On the Naturalness of Higgs Inflation (0903.0355v2)

Abstract: We critically examine the recent claim that the Standard Model Higgs boson ${\cal H}$ could drive inflation in agreement with observations if $|{\cal H}|^2$ has a strong coupling $\xi\sim 10^4$ to the Ricci curvature scalar. We first show that the effective theory approach upon which that claim is based ceases to be valid beyond a cutoff scale $\Lambda=m_p/\xi$, where $m_p$ is the reduced Planck mass. We then argue that knowing the Higgs potential profile for the field values relevant for inflation ($|{\cal H}|>m_p/\sqrt{\xi}\gg \Lambda$) requires knowledge of the ultraviolet completion of the SM beyond $\Lambda$. In absence of such microscopic theory, the extrapolation of the pure SM potential beyond $\Lambda$ is unwarranted and the scenario is akin to other ad-hoc inflaton potentials afflicted with significant fine-tuning. The appealing naturalness of this minimal proposal is therefore lost.

• The paper presents an analysis showing that a large nonminimal coupling (ξ ≈ 10) is required for Higgs inflation to meet inflationary constraints, which in turn demands significant fine-tuning.
• The study reveals that the effective cutoff (Λ = m_p/ξ) and UV sensitivity critically undermine the naturalness of the inflationary plateau.
• By applying Weyl transformations from the Jordan to the Einstein frame, the research exposes non-renormalizable operators that add complexity to the inflationary model.

Insights into the Naturalness of Higgs Inflation

The paper under review presents an analysis of the concept that the Standard Model Higgs boson could potentially serve as the driver of cosmic inflation through strong coupling to the Ricci curvature scalar. This notion suggests that the Higgs boson, with a coupling parameter $\xi$, can satisfy inflationary constraints if suitably large $\xi$ values around 10 are chosen. The paper provides a thorough examination of the effective theory approach used to support these claims while highlighting potential areas of fine-tuning and dubious naturalness.

Key Findings

1. Effective Theory Limitations: The researchers identify the effective cutoff of the considered Lagrangian as $\Lambda = m_p/\xi$, emphasizing that this is significantly below the energy scales relevant for the inflationary plateau. This observation suggests substantial fine-tuning is inherent in this model, contradicting its alleged naturalness.
2. Ultraviolet Sensitivity: The decay of the "natural" inflationary plateau, sensitive to operators above the cutoff scale, indicates the inevitable fine-tuning associated with Higgs inflation when relying on current UV theories. The paper draws parallels between Higgs inflation and ad-hoc inflaton potentials, showing significant susceptibility to UV physics.
3. Field Transformations: By employing a Weyl transformation, the effective Lagrangian is metamorphosed from a Jordan frame to an Einstein frame, thus unveiling a complex potential in terms of a canonical scalar field $\phi$. The transformation exposes new non-renormalizable operators of dimension six indicating hidden complexities even in its canonical form.
4. Radiative Corrections Influence: The paper stresses that radiative corrections render the potential tremendously fine-tuned, as the naive inflation scale hardly reflects a truly natural scenario. The analyses reveal that these corrections versatilely alter predictions depending on the form and influence of higher-order operators.

Theoretical and Practical Implications

From a theoretical standpoint, these results question the viability of using the Higgs boson as an inflaton within the framework of the Standard Model without additional assumptions or constraints. The detailed exposure of delicate tuning involved in achieving acceptable inflationary dynamics poses a significant challenge to the perceived simplicity of the Higgs inflation model.

Interesting practical implications arise from the exploration of this minimalistic inflation model. Further judgments on its viability potentially require extensions to the Standard Model or alternate routes such as a more profound understanding of strong Ricci coupling dynamics.

Future Directions

• Exploration Beyond the Standard Model: Future research could explore modifications to the Standard Model or additional symmetries that might stabilize inflationary characteristics beyond the established energy threshold, mitigating fine-tuning concerns.
• Deeper UV Completion Understanding: Enhancing the current understanding of potential UV completions can illuminate new pathways where the Higgs boson remains a credible inflaton without incurring infeasible fine-tuning.
• Experimental Validation: Attempt to formulate and validate predictions based on this model within the ambit of observable inflationary parameters, possibly guiding experimental physicists toward metrics that may confirm or falsify these mechanisms.

In summary, the assessment presented in this paper underscores the intricate balance and complexity involved in Higgs-driven inflation, offering valuable insights and steering ongoing discourse towards new conceptions of naturalness and cosmic inflation models.