On Inflation with Non-minimal Coupling
  A simple realization of inflation consists of adding the following operators
to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R,
with xi a large non-minimal coupling. Recently there has been much discussion
as to whether such theories make sense quantum mechanically and if the inflaton
phi can also be the Standard Model Higgs. In this note we answer these
questions. Firstly, for a single scalar phi, we show that the quantum field
theory is well behaved in the pure gravity and kinetic sectors, since the
quantum generated corrections are small. However, the theory likely breaks down
at ~ m_pl / xi due to scattering provided by the self-interacting potential
lambda phi^4. Secondly, we show that the theory changes for multiple scalars
phi with non-minimal coupling xi phi dot phi R, since this introduces
qualitatively new interactions which manifestly generate large quantum
corrections even in the gravity and kinetic sectors, spoiling the theory for
energies > m_pl / xi. Since the Higgs doublet of the Standard Model includes
the Higgs boson and 3 Goldstone bosons, it falls into the latter category and
therefore its validity is manifestly spoiled. We show that these conclusions
hold in both the Jordan and Einstein frames and describe an intuitive analogy
in the form of the pion Lagrangian. We also examine the recent claim that
curvature-squared inflation models fail quantum mechanically. Our work appears
to go beyond the recent discussions.
