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2021

On the number of $e$-folds in the Jordan and Einstein frames

Racioppi, Antonio, Vasar, Martin

Understand

We investigate how inflationary predictions are affected by the difference in the number of $e$-folds between the Jordan and Einstein frames.

We study several test models in relation to a Jordan frame defined by the common Higgs-inflation-like non-minimal coupling to gravity and consider two different formulations of gravity: metric and Palatini.
We find that the difference is quite contained in case of a metric Jordan frame while can be quite remarkable in case of a Palatini Jordan frame.
We also discuss a way to overcome the discrepancy by introducing a frame invariant physical distance and a consequently frame invariant number of $e$-folds.