  To find out the possible scenarios for quantum gravity consistent with the
observed universe, we numerically investigate the non-perturbative
renormalization group equations of a general quadratic gravity theory recently
derived by Sen, Wetterich and Yamada (\textit{JHEP} 03 (2022) 130). As boundary
conditions, we impose consistency with the Hubble scale and the laboratory
scale experiments, and the Starobinsky model of inflation. We find two kinds of
trajectories which go to different regime at the trans-Planckian scales: i) a
trajectory which flows to the asymptotically free regime, and ii) a trajectory
which flows to the asymptotically safe regime. To determine the early-time
cosmological scenario, an additional observational data from beyond the
homogeneous and isotropic space-time is necessary.
