Upon expressing the Higgs potential in terms of the field H0, we find
The first term in V is a constant energy density which can be interpreted as a contribution to the vacuum energy,
Although the parameter
is unknown, we can get a feeling for the scale of the Higgs vacuum energy by supposing
. The Higgs vacuum energy contributes to the cosmological constant of general relativity an amount
. Such a term would have a remarkable effect on the geometry of spacetime, manifesting itself over a distance scale of
! The present limit on the cosmological constant is
(RPP 1990). There must then be some important and non-trivial physics which forces the suppression or cancellation of the vacuum energy by roughly fifty orders of magnitude.
(J. Donoghue, E. Golowich, B. Holstein, Dynamics of the Standard Model, Cambridge U.P 1992, p.416)
