Generalized Higgs inflation

TL;DR

The paper places Higgs inflation models within the most general single-field framework with second-order equations, generalized $G$-inflation, showing that four established Higgs-inflation variants and a newly proposed running Einstein inflation can be treated uniformly. It introduces key combinations $u( obreak obreak phi)$ and $v( obreak obreak phi)$ and derives generalized slow-roll dynamics via an effective potential $U( obreak phi)$ and a friction function $W$, enabling a compact description of background evolution. The perturbation analysis yields concise expressions for tensor and scalar power spectra ${\\cal P}_T$ and ${\cal P}_\zeta$, along with $n_T$, $n_s$, and $r$, and discusses non-Gaussianity across regimes, including potential enhancements when $c_s^2$ becomes large. This framework facilitates simultaneous parameter exploration of all five models and helps connect theoretical predictions to upcoming Planck and LHC data, while acknowledging stability concerns in the SM Higgs sector and the need for further investigation of RG running and higher-derivative effects.

Abstract

We study Higgs inflation in the context of generalized G-inflation, i.e. the most general single-field inflation model with second-order field equations. The four variants of Higgs inflation proposed so far in the literature can be accommodated at one time in our framework. We also propose yet another class of Higgs inflation, the running Einstein inflation model, that can naturally arise from the generalized G-inflation framework. As a result, five Higgs inflation models in all should be discussed on an equal footing. Concise formulas for primordial fluctuations in these generalized Higgs inflation models are provided, which will be helpful to determine which model is favored from the future experiments and observations such as the Large Hadron Collider and the Planck satellite.