Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity

Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wave-function renormalization of the ghost fields. The latter induces non-trivial corrections to the beta-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point in agreement with the asymptotic safety conjecture, which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is $\eta_c^* = -1.8$, supporting space-time being effectively two-dimensional at short distances.Comment: 23 pages, 4 figure

Common Sense or World Knowledge? Investigating Adapter-Based Knowledge Injection into Pretrained Transformers

Following the major success of neural language models (LMs) such as BERT or GPT-2 on a variety of language understanding tasks, recent work focused on injecting (structured) knowledge from external resources into these models. While on the one hand, joint pretraining (i.e., training from scratch, adding objectives based on external knowledge to the primary LM objective) may be prohibitively computationally expensive, post-hoc fine-tuning on external knowledge, on the other hand, may lead to the catastrophic forgetting of distributional knowledge. In this work, we investigate models for complementing the distributional knowledge of BERT with conceptual knowledge from ConceptNet and its corresponding Open Mind Common Sense (OMCS) corpus, respectively, using adapter training. While overall results on the GLUE benchmark paint an inconclusive picture, a deeper analysis reveals that our adapter-based models substantially outperform BERT (up to 15-20 performance points) on inference tasks that require the type of conceptual knowledge explicitly present in ConceptNet and OMCS

The Renormalization Group, Systems of Units and the Hierarchy Problem

In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be based on Newton's constant or on the Higgs mass. These quantities are not invariant under the RG, and the ratio between the units is scale-dependent. In the toy model, strong RG running occurs in the intermediate regime between the Higgs and the Planck scale, reproducing the results of the Randall-Sundrum I model. Possible connections with the problem of the mass hierarchy are pointed out.Comment: Plain TEX, 16 pages. Some revisions, some references adde

On the renormalization group flow of f(R)-gravity

We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including $\int d^dx \sqrt{g} \ln(R)$ and $\int d^dx \sqrt{g} R^{-n}$ interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $R^{-n}$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $\ln(R)$-truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.Comment: 55 pages, 7 figures, typos corrected, references added, version to appear in Phys. Rev.

Averaging procedure in variable-G cosmologies

Previous work in the literature had built a formalism for spatially averaged equations for the scale factor, giving rise to an averaged Raychaudhuri equation and averaged Hamiltonian constraint, which involve a backreaction source term. The present paper extends these equations to include models with variable Newton parameter and variable cosmological term, motivated by the nonperturbative renormalization program for quantum gravity based upon the Einstein-Hilbert action. We focus on the Brans-Dicke form of the renormalization-group improved action functional. The coupling between backreaction and spatially averaged three-dimensional scalar curvature is found to survive, and a variable-G cosmic quintet is found to emerge. Interestingly, under suitable assumptions, an approximate solution can be found where the early universe tends to a FLRW model, while keeping track of the original inhomogeneities through three effective fluids. The resulting qualitative picture is that of a universe consisting of baryons only, while inhomogeneities average out to give rise to the full dark-side phenomenology.Comment: 20 pages. In the new version, all original calculations have been improved, and the presentation has been further improved as wel

Fractal Structure of Loop Quantum Gravity

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decrees from high to low energy. We have calculated the spectral dimension of the space-time also using results from spin-foam models, obtaining a 2-dimensional effective manifold at hight energy. Our result is consistent with other two approach to non perturbative quantum gravity: causal dynamical triangulation and asymptotic safety quantum gravity.Comment: 5 pages, 5 figure

Scale-dependent metric and causal structures in Quantum Einstein Gravity

Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) and the resulting families of resolution dependent metrics are discussed. The status of scale dependent vs. scale independent diffeomorphisms is clarified, and the difference between isometries implemented by scale dependent and independent Killing vectors is explained. A concept of scale dependent causality is proposed and illustrated by various simple examples. The possibility of assigning an "intrinsic length" to objects in a QEG spacetime is also discussed.Comment: 52 page

Fixed points of quantum gravity in extra dimensions

We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low-scale gravity and compact extra dimensions.Comment: Wording sharpened, refs added, to appear in PL

Primordial Entropy Production and Lambda-driven Inflation from Quantum Einstein Gravity

We review recent work on renormalization group (RG) improved cosmologies based upon a RG trajectory of Quantum Einstein Gravity (QEG) with realistic parameter values. In particular we argue that QEG effects can account for the entire entropy of the present Universe in the massless sector and give rise to a phase of inflationary expansion. This phase is a pure quantum effect and requires no classical inflaton field.Comment: 12 pages, 4 figures, IGCG-07 Pun

Critical exponents from optimised renormalisation group flows

Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared regularisation. The Wilson-Fisher fixed point in d=3 is studied using an optimised flow. We compute critical exponents and subleading corrections-to-scaling to high accuracy from the eigenvalues of the stability matrix at criticality for all N. We establish that the optimisation is responsible for the rapid convergence of the flow and polynomial truncations thereof. The scheme dependence of the leading critical exponent is analysed. For all N > 0, it is found that the leading exponent is bounded. The upper boundary is achieved for a Callan-Symanzik flow and corresponds, for all N, to the large-N limit. The lower boundary is achieved by the optimised flow and is closest to the physical value. We show the reliability of polynomial approximations, even to low orders, if they are accompanied by an appropriate choice for the regulator. Possible applications to other theories are outlined.Comment: 34 pages, 15 figures, revtex, to appear in NP