The Higgs field as an inflaton

TL;DR

The paper investigates whether the Standard Model Higgs field, non-minimally coupled to gravity, can drive cosmic inflation consistent with Planck CMB measurements without introducing new particles. It develops the Einstein-frame formulation, derives slow-roll predictions, and analyzes post-inflationary reheating, while addressing unitarity, quantization ambiguities, and loop corrections. It shows that HI can yield CMB observables in excellent agreement with data in certain parameter regimes, but its UV completeness remains unresolved and depends on the assumed completion of high-energy physics. The work also surveys variations and UV completions, highlighting how additional scalars or derivative couplings can modify predictions and unitarity, with future data on the Higgs mass, top mass, and B-mode polarization as crucial tests. Overall, HI offers an economical inflationary scenario tightly linked to Higgs physics, awaiting a full UV completion and further experimental scrutiny.

Abstract

The Higgs field of the pure Standard Model can lead to the inflationary expansion of the early Universe if it is non-minimally coupled to gravity. The model predicts Cosmic Microwave Background (CMB) parameters in perfect agreement with the current observations and has implications for the Higgs boson mass. We review the model, its predictions, problems arising with its quantization and some closely related models.

Figures (4)

• Figure 1: Left: dependence of $\chi$ (the Einstein frame Higgs field) on $h$ (the Jordan frame Higgs field), logarithmic scale. Right: effective potential in the Einstein frame. The insert magnification is not to scale.
• Figure 2: Predictions (at a tree level, which coincides with the radiatively corrected results in the scale-invariant quantization, choice I of section \ref{['sec:mass']}) from the inflationary models Bezrukov:2007epBezrukov:2011gpBezrukov:2013fca and the Planck satellite Ade:2013uln observed bounds.
• Figure 3: Schematic depiction of the cut-offs (scales of violation of the tree-level unitarity) in the Jordan (left) and Einstein (right) frames for different sectors of the theory. $\Lambda_\text{g-s}$ corresponds to the inflaton (scalar sector) scatterings, $\Lambda_\text{gauge}$ to the gauge boson scattering and $\Lambda_\text{Planck}$ is the graviton scattering.
• Figure 4: The predictions for the spectral index $n_s$ (left) and tensor-to-scalar ratio $r$ (right) with radiative corrections Bezrukov:2009db. Note that for the scale-invariant normalization prescription I, the predictions coincide with the tree level, while in the prescription II, the difference becomes more significant at low values of the Higgs mass.