On non-minimal coupling of the inflaton

TL;DR

This paper investigates the role of non-minimal coupling of the inflaton to gravity, revealing that such coupling cannot generally be removed by conformal transformations, with implications for inflation models like Higgs inflation.

Contribution

It provides a field-theoretic analysis showing the inherent non-removability of non-minimal coupling due to renormalizability and finiteness constraints, challenging common assumptions in inflationary model transformations.

Findings

Large non-minimal coupling $\xi$ helps match CMB data.

Small $\xi$ around 1/6 is favored by spectral index.

Non-minimal coupling cannot be eliminated by conformal transformations.

Abstract

The non-minimal coupling of the inflaton to gravity, $\xi R\phi^2$, is known to alleviate the smallness (fine-tuning) of the quartic coupling $\lambda$ in the chaotic inflation with $\phi^4$ potential. A large $\xi$ is required to obtain the correct CMB power spectrum while we find that a small value $\sim 1/6$ seems to be preferred from spectral index. There are issues related to conformal transformations, choice of frame and natural value(s) of $\xi$ for a given potential. We revisit some of these issues and invoke certain field theoretic arguments in order to address the same. A rather strong and general conclusion reached, based on the requirements of renormalizability and finiteness of specific matrix elements in a quantum theory, is that it is generically not possible to eliminate the non-minimal coupling by going from the Jordan to the Einstein frame via conformal transformations. We also comment on Higgs inflation.