Higgs Inflation and the Electroweak Gauge Sector

Abstract

We introduce a method that allows the Higgs to be the inflaton. The Higgs is considered as a pseudo-Nambu-Goldstone (pNG) boson of a global coset symmetry $G/H$, which is spontaneously breaks at an energy scale $\sim 4\pi f$. A suitable $SU\left(2\right)\subset G$ Chern−Simons (CS) interaction is given to it, with $\beta$ representing the dimensionless CS coupling strength and $f$ an $SU\left(2\right)$ decay constant. As a result, slow-roll inflation occurs via $SU\left(2\right)$-induced friction down a steep sinusoidal potential. To obey electroweak $SU{\left(2\right)}_L\times U{\left(1\right)}_Y$ symmetry, the lowest-order CS interaction is required to be quadratic in the Higgs, with the coupling strength $\propto {\beta }^2/f^2$. Higher-order interaction terms keep the full Lagrangian nearly invariant under the approximate pNG shift symmetry. Employing the simplest symmetry coset $SU\left(5\right)/SO\left(5\right)$, $N$ $e$-folds of inflation occur when $N\approx 60{\left(g,/,0.64\right)}^2{\left(\beta ,/,\left(3,\times ,{10}^6\right)\right)}^{8/3}{\left(f,/,\left(5,\times ,{10}^{11},,\mathrm{GeV}\right)\right)}^{2/3}$. Successfully explaining inflation necessitates small values of the decay constant, $f\lesssim 5\times {10}^{11}\mathrm{GeV}$; this in turn requires large $\beta$, which is ruled out by electric dipole measurements. Although the electroweak hierarchy problem while achieving successful inflation, the real benefit is found in providing a different path to identifying the Higgs as the inflaton, outside the standard modified-gravity framework.