372 research outputs found
Contraints on Matter from Asymptotic Safety
Recent studies of the ultraviolet behaviour of pure gravity suggest that it
admits a non-Gaussian attractive fixed point, and therefore that the theory is
asymptotically safe. We consider the effect on this fixed point of massless
minimally coupled matter fields. The existence of a UV attractive fixed point
puts bounds on the type and number of such fields.Comment: 5 pages, 2 figures, revtex4; introduction expande
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
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
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
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
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
Renormalization group improved gravitational actions: a Brans-Dicke approach
A new framework for exploiting information about the renormalization group
(RG) behavior of gravity in a dynamical context is discussed. The
Einstein-Hilbert action is RG-improved by replacing Newton's constant and the
cosmological constant by scalar functions in the corresponding Lagrangian
density. The position dependence of and is governed by a RG
equation together with an appropriate identification of RG scales with points
in spacetime. The dynamics of the fields and does not admit a
Lagrangian description in general. Within the Lagrangian formalism for the
gravitational field they have the status of externally prescribed
``background'' fields. The metric satisfies an effective Einstein equation
similar to that of Brans-Dicke theory. Its consistency imposes severe
constraints on allowed backgrounds. In the new RG-framework, and
carry energy and momentum. It is tested in the setting of homogeneous-isotropic
cosmology and is compared to alternative approaches where the fields and
do not carry gravitating 4-momentum. The fixed point regime of the
underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure
Infrared fixed point in quantum Einstein gravity
We performed the renormalization group analysis of the quantum Einstein
gravity in the deep infrared regime for different types of extensions of the
model. It is shown that an attractive infrared point exists in the broken
symmetric phase of the model. It is also shown that due to the Gaussian fixed
point the IR critical exponent of the correlation length is 1/2. However,
there exists a certain extension of the model which gives finite correlation
length in the broken symmetric phase. It typically appears in case of models
possessing a first order phase transitions as is demonstrated on the example of
the scalar field theory with a Coleman-Weinberg potential.Comment: 9 pages, 7 figures, final version, to appear in JHE
Quantum cosmology with big-brake singularity
We investigate a cosmological model with a big-brake singularity in the
future: while the first time derivative of the scale factor goes to zero, its
second time derivative tends to minus infinity. Although we also discuss the
classical version of the model in some detail, our main interest lies in its
quantization. We formulate the Wheeler-DeWitt equation and derive solutions
describing wave packets. We show that all such solutions vanish in the region
of the classical singularity, a behaviour which we interpret as singularity
avoidance. We then discuss the same situation in loop quantum cosmology. While
this leads to a different factor ordering, the singularity is there avoided,
too.Comment: 24 pages, 7 figures, figures improved, references added, conceptual
clarifications include
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
- …