Hamiltonian Analysis of Asymptotically Safe Gravity
  Recent results based on renormalization group approaches to Quantum Gravity
suggest that the Newton's and cosmological constants should be treated as
dynamical variables whose evolution depend on the characteristic energy scale
of the system. An open question is how to embed this modified Einstein's theory
in the Dirac constrained dynamics. In this work, the Hamiltonian formalism for
a renormalization-group scale dependent Einstein-Hilbert action is discussed
paying particular attention to Dirac's constraint analysis. It is shown that
the algebra of the Dirac's constraints, in some cases, is closed. Applications
to the physics of the Early Universe are explicitly discussed assuming the
framework of Asymptotic Safety. In particular, it is shown that in the
minisuperspace with FLRW metric, RG-improved Friedmann equations have bouncing
and emergent Universes solutions also for flat and negative curvature.
