Abstract
In the standard model the (Brout-Englert-)Higgs quartic coupling becomes negative at high energies rendering our current electroweak vacuum metastable, but with an instability timescale much longer than the age of the Current Universe. During cosmological Inflation, unless there is a non-minimal coupling to gravity, the Higgs field is pushed away from the origin of its potential due to quantum fluctuations. It is therefore a mystery how we have remained in our current vacuum if we went through such a period of Inflation. In this work we study the effect of top quarks created gravitationally during Inflation and their effect upon the Higgs potential using only General Relativity with minimal couplings and Standard Model particle physics. We show how the evolution of the Higgs field during Inflation is modified coming to the conclusion that this effect is non negligible for scales of Inflation close to or larger than the stability scale but small for scales where the Higgs is stable. Also, we briefly discuss the effect of other fermions to the Higgs instability.
Highlights
The measurement of the actual Higgs and the top quark masses at the LHC and other colliders [1,2,3] leads to an interesting effect when one calculates their renormalization group running in that the quartic Higgs self-interaction coupling λ becomes negative above around 1010 GeV [4,5,6,7]
The implication of this is clear: in the absence of physics beyond the Standard Model affecting the running of the coupling constants, our current electroweak vacuum favors a metastable solution over an absolute stable vacuum [9,10,11,12,13,14]
With only Standard Model particle physics, the Higgs field h seems to become unstable at renormalization scale μ > 1010 GeV, and from the nondetection of primordial tensor perturbations we know that during inflation H < 1013 GeV
Summary
The measurement of the actual Higgs and the top quark masses at the LHC and other colliders [1,2,3] leads to an interesting effect when one calculates their renormalization group running in that the quartic Higgs self-interaction coupling λ becomes negative above around 1010 GeV [4,5,6,7] This high energy scale cannot be probed at current colliders but is much smaller than the Planck mass and is in a region where all the couplings remain perturbative, so there is no reason not to take this extrapolation seriously.
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