On inflation with non-minimal coupling

Abstract

A simple realization of inflation consists of adding the following operators to the Einstein-Hilbert action: (∂ϕ)2, λϕ4, and ξϕ2R, with ξ a large non-minimal coupling. Recently there has been much discussion as to whether such theories make sense quantum mechanically and if the inflaton ϕ can also be the Standard Model Higgs. In this work we answer these questions. Firstly, for a single scalar ϕ, 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 ~mPl/ξ due to scattering provided by the self-interacting potential λϕ4. Secondly, we show that the theory changes for multiple scalars $ \overrightarrow \phi $ with non-minimal coupling $ \xi \overrightarrow \phi \cdot \overrightarrow \phi \mathcal{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 ≳ mPl/ξ. 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.