Nonlocal quantum gravity and the size of the universe

Abstract

Motivated by the conjecture that the cosmological constant problem is solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a class of nonlocal effective actions. They consist of the Einstein-Hilbert term and a general nonlinear function F k (V ) of the Euclidean spacetime volume V . For the V + V ln V -invariant the renormalization group running enormously suppresses the value of the renormalized curvature which results from Planck-size parameters specified at the Planck scale. One obtains very large, i.e., almost flat universes without finetuning the cosmological constant. A critical infrared fixed point is found where gravity is scale invariant.

Asymptotic Safety, Fractals, and Cosmology

“…We shall again approximate the latter by the Einstein-Hilbert truncation (16). The corresponding effective field equation is given by (26).…”

Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity

“…[48] the simple choice k ∝ 1/t can be justified on the ground that, if there are no other scales in the system when the Universe had age t, fluctuations with frequency greater than 1/t may not have played any role as yet, and the running must be stopped at k ∝ 1/t. On the other hand, recent works [38][39][40] have argued that the Hubble parameter defined in Eq. (3.3) is a physically meaningful cutoff as it measures the curvature of the spacetime, and it also reproduces the 1/t cutoff for any power-law dependence of ℓ(t) in Eq.(3.2).…”

“…The two approaches discussed above are obviously related, at least in some limit. In the case of Robertson-Walker spaces it will be shown that due to the very high degree of symmetry of the spacetime, the time-scale defined by "Hubble parameter" behaves essentially like the characteristic time scale associated to the relevant curvature invariants [38][39][40]. In the case of spherically symmetric spacetimes [30,31,41,42], near the singularity the proper distance of a radially free falling observer behaves essentially as 1/ √ Ψ 2 , being Ψ 2 the "Coulombian" component of the Weyl tensor.…”

“…Several investigations [38,[58][59][60][61] have shown that in this framework a solution of the "cosmic coincidence problem" arises naturally without the introduction of a quintessence field. In particular in the fixed point regime the vacuum energy density ρ Λ ≡ Λ/8πG is automatically adjusted so as to equal the matter energy density, i.e.…”

The role of background independence for asymptotic safety in Quantum Einstein Gravity

“…(A) Asymptotic safety In the following we investigate a particular aspect of background (in)dependence which is particularly important in the context of asymptotic safety [6][7][8][9][10][11][12][13][14][15][16][17][18], (for reviews see [19][20][21]), , (for detailed reviews of asymptotic safety in gravity see [43,44]). In this approach gravity is described by a quantum field theory of the metric tensor which is renormalized at a non-Gaussian renormalization group (RG) fixed point.…”