Background independent quantum field theory and gravitating vacuum fluctuations

Abstract

The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a tadpole condition, a generalization of Einstein's equation. Self-consistent backround spacetimes are scale dependent, and therefore "going on-shell" at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an equally important indirect one related to the continual re-adjustment of the background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. Among other things, it encodes the complete information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories (Type IIIa) we discover a seemingly paradoxical behavior that differs substantially from the off-shell based expectations: A Background Independent theory of (matter coupled) quantum gravity looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this "rigid picture" breaks down after a very short RG time already (less than one decade of scales) because of a "scale horizon" that forms. Furthermore, we critically reanalyze, and refute the frequent claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant. arXiv:1906.02507v1 [gr-qc] 6 Jun 2019 1 Writing the dimensionless ratio Λ/m 2 Pl and the energy density ρ Λ ≡ Λ/ (8πG), with m Pl ≡ G −1/2 , in the style Λ/m 2 Pl = ΛG = Ω Λ h 2 ×9.15·10 −122 and ρ Λ = Ω 1/4 Λ h 1/2 × 3.0 meV 4 , the recently measured Ω Λ ≈ 0.68, h ≈ 0.67 yield the observational values Λ/m 2 Pl ≈ 2.8 · 10 −122 and ρ Λ = [2.2 meV] 4 , respectively [5].

Ward-constrained melonic renormalization group flow for the rank-four ϕ6 tensorial group field theory

“…which is nothing but the first equation (1). At one-loop, and at the first order in , the non-Gaussian fixed point (4) is then compatible with the Ward identities.…”

“…Group field theories (GFTs) are a type of non-local fields theories defined on d-copies of a group manifold. From more than one decade, they have been considered as a promising way to quantize gravity [1]- [6]. A well defined theory for quantum gravity is necessary to understand the nature of space, time and geometry, and especially to address the questions about the origins of our universe.…”

Critical Reflections on Asymptotically Safe Gravity

“…As a self-consistent truncation scheme appears to be available for quantum gravity, the apparent convergence of fixed-point results is a key goal. It is fair to say that the status of results is rather encouraging with regard to this question, see [91,118,119,124,125,132,175,[185][186][187][188][189][190][191][192][193][194][195][196][197][198][199][200]. This has given rise to the general expectation that the Reuter fixed point indeed exists in full theory space, and provides a universality class for quantum gravity.…”

“…In practice, the solutions of the Ward identity has only been possible for the simplest approximations [108,155,[203][204][205][206]. (3) When Ŵ k and with it (ḡ sc k ) µν show a strong k dependence, the effective spacetime is likely to possess multi-fractal properties which were argued to lead to a dimensional reduction in the ultraviolet [133,[208][209][210] and to a "fuzzy" spacetime structure at even lower scales [198,211,212]. In the existing analyses the fractal-like properties were characterized in terms of ordinary, i.e., smooth classical metrics, the trick being that one and the same spacetime manifold was equipped not with one but rather the one-parameter family of classical metrics, {(ḡ sc k ) µν }.…”

“…Moreover, the importance of properly accounting for the (k-dependent) ground state in studies of the flow is emphasized in a recent background-independent re-analysis of the cosmological constant problem allegedly caused by quantum vacuum fluctuations. Paying careful attention to identifying the correct ground state, the often discussed naturalness problem disappears, see [198].…”