  The Starobinsky model of cosmological inflation in four spacetime dimensions
is reviewed with the emphasis on impact of quantum gravity corrections. As a
specific example of the quantum corrections, the Grisaru-Zanon quartic
curvature terms in the gravitational effective action of closed superstrings
are chosen. Those quartic curvature terms are compared to the Bel-Robinson
tensor squared in a flat Friedman universe, and the upper bound on the
effective string coupling constant is found by demanding unitarity (causality)
and the absence of ghosts. It is found that the quantum corrections to the
observables (tilts) of the cosmic microwave background radiation in the
Starobinsky inflation may be of the same order of magnitude as the
next-to-next-to-next classical contributions in the Starobinsky model with
respect to the inverse powers of the e-folding number at the horizon crossing.
