The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling

TL;DR

This paper demonstrates that conformal transformations simplify calculations in non-minimal single field inflation models, showing that cosmological correlation functions are frame-independent and invariant under conformal changes.

Contribution

It extends the conformal transformation method to general single field inflation models with non-minimal coupling, simplifying perturbation calculations to all orders.

Findings

Perturbation variables are conformally invariant to all orders.

Quantization in Jordan and Einstein frames are equivalent.

N-point correlation functions are independent of the conformal frame.

Abstract

The method of a conformal transformation is applied to a general class of single field inflation models with non-minimal coupling to gravity and non-standard kinetic terms, in order to reduce the cosmological perturbative calculation to the conventional minimal coupling case to all orders in perturbation theory. Our analysis is made simple by the fact that all perturbation variables in the comoving gauge are conformally invariant to all orders. The structure of the vacuum, on which cosmological correlation functions are evaluated, is also discussed. We show how quantization in the Jordan frame for non-minimally coupled inflation models can be equivalently implemented in the Einstein frame. It is thereafter argued that the general N-point cosmological correlation functions (of the curvature perturbation) are independent of the conformal frame.