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The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced Einstein-Hilbert action. Our findings reveal that, due to the distinctive nature of gravity, the anomalous dimension η of the Newton's constant cannot be constrained to have one single value: the ultraviolet critical manifold is characterized by a line of fixed points (g ⁎ (η) , λ ⁎ (η)) , with a discrete (infinite) set of eigenoperators associated to each fixed point. More specifically, we find three ranges of η corresponding to different properties of both fixed points and eigenoperators and, in particular, for the range η < η c ≈ 0.96 the ultraviolet critical manifolds has finite dimensionality. [ABSTRACT FROM AUTHOR]

Asymptotic safety, based on a non-Gaussian fixed point of the gravitational renormalization group flow, provides an elegant mechanism for completing the gravitational force at sub-Planckian scales. At high energies, the fixed point controls the scaling of couplings such that unphysical divergences are absent, while the emergence of classical low-energy physics is linked to a crossover between two renormalization group fixed points. These features make asymptotic safety an attractive framework for the building of a cosmological model. The resulting scenarios may naturally give rise to a quantum-gravity-driven inflationary phase in the very early universe and an almost scale-free fluctuation spectrum. Moreover, effective descriptions arising from an improvement of the renormalization group permit a direct comparison to cosmological observations as, e.g., Planck data. [ABSTRACT FROM AUTHOR]

We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability-induced renormalization triggered by the low-energy quantum fluctuations in a Universe with a positive cosmological constant. We use the dynamical systems approach to study the qualitative behavior of the Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize 'two regimes' dark energy phases, where an unstable early phase of power-law evolution of the scale factor is followed by an accelerated expansion era at late times. [ABSTRACT FROM AUTHOR]

The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector. [ABSTRACT FROM AUTHOR]

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling. [ABSTRACT FROM AUTHOR]