Cosmological Evolution of the Higgs Boson’s Vacuum Expectation Value

We point out that the expansion of the universe leads to a cosmological time evolution of the vacuum expectation of the Higgs boson. Within the standard model of particle physics, the cosmological time evolution of the vacuum expectation of the Higgs leads to a cosmological time evolution of the masses of the fermions and of the electroweak gauge bosons while the scale of Quantum Chromodynamics (QCD) remains constant. Precise measurements of the cosmological time evolution of μ = me/mp, where me and mp are respectively the electron and proton mass (which is essentially determined by the QCD scale), therefore provide a test of the standard models of particle physics and of cosmology. This ratio can be measured using modern atomic clocks. [email protected] The idea that physical constants could experience a cosmological time evolution has received much attention, see for example [1–13,16,17]. The most recent of these investigations were motivated by cosmological observations that some of the fundamental constants of nature may not be that constant after all, see e.g. [18]. In this work, we point out that the expansion of the universe leads to a cosmological time evolution of the vacuum expectation of the Higgs boson. Within the standard model of particle physics, the cosmological time evolution of the vacuum expectation of the Higgs boson leads to a cosmological time evolution of the masses of the fermions and of the electroweak gauge bosons while the scale of Quantum Chromodynamics (QCD) and thus the proton mass remain constant. Strictly speaking, quark masses also contribute to the proton mass and would lead to a small time dependence of the proton mass, but this is a tiny and thus negligible effect as the main contribution from the QCD scale to the proton mass remains constant. We show that precise measurements of the cosmological time evolution of μ = me/mp, where me and mp are respectively the electron and proton mass, therefore provide a test of the standard models of particle physics and of cosmology. The discovery of the Higgs boson at the Large Hadron Collider in 2012 with a mass of 125 GeV was an amazing confirmation of the standard model of particle physics. The standard model of cosmology ΛCDM which posits the existence of cold dark matter and of a cosmological constant is equivalently successful. The cosmological model assumes that the expansion of the universe is described by the Friedmann-Lemâıtre-Robertson-Walker (FLRW) metric ds = −dt +R(t) [ dr 1− kr2 + rdΩ ] (1) which corresponds to an homogeneous and isotropic universe. Here k is the curvature signature and R is the expansion factor, whose time change is given by the Friedmann equation H(t) = ( Ṙ R )2 = 8πG 3 ρtot − k R2 , (2) where the cosmological constant is included in the total energy density ρtot. The total energy density contains not only the dark energy but also dark matter and the visible matter. The value of the cosmological constant is such that our universe is currently undergoing a phase of accelerated expansion as the cosmological constant starts to dominate over all other forms of energy. In the standard model of particle physics, the Higgs boson is part of a SU(2)L doublet H which in the unitarity gauge takes the form H = 1/ √ 2(0, φ(~x, t) + v)> where v = 246 GeV is the vacuum expectation value of the Higgs field φ(~x, t). In flat space-time v is a constant,