Comment on Higgs Inflation and Naturalness

TL;DR

This paper critically examines claims about unitarity in Higgs inflation, demonstrating that unitarity issues persist in both Einstein and Jordan frames due to non-minimal couplings, challenging previous assertions of their resolution.

Contribution

It provides a detailed analysis showing that unitarity problems in Higgs inflation cannot be avoided by simple field redefinitions or gauge choices, clarifying the nature of these issues.

Findings

Unitarity problems arise from non-minimal Higgs self-couplings in covariant gauges.

Unitarity issues also stem from Higgs-gauge couplings in unitary gauge.

Previous claims of unitarity above the cutoff are challenged by explicit calculations.

Abstract

We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.