# Constraints on non-minimal coupling from quantum cosmology

## TL;DR

This paper explores how quantum cosmology constrains the non-minimal coupling parameter of a scalar field in a de Sitter universe, revealing unexpected restrictions based on regularity conditions of quantum states.

## Contribution

It demonstrates that quantum state regularity imposes constraints on the non-minimal coupling parameter, a novel insight in quantum cosmology with non-minimally coupled fields.

## Key findings

- Regularity conditions restrict the allowed values of the coupling parameter ξ.
- Constraints depend on the combination m^2 + ξ R, not on ξ alone.
- The result is surprising given the field dynamics depend only on m^2 + ξ R.

## Abstract

Quantum cosmology is investigated in a de Sitter minisuperspace model with a quantized scalar field non-minimally coupled to curvature. Quantum states of the scalar field must satisfy the regularity condition, which requires that the probability of field fluctuations should not increase with their amplitude. We show that this condition imposes constraints on the allowed values of the curvature coupling parameter $\xi$. This is a surprising result, since the field dynamics depends only on the combination $m^2+\xi R$, where $m$ is the field mass and $R = \mathrm{const}$ is the curvature, and does not depend on $\xi$ separately.