Starobinsky inflation beyond the leading order

The Starobinsky model of cosmological inflation in four spacetime dimensions is reviewed with the emphasis on the 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.