Slow-Roll Inflation in the Jordan Frame

TL;DR

This paper develops slow-roll inflation conditions directly in the Jordan frame of scalar-tensor gravity theories, enabling analysis without transforming to the Einstein frame, and applies these to specific models comparing with observations.

Contribution

It formulates slow-roll conditions in the Jordan frame, providing a new method to analyze inflation models directly in that frame without transformation.

Findings

Derived simple equations for inflation observables in the Jordan frame.

Applied the framework to generalized induced gravity models.

Compared model predictions with latest observational data.

Abstract

Inflation models based on scalar-tensor theories of gravity are formulated in the Jordan frame but most often analysed in the Einstein frame. The transformation between the frames is not always desirable. In this work we formulate slow-roll conditions in the Jordan frame. This is achieved by comparing different background quantities and approximations on the same spatial slice in both frames. We use these approximations to derive simple equations that can be applied to compute inflation model observables in terms of Jordan frame quantities only. Finally, we apply some of the results to analyse generalised induced gravity models and compare them with the latest observations.