Higgs Inflation and Standard Model Criticality

Abstract

In this chapter, we investigate the possibility that the SM Higgs boson plays the role of an inflation in light of the discovery of the Higgs boson. In 2007, Bezurkov and Shaposhnikov first pointed out this possibility. The successful Higgs inflation is realized if the non-minimal coupling between the Higgs H and scalar curvature $\mathcal {R}$, $\xi |H|^2 \mathcal {R}$, is introduced. $\xi$ is the coupling constant, and very large value, $\xi \sim 10^5$, is required for successful inflation. However, the observation of the Higgs and determination of its mass changes the situation. As we have seen in Chap. 2, the Higgs self coupling and its beta function becomes zero at very high scale, which means that the Higgs potential is very flat around string/Planck scale. This opens up the new possibilities of the Higgs inflation, which we will present here. In Sect. 3.1, we present the general argument of the Higgs inflation above the SM cutoff $\Lambda$. In Sect. 3.2, we show that non-minimal coupling $\xi$ can be as small as $\mathcal {O}(10)$.