  We present the effects of vector-like fermions (VLF) on the stability of the
Higgs electroweak vacuum, using the renormalization group improved Higgs
effective potential. We review the calculation of the one-loop beta-functions
of the standard model couplings, paying particular attention to the fermion
contributions. From this, we derive the VLF contributions to the
beta-functions. We also include the significant two-loop contributions to the
beta-functions. Using these beta-functions we determine the scale at which the
effective Higgs quartic-coupling becomes zero and goes negative, signaling
vacuum instability. We find that for certain VLF masses and Yukawa couplings,
the Higgs quartic stays positive for field values all the way up to the Planck
scale, implying that the meta-stable vacuum of the standard model can be
rendered absolutely stable if VLFs are present with certain parameters. For
other values of VLF parameters, the Higgs vacuum is metastable as in the
standard model. For cases where the vacuum is metastable, we compute the
probability of quantum tunneling from the false electroweak vacuum into a
deeper true vacuum in our Hubble volume by numerically solving for the bounce
configuration in Euclidean space-time and computing the bounce action for it.
We compare our numerical solution with the analytical approximation for the
bounce action commonly used in the literature and comment on when the latter
may be used.
