  In the standard model the (Brout-Englert-)Higgs quartic coupling becomes
negative at high energies rendering our current electroweak vacuum metastable,
but with an instability timescale much longer than the age of the Current
Universe. During cosmological Inflation, unless there is a non-minimal coupling
to gravity, the Higgs field is pushed away from the origin of its potential due
to quantum fluctuations. It is therefore a mystery how we have remained in our
current vacuum if we went through such a period of Inflation. In this work we
study the effect of top quarks created gravitationally during Inflation and
their effect upon the Higgs potential using only General Relativity with
minimal couplings and Standard Model particle physics. We show how the
evolution of the Higgs field during Inflation is modified coming to the
conclusion that this effect is non negligible for scales of Inflation close to
or larger than the stability scale but small for scales where the Higgs is
stable. Also, we briefly discuss the effect of other fermions to the Higgs
instability.
