  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.
