach to analyze inflation in nonminimally coupled scalar field models within the Jordan frame, providing a detailed phase space analysis and initial conditions for inflation.

Contribution

It offers a comprehensive phase space analysis of nonminimal inflation models, distinguishing asymptotic states and exploring initial conditions for inflation in the Jordan frame.

Findings

Inflationary trajectories originate from specific asymptotic points in phase space.

Increasing nonminimal coupling affects the range of initial conditions for inflation.

The slow roll approximation aligns with the attractor solutions in the phase space.

Abstract

We reconsider the dynamical systems approach to analyze inflationary universe in the Jordan frame models of scalar field nonminimally coupled to curvature. 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 slow roll conditions applicable in the Jordan frame and show how they approximate the leading inflationary "attractor solution". As particular examples we portrait quadratic and quartic potential models and note that increasing the nonminimal coupling diminishes the range of good initial conditions in the quadratic case, but enlarges is in the quartic case.