  We study inflation for a quantum scalar electrodynamics model in curved
space-time and for higher-derivative quantum gravity (QG) coupled with scalar
electrodynamics. The corresponding renormalization-group (RG) improved
potential is evaluated for both theories in Jordan frame where non-minimal
scalar-gravitational coupling sector is explicitly kept. The role of one-loop
quantum corrections is investigated by showing how these corrections enter in
the expressions for the slow-roll parameters, the spectral index and the
tensor-to-scalar ratio and how they influence the bound of the Hubble parameter
at the beginning of the primordial acceleration. We demonstrate that the viable
inflation maybe successfully realized, so that it turns out to be consistent
with last Planck and BICEP2/Keck Array data.
