Hamiltonian Analysis of Asymptotically Safe Gravity

TL;DR

This paper develops a Hamiltonian formalism for scale-dependent gravity theories inspired by Asymptotic Safety, revealing potential bouncing and emergent universe solutions within a constrained dynamical framework.

Contribution

It introduces a Hamiltonian analysis of a renormalization-group scale dependent Einstein-Hilbert action, exploring its constraint structure and cosmological implications.

Findings

The Dirac constraint algebra can be closed in certain cases.

RG-improved Friedmann equations admit bouncing universe solutions.

The framework applies to flat and negatively curved universes.

Abstract

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.