  In a recently proposed scenario for primordial inflation, where the Standard
Model (SM) Higgs boson plays a role of the inflation field, an effective field
theory (EFT) approach is the most convenient for working out the consequences
of breaking of perturbative unitarity, caused by the strong coupling of the
Higgs field to the Ricci scalar. The domain of validity of the EFT approach is
given by the ultraviolet (UV) cutoff, which, roughly speaking, should always
exceed the Hubble parameter in the course of inflation. On the other hand,
applying the trusted principles of quantum gravity to a local EFT demands that
it should only be used to describe states in a region larger than their
corresponding Schwarschild radius, manifesting thus a sort of UV/IR
correspondence. We consider both constraints on EFT, to ascertain which models
of the SM Higgs inflation are able to simultaneously comply with them. We also
show that if the gravitational coupling evolves with the scale factor, the
holographic constraint can be alleviated significantly with minimal set of
canonical assumptions, by forcing the said coupling to be asymptotically free.
