Higgs inflation at the critical point (1403.6078v2)

Abstract: Higgs inflation can occur if the Standard Model (SM) is a self-consistent effective field theory up to inflationary scale. This leads to a lower bound on the Higgs boson mass, $M_h \geq M_{\text{crit}}$. If $M_h$ is more than a few hundreds of MeV above the critical value, the Higgs inflation predicts the universal values of inflationary indexes, $r\simeq 0.003$ and $n_s\simeq 0.97$, independently on the Standard Model parameters. We show that in the vicinity of the critical point $M_{\text{crit}}$ the inflationary indexes acquire an essential dependence on the mass of the top quark $m_t$ and $M_h$. In particular, the amplitude of the gravitational waves can exceed considerably the universal value.

Higgs Inflation at the Critical Point

The paper "Higgs inflation at the critical point" by Fedor Bezrukov and Mikhail Shaposhnikov explores a refined inflationary model where the Standard Model (SM) Higgs boson is postulated as the inflaton. The research aims to conceptualize the inflaton dynamics specifically in the vicinity of a critical mass of the Higgs boson, $M_{\text{crit}}$. Here, the authors delve into the intricate relationship between the Higgs boson mass and the inflationary parameters, namely, the scalar tilt $n_s$ and the tensor-to-scalar ratio $r$.

The model extends the conventional Higgs inflation scenario, which integrates the Higgs boson with a non-minimal coupling to gravity, to elucidate the universe's inflationary epoch. In such a model, the SM is considered a self-consistent effective field theory that safely scales up to the inflationary regime. A significant contribution of this work is the assessment of the mass relation $M_h \geq M_{\text{crit}}$ as a pivotal condition for Higgs inflation. Here, $M_h$ represents the Higgs boson mass, and the paper provides a formula to determine $M_{\text{crit}}$, which is dependent on the top Yukawa coupling and QCD coupling $\alpha_s$, incorporating the uncertainties due to quantum radiative corrections.

The paper presents a noteworthy conclusion that extends previous models by illustrating how, near the critical Higgs mass $M_{\text{crit}}$, inflationary indices $n_s$ and $r$ become significantly sensitive to the top quark mass $m_t$ and the Higgs mass $M_h$. This sensitivity translates into variability in predictions, where deviations from canonical SM predictions are indicative of conditions at or near the critical point. Such deviations could potentially manifest in observable cosmological parameters, implying that precise measurements of $n_s$ and $r$ can shed light on the fundamental nature of the Higgs boson and its interactions in the early universe.

Further, the research investigates the attenuation of the coupling constant $\xi$, typically necessary for the Higgs-inflation model, when the model operates at the critical point. A reduced value of $\xi$ implies lesser fine-tuning and an alleviated need for a theoretical UV completion of the SM below the Planck scale.

In terms of the practical ramifications, the findings suggest a pathway to probe the high-energy characteristics of the SM via cosmological observations. For example, specific values of $n_s$ and $r$ could retro-diagnose the parameters of the SM at inflationary scales, tying the dynamics of the early universe to particle physics phenomena. An exciting implication of this paper is that a significant discrepancy in the known values of inflationary indices could affirm the theoretical prospect of the Higgs boson operating at the critical point.

Finally, the paper carefully notes that if real-world cosmological observations support this model, it may steer future investigations in high-energy physics and cosmology. However, these inferences are contingent upon the assumption of the SM's validity extending to the Planck scale, inviting further scrutiny or exploration of potential physics beyond the SM.

In conclusion, this work provides a coherent theoretical framework underpinning Higgs inflation at the critical point, presenting a significant step towards synthesizing particle physics and cosmological paradigms, thereby enriching our theoretical toolkit to understand the early universe's inflationary phase.