HIGGS INFLATION AND THE COSMOLOGICAL CONSTANT

We discuss the impact of the Higgs discovery and its revealing a very peculiar value for the Higgs mass. It turns out that the Higgs not only induces the masses of all SM particles, the Higgs, given its special mass value, is the natural candidate for the inflaton and in fact is ruling the evolution of the early universe, by providing the necessary dark energy which remains the dominant energy density. In a previous paper I have shown that running couplings not only allow us to extrapolate SM physics up to the Planck scale, but equally important they are triggering the Higgs mechanism when the universe cools down to lower temperatures. This is possible by the fact that the bare mass term in the Higgs potential changes sign at about μ0 ≃ 1.4× 10 16 GeV and in the symmetric phase is enhanced by quadratic terms in the Planck mass. Such a huge Higgs mass term is able to play a key role in triggering inflation in the early universe. In this article we extend our previous investigation by working out the details of a Higgs inflation scenario. We show how different terms contributing to the Higgs Lagrangian are affecting inflation. Given the SM and its extrapolation to scales μ > μ0 we find a calculable cosmological constant V (0) which is weakly scale dependent and actually remains large during inflation. This is different to the Higgs fluctuation field dependent ∆V (φ), which decays exponentially during inflation, and actually would not provide a sufficient amount of inflation to solve the CMB horizon problem. The fluctuation field has a different effective mass which shifts the bare Higgs transition point to a lower value μ′0 ≃ 7.7 × 10 14 GeV . We also show that for SM inflation standard slow-roll inflation criteria are obsolete. Miraculously, the huge difference between bare and renormalized cosmological constant is nullified either by the running of the SM couplings or by vacuum rearrangement somewhat before the Higgs phase transition takes place. This solves the notorious cosmological constant problem. Like in the case of the standard hierarchy problem concerning the quadratic divergences, also the quartically divergent vacuum energy exhibits a coefficient function which exhibits a zero very close to the zero of the quadratic coefficient function. While the Higgs today is only talking very weakly to the rest of the world, in the early universe it was all-dominating and shaping the universe to look as we see it today. The role of the Higgs in reheating and baryogenesis is emphasized. SM inflation implies reheating by production of top–anti-top pairs predominantly.