On non-minimal coupling of the inflaton

The non-minimal coupling of the inflaton to gravity, $ξRϕ^2$, is known to alleviate the smallness (fine-tuning) of the quartic coupling $λ$ in the chaotic inflation with $ϕ^4$ potential. A large $ξ$ 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 $ξ$ 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.

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