Dynamics of Non-minimally Coupled Scalar Fields in the Jordan Frame

TL;DR

This paper introduces a method to analyze the dynamics of non-minimally coupled scalar fields directly in the Jordan frame, enabling studies of complex early universe scenarios without transforming to the Einstein frame.

Contribution

We develop an algorithm for solving scalar field dynamics in the Jordan frame, accommodating multiple fields and non-linear effects, which was previously limited to the Einstein frame.

Findings

Applied to geometric preheating with a non-minimally coupled scalar.

Demonstrated the method's ability to handle inhomogeneous and non-linear dynamics.

Provided insights into the equivalence of Jordan and Einstein frames at the quantum level.

Abstract

The presence of scalar fields with non-minimal gravitational interactions of the form $\xi |\phi|^2 R$ may have important implications for the physics of the early universe. While many studies solve the dynamics of non-minimally coupled scalars in the Einstein frame, where gravity is simply described by the Einstein-Hilbert action, we instead propose a procedure to solve the dynamics directly in the original Jordan frame where the non-minimal couplings are maintained explicitly. Our algorithm can be applied to scenarios that include minimally coupled fields and an arbitrary number of non-minimally coupled scalars, with the expansion of the universe sourced by all fields present. This includes situations when the dynamics become fully inhomogeneous, fully non-linear (due to e.g.~backreaction or mode rescattering effects), and/or when the expansion of the universe is dominated by non-minimally coupled species. As an example, we study geometric preheating with a non-minimally coupled scalar spectator field when the inflaton oscillates following the end of inflation. In the future, our technique may be used to shed light on aspects of the equivalence of the Jordan and Einstein frames at the quantum level.