On Inflation with Non-minimal Coupling

TL;DR

This paper investigates the quantum consistency of inflation models with non-minimal coupling, showing that single scalar theories are well-behaved up to a certain scale, but multiple scalars like the Standard Model Higgs introduce problematic quantum corrections.

Contribution

It provides a detailed analysis of the quantum behavior of non-minimally coupled inflation models, especially highlighting issues with multiple scalars such as the Higgs doublet.

Findings

Single scalar theories are quantum mechanically consistent below ~ m_pl / xi.

Multiple scalars with non-minimal coupling generate large quantum corrections.

The Standard Model Higgs field's validity as an inflaton is compromised at high energies.

Abstract

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.