Asymptotic safety and the cosmological constant

Abstract

Abstract:We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. If only the conformal fluctuations are quantised we find an asymptotically safe fixed point predicting a vanishing cosmological constant on all scales. At this fixed point we reproduce the critical exponent, ν = 1/3, found in numerical lattice studies by Hamber. Returning to the full theory we find that by setting the cosmological constant to zero the critical exponent agrees with the conformally reduced theory. This suggests the fixed point may be physical while hinting at solution to the cosmological constant problem.

Asymptotic safety of gravity-matter systems

“…Note, that the evaluation of the two-point function at M 2 = 0 ensures that only the momentum dependent part of the latter enters for the class of regulators defined by (31). Since the effective graviton mass M 2 is the only mass parameter in the present truncation the above definition implies that Γ (22). This generic class covers the regulator choices in the literature, and implements the correct renormalisation group scaling of the effective action as discussed in [8,41,60].…”

“…Here d is the dimension of spinor space, which we set to d = 4 throughout. Since (22), (26) and (28) are of the same form, we apply the same bilocal momentum projection for the extraction of the respective momentum dependent anomalous dimensions. This crucial procedure is discussed in more detail in the next section.…”

“…The development of modern functional renormalisation group (FRG) techniques and their application to quantum gravity [3,4] has led to strong evidence for the nontrivial UV fixed point for pure gravity. It was first found in basic Einstein-Hilbert approximations [3,5,6] and later confirmed in more elaborate truncations [1,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], for reviews see [25][26][27][28].…”

Graviton fluctuations erase the cosmological constant

“…The absence of a mass-like term in the "on-shell" propagator of the graviton is well known in general relativity and cosmology and has been discussed for the renormalization flow in refs. [53,54]. It is at the origin of scepticism about the relevance of the "avoidance of instabilities" for observable cosmology.…”

Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system

“…for gravity with matters and gauge fields ; for higher derivative gravity with f (R)type truncation [71][72][73][74][75][76][77][78][79][80][81][82][83][84]; R µν R µν [85][86][87][88][89][90][91][92]; and the Goroff-Sagnotti term [93]; see also [94][95][96][97][98][99][100] for review papers. 5 Also studies based on the vertex expansion have been performed in [125][126][127][128][129][130][131][132].…”