Abstract
The measured values of the Higgs and top quark masses imply that the Standard Model potential is very likely to be unstable at large Higgs values. This is particularly problematic during inflation, which sources large perturbations of the Higgs. The instability could be cured by a threshold effect induced by a scalar with a large vacuum expectation value and directly connected to the Standard Model through a Higgs portal coupling. However, we find that in a minimal model in which the scalar generates inflation, this mechanism does not stabilize the potential because the mass required for inflation is beyond the instability scale. This conclusion does not change if the Higgs has a direct weak coupling to the scalar curvature. On the other hand, if the potential is absolutely stable, successful inflation in agreement with current CMB data can occur along a valley of the potential with a Mexican hat profile. We revisit the stability conditions, independently of inflation, and clarify that the threshold effect cannot work if the Higgs portal coupling is too small. We also show that inflation in a false Higgs vacuum appearing radiatively for a tuned ratio of the Higgs and top masses leads to an amplitude of primordial gravitational waves that is far too high, ruling out this possibility.
Highlights
While most models of primordial inflation involve one or more scalars to drive the accelerated expansion of the universe, the Higgs boson is the only known elementary scalar that has been found in nature so far
This is motivated by the obvious requirement of reheating the universe at the end of inflation and by the role of the large quantum fluctuations that are induced on light fields during inflation
S, coupling to the Higgs through a portal can provide a stabilization mechanism via a tree-level threshold [28, 29], it is important to determine whether this scalar could drive inflation as well
Summary
While most models of primordial inflation involve one or more scalars to drive the accelerated expansion of the universe, the Higgs boson is the only known elementary scalar that has been found in nature so far. In models in which an inflaton coupled to the Higgs gets a large VEV, the interactions among the two may deform the potential energy valleys supporting inflation, causing them to reach into large values of the Higgs field and becoming sensitive to the destabilizing effect of the top quark. This effect could ruin the prospects for inflation itself, since the classical trajectories could be drawn towards the instability region, regardless of quantum fluctuations. Three appendices are provided: section A gives the two-loop RG equations that we use, section B reviews the matching of the relevant SM parameters to experimental measurements, and section C contains the details about the matching between the SM and SMS
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