The Electroweak Horizon Problem

Spontaneously broken symmetries in particle physics may have producedseveral phase transitions in cosmology, e.g., at the GUT energy scale($\sim 10^{15}$ GeV), resulting in a quasi-de Sitter inflationary expansion,solving the background temperature horizon problem. This transition wouldhave occurred at $t\sim 10^{-36}-10^{-33}$ seconds, leading to a separationof the strong and electroweak forces. The discovery of the Higgs boson confirmsthat the Universe must have undergone another phase transition at theelectroweak (EWPT) scale $159.5\pm1.5$ GeV, about $10^{-11}$ seconds later,when fermions and the $W^\pm$ and $Z^0$ bosons gained mass, leading to theseparation of the electric and weak forces. But today the vacuum expectationvalue ({\it vev}) of the Higgs field appears to be uniform throughout thevisible Universe, a region much larger than causally-connected volumesat the EWPT. The discovery of the Higgs boson thus creates another serioushorizon problem for $\Lambda$CDM, for which there is currently no establishedtheoretical resolution. The EWPT was a smooth crossover, however,so previously disconnected electroweak vacuua might have homogenized as theygradually came into causal contact. But using the known Higgs potential and{\it vev}, we estimate that this process would have taken longer than the ageof the Universe, so it probably could not have mitigated the emergence ofdifferent standard model parameters across the sky. The EWPT horizon problemthus argues against the expansion history of the early Universe predicted bystandard cosmology.