Inflation and the semiclassical dynamics of a conformal scalar field
G. L. Alberghi, C. Appignani, R. Casadio, F. Sbis\'a, A. Tronconi
TL;DR
This paper derives the semiclassical evolution of a conformally coupled scalar field in de Sitter space, revealing that quantum gravitational corrections do not affect the dispersion relation up to second order in the Planck length.
Contribution
It introduces a novel derivation of scalar field dynamics in de Sitter space showing no significant quantum gravitational corrections to dispersion relations for conformally coupled fields.
Findings
Quantum gravitational corrections are independent of scalar mode momentum.
No relevant modifications to the dispersion relation up to second order in Planck length.
Distinct behavior compared to minimally coupled scalar fields.
Abstract
We derive the semiclassical evolution of massless conformally coupled scalar matter in the de Sitter space-time from the Born-Oppenheimer reduction of the Wheeler-DeWitt equation. We find a remarkable difference with respect to the minimally coupled case: the effect of the quantum gravitational corrections do not depend on the momentum of the scalar mode up to second order in the Planck length and, therefore, there are no relevant corrections to the dispersion relation.
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