Metastable Electroweak Vacuum: Implications for Inflation

Abstract

Within the Standard Model, the current Higgs and top quark data favor metastability of the electroweak vacuum, although the uncertainties are still significant. The true vacuum is many orders of magnitude deeper than ours and the barrier separating the two is tiny compared to the depth of the well. This raises a cosmological question: how did the Higgs field get trapped in the shallow minimum and why did it stay there during inflation? The Higgs initial conditions before inflation must be fine--tuned to about one part in 10^8 in order for the Higgs field to end up in the right vacuum. In this note, we show that these problems can be resolved if there is a small positive coupling between the Higgs and the inflaton.

Figures (2)

• Figure 1: A $schematic$ view of the Higgs potential ($\Lambda \sim 10^{10}$ GeV $\ll { M_{\rm Pl}}$).
• Figure 2: Evolution of the Higgs field (solid) and the inflaton (dashed) as a function of the number of $e$--folds $N_e$. The log--scale plot shows the absolute value of $h$ which goes through zero during each oscillation, but gets cut off at a finite value for numerical reasons. The initial values are $\phi_0=32$, $h_0=0.1$ and $\xi=10^{-6}$.