The Standard Model scalar potential contains a minimum at the Electroweak
scale, responsible for the masses of the weak gauge bosons
through the Higgs mechanism. However, if the Electroweak minimum is
only a local minimum, and there exists a global minimum at a higher
energy in the Higgs potential, then in a su ciently old universe we would
expect the vacuum expectation value to be at the global minimum. The
absence of a global minimum at higher energy is related to the condition
that the Higgs self coupling is greater than or equal to zero for all energies.
For any model that fails this, we expect new physics to enter before
the energy at which the coupling becomes negative. We developed tools
to automate the derivation of beta functions for renormalisable gauge
theories, and used these to carry out evolution of the renormalisation
group equations for the Standard Model and three extensions to the
Standard Model | the Standard Model with a fourth generation, the
Standard Model with right-handed neutrinos and a Left-Right Symmetric
Model. We conclude that of these four models, the Standard Model
is the only one in which all the couplings remain perturbative, and in
which the Electroweak minimum is a global minimum