473 research outputs found
Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
We summarize recent evidence supporting the conjecture that four-dimensional
Quantum Einstein Gravity (QEG) is nonperturbatively renormalizable along the
lines of Weinberg's asymptotic safety scenario. This would mean that QEG is
mathematically consistent and predictive even at arbitrarily small length
scales below the Planck length. For a truncated version of the exact flow
equation of the effective average action we establish the existence of a
non-Gaussian renormalization group fixed point which is suitable for the
construction of a nonperturbative infinite cutoff-limit. The cosmological
implications of this fixed point are discussed, and it is argued that QEG might
solve the horizon and flatness problem of standard cosmology without an
inflationary period.Comment: 10 pages, latex, 1 figur
Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
We study the renormalization group flow for the Higgs self coupling in the
presence of gravitational correction terms. We show that the resulting equation
is equivalent to a singular linear ODE, which has explicit solutions in terms
of hypergeometric functions. We discuss the implications of this model with
gravitational corrections on the Higgs mass estimates in particle physics
models based on the spectral action functional.Comment: 25 pages, LaTeX, 8 PDF figure
Improved Action Functionals in Non-Perturbative Quantum Gravity
Models of gravity with variable G and Lambda have acquired greater relevance
after the recent evidence in favour of the Einstein theory being
non-perturbatively renormalizable in the Weinberg sense. The present paper
builds a modified Arnowitt-Deser-Misner (ADM) action functional for such models
which leads to a power-law growth of the scale factor for pure gravity and for
a massless phi**4 theory in a Universe with Robertson-Walker symmetry, in
agreement with the recently developed fixed-point cosmology. Interestingly, the
renormalization-group flow at the fixed point is found to be compatible with a
Lagrangian description of the running quantities G and Lambda.Comment: Latex file. Record without file already exists on SLAC-SPIRES, and
hence that record and the one for the present arxiv submission should become
one record onl
A Class of Renormalization Group Invariant Scalar Field Cosmologies
We present a class of scalar field cosmologies with a dynamically evolving
Newton parameter and cosmological term . In particular, we discuss
a class of solutions which are consistent with a renormalization group scaling
for and near a fixed point. Moreover, we propose a modified
action for gravity which includes the effective running of and
near the fixed point. A proper understanding of the associated variational
problem is obtained upon considering the four-dimensional gradient of the
Newton parameter.Comment: 10 pages, RevTex4, no figures, to appear on GR
Background Independence and Asymptotic Safety in Conformally Reduced Gravity
We analyze the conceptual role of background independence in the application
of the effective average action to quantum gravity. Insisting on a background
independent renormalization group (RG) flow the coarse graining operation must
be defined in terms of an unspecified variable metric since no rigid metric of
a fixed background spacetime is available. This leads to an extra field
dependence in the functional RG equation and a significantly different RG flow
in comparison to the standard flow equation with a rigid metric in the mode
cutoff. The background independent RG flow can possess a non-Gaussian fixed
point, for instance, even though the corresponding standard one does not. We
demonstrate the importance of this universal, essentially kinematical effect by
computing the RG flow of Quantum Einstein Gravity in the ``conformally
reduced'' Einstein--Hilbert approximation which discards all degrees of freedom
contained in the metric except the conformal one. Without the extra field
dependence the resulting RG flow is that of a simple -theory. Including
it one obtains a flow with exactly the same qualitative properties as in the
full Einstein--Hilbert truncation. In particular it possesses the non-Gaussian
fixed point which is necessary for asymptotic safety.Comment: 4 figures
Asymptotic Safety of Gravity Coupled to Matter
Nonperturbative treatments of the UV limit of pure gravity suggest that it
admits a stable fixed point with positive Newton's constant and cosmological
constant. We prove that this result is stable under the addition of a scalar
field with a generic potential and nonminimal couplings to the scalar
curvature. There is a fixed point where the mass and all nonminimal scalar
interactions vanish while the gravitational couplings have values which are
almost identical to the pure gravity case. We discuss the linearized flow
around this fixed point and find that the critical surface is four-dimensional.
In the presence of other, arbitrary, massless minimally coupled matter fields,
the existence of the fixed point, the sign of the cosmological constant and the
dimension of the critical surface depend on the type and number of fields. In
particular, for some matter content, there exist polynomial asymptotically free
scalar potentials, thus providing a solution to the well-known problem of
triviality.Comment: 18 pages,typeset with revtex
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
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
Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
We find considerable evidence supporting the conjecture that four-dimensional
Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This
would mean that the theory is likely to be nonperturbatively renormalizable and
thus could be considered a fundamental (rather than merely effective) theory
which is mathematically consistent and predictive down to arbitrarily small
length scales. For a truncated version of the exact flow equation of the
effective average action we establish the existence of a non-Gaussian
renormalization group fixed point which is suitable for the construction of a
nonperturbative infinite cutoff-limit. The truncation ansatz includes the
Einstein-Hilbert action and a higher derivative term.Comment: 18 pages, latex, 3 figure
Noncommutative Geometry and the standard model with neutrino mixing
We show that allowing the metric dimension of a space to be independent of
its KO-dimension and turning the finite noncommutative geometry F-- whose
product with classical 4-dimensional space-time gives the standard model
coupled with gravity--into a space of KO-dimension 6 by changing the grading on
the antiparticle sector into its opposite, allows to solve three problems of
the previous noncommutative geometry interpretation of the standard model of
particle physics:
The finite geometry F is no longer put in "by hand" but a conceptual
understanding of its structure and a classification of its metrics is given.
The fermion doubling problem in the fermionic part of the action is resolved.
The spectral action of our joint work with Chamseddine now automatically
generates the full standard model coupled with gravity with neutrino mixing and
see-saw mechanism for neutrino masses. The predictions of the Weinberg angle
and the Higgs scattering parameter at unification scale are the same as in our
joint work but we also find a mass relation (to be imposed at unification
scale).Comment: Typos removed, to appear in JHE
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