Comment on Higgs Inflation and Naturalness

TL;DR

This paper analyzes the unitarity of Higgs inflation with a large non-minimal coupling in both Jordan and Einstein frames, using covariant and unitary gauges. It shows that unitarity violations occur at the cutoff Λ = M_p/ξ due to non-minimal Higgs interactions and curved field-space, with high-energy amplitudes scaling as A(E) ~ (E/Λ)^2. These results reinforce prior power-counting arguments and imply the semiclassical effective field theory breaks down near inflationary scales, necessitating new high-energy physics to justify the inflationary scenario. The authors challenge claims that Einstein-frame analyses avoid these issues, and they discuss background-dependence considerations and subsequent responses from the community.

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.

Figures (1)

• Figure 1: Scalar scattering at high energies that leads to unitarity violation at the scale $\sim \Lambda$ in the Jordan frame.