  We investigate the compatibility of cosmological constraints on inflation and
the cosmological constant with the asymptotic safety scenario of quantum
gravity. The effective action is taken to be of $f(R)$ form, truncated to
second order. The flow generated by the Functional Renormalisation Group
Equation is analysed and it is found to allow for trajectories that are
compatible with the observational constraints on the parameters of the action,
both at early and late cosmological times. In particular, the gravitational
effective dynamics generated in the trans-Planckian regime flows to Starobinsky
inflation at early times and to standard Einstein Gravity with a cosmological
constant at late times. Moreover, the cosmological constant acquires an energy
dependence at $10^{-2}$ eV, increasing from its current value of $10^{-66}
\,\text{eV}^{2}$ on Hubble scale to a value of $10^{30}\, \text{eV}^{2}$ at
inflation scale.
