368 research outputs found
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 , supporting
space-time being effectively two-dimensional at short distances.Comment: 23 pages, 4 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
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
The Accelerated expansion of the Universe as a crossover phenomenon
We show that the accelerated expansion of the Universe can be viewed as a
crossover phenomenon where the Newton constant and the Cosmological constant
are actually scaling operators, dynamically evolving in the attraction basin of
a non-Gaussian infrared fixed point, whose existence has been recently
discussed. By linearization of the renormalized flow it is possible to evaluate
the critical exponents, and it turns out that the approach to the fixed point
is ruled by a marginal and a relevant direction. A smooth transition between
the standard Friedmann--Lemaitre--Robertson--Walker (FLRW) cosmology and the
observed accelerated expansion is then obtained, so that at late times.Comment: 12 pages, latex, use bibtex. In the final version, the presentation
has been improved, and new references have been 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 . 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 and 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 -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 -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.
The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
We discuss various basic conceptual issues related to coarse graining flows
in quantum gravity. In particular the requirement of background independence is
shown to lead to renormalization group (RG) flows which are significantly
different from their analogs on a rigid background spacetime. The importance of
these findings for the asymptotic safety approach to Quantum Einstein Gravity
(QEG) is demonstrated in a simplified setting where only the conformal factor
is quantized. We identify background independence as a (the ?) key prerequisite
for the existence of a non-Gaussian RG fixed point and the renormalizability of
QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum
Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to
appear in General Relativity and Gravitatio
Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
The emergence of fractal features in the microscopic structure of space-time
is a common theme in many approaches to quantum gravity. In this work we carry
out a detailed renormalization group study of the spectral dimension and
walk dimension associated with the effective space-times of
asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling
regimes where these generalized dimensions are approximately constant for an
extended range of length scales: a classical regime where , a
semi-classical regime where , and the UV-fixed point
regime where . On the length scales covered by
three-dimensional Monte Carlo simulations, the resulting spectral dimension is
shown to be in very good agreement with the data. This comparison also provides
a natural explanation for the apparent puzzle between the short distance
behavior of the spectral dimension reported from Causal Dynamical
Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic
Safety.Comment: 26 pages, 6 figure
Putting a cap on causality violations in CDT
The formalism of causal dynamical triangulations (CDT) provides us with a
non-perturbatively defined model of quantum gravity, where the sum over
histories includes only causal space-time histories. Path integrals of CDT and
their continuum limits have been studied in two, three and four dimensions.
Here we investigate a generalization of the two-dimensional CDT model, where
the causality constraint is partially lifted by introducing weighted branching
points, and demonstrate that the system can be solved analytically in the
genus-zero sector.Comment: 17 pages, 4 figure
Fractal Spacetime Structure in Asymptotically Safe Gravity
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an
asymptotically safe theory which is applicable at arbitrarily small distance
scales. On sub-Planckian distances it predicts that spacetime is a fractal with
an effective dimensionality of 2. The original argument leading to this result
was based upon the anomalous dimension of Newton's constant. In the present
paper we demonstrate that also the spectral dimension equals 2 microscopically,
while it is equal to 4 on macroscopic scales. This result is an exact
consequence of asymptotic safety and does not rely on any truncation. Contact
is made with recent Monte Carlo simulations.Comment: 20 pages, late
Running Gauge Coupling in Asymptotically Safe Quantum Gravity
We investigate the non-perturbative renormalization group behavior of the
gauge coupling constant using a truncated form of the functional flow equation
for the effective average action of the Yang-Mills-gravity system. We find a
non-zero quantum gravity correction to the standard Yang-Mills beta function
which has the same sign as the gauge boson contribution. Our results fit into
the picture according to which Quantum Einstein Gravity (QEG) is asymptotically
safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page
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