810 research outputs found
Regional averaging and scaling in relativistic cosmology
Averaged inhomogeneous cosmologies lie at the forefront of interest, since
cosmological parameters like the rate of expansion or the mass density are to
be considered as volume-averaged quantities and only these can be compared with
observations. For this reason the relevant parameters are intrinsically
scale-dependent and one wishes to control this dependence without restricting
the cosmological model by unphysical assumptions. In the latter respect we
contrast our way to approach the averaging problem in relativistic cosmology
with shortcomings of averaged Newtonian models. Explicitly, we investigate the
scale-dependence of Eulerian volume averages of scalar functions on Riemannian
three-manifolds. We propose a complementary view of a Lagrangian smoothing of
(tensorial) variables as opposed to their Eulerian averaging on spatial
domains. This program is realized with the help of a global Ricci deformation
flow for the metric. We explain rigorously the origin of the Ricci flow which,
on heuristic grounds, has already been suggested as a possible candidate for
smoothing the initial data set for cosmological spacetimes. The smoothing of
geometry implies a renormalization of averaged spatial variables. We discuss
the results in terms of effective cosmological parameters that would be
assigned to the smoothed cosmological spacetime.Comment: LateX, IOPstyle, 48 pages, 11 figures; matches published version in
C.Q.
Cosmological parameters are dressed
In the context of the averaging problem in relativistic cosmology, we provide
a key to the interpretation of cosmological parameters by taking into account
the actual inhomogeneous geometry of the Universe. We discuss the relation
between `bare' cosmological parameters determining the cosmological model, and
the parameters interpreted by observers with a ``Friedmannian bias'', which are
`dressed' by the smoothed-out geometrical inhomogeneities of the surveyed
spatial region.Comment: LateX, PRLstyle, 4 pages; submitted to PR
Invariants of spin networks with boundary in Quantum Gravity and TQFT's
The search for classical or quantum combinatorial invariants of compact
n-dimensional manifolds (n=3,4) plays a key role both in topological field
theories and in lattice quantum gravity. We present here a generalization of
the partition function proposed by Ponzano and Regge to the case of a compact
3-dimensional simplicial pair . The resulting state sum
contains both Racah-Wigner 6j symbols associated with
tetrahedra and Wigner 3jm symbols associated with triangular faces lying in
. The analysis of the algebraic identities associated with the
combinatorial transformations involved in the proof of the topological
invariance makes it manifest a common structure underlying the 3-dimensional
models with empty and non empty boundaries respectively. The techniques
developed in the 3-dimensional case can be further extended in order to deal
with combinatorial models in n=2,4 and possibly to establish a hierarchy among
such models. As an example we derive here a 2-dimensional closed state sum
model including suitable sums of products of double 3jm symbols, each one of
them being associated with a triangle in the surface.Comment: 9 page
Quantum Tetrahedra
We discuss in details the role of Wigner 6j symbol as the basic building
block unifying such different fields as state sum models for quantum geometry,
topological quantum field theory, statistical lattice models and quantum
computing. The apparent twofold nature of the 6j symbol displayed in quantum
field theory and quantum computing -a quantum tetrahedron and a computational
gate- is shown to merge together in a unified quantum-computational SU(2)-state
sum framework
12j-symbols and four-dimensional quantum gravity
We propose a model which represents a four-dimensional version of Ponzano and
Regge's three-dimensional euclidean quantum gravity. In particular we show that
the exponential of the euclidean Einstein-Regge action for a -discretized
block is given, in the semiclassical limit, by a gaussian integral of a
suitable -symbol. Possible developments of this result are discussed.Comment: 12 pages, Late
The geometry of dynamical triangulations
We discuss the geometry of dynamical triangulations associated with
3-dimensional and 4-dimensional simplicial quantum gravity. We provide
analytical expressions for the canonical partition function in both cases, and
study its large volume behavior. In the space of the coupling constants of the
theory, we characterize the infinite volume line and the associated critical
points. The results of this analysis are found to be in excellent agreement
with the MonteCarlo simulations of simplicial quantum gravity. In particular,
we provide an analytical proof that simply-connected dynamically triangulated
4-manifolds undergo a higher order phase transition at a value of the inverse
gravitational coupling given by 1.387, and that the nature of this transition
can be concealed by a bystable behavior. A similar analysis in the
3-dimensional case characterizes a value of the critical coupling (3.845) at
which hysteresis effects are present.Comment: 166 pages, Revtex (latex) fil
Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity
We provide a non-perturbative geometrical characterization of the partition
function of -dimensional quantum gravity based on a coarse classification of
riemannian geometries. We show that, under natural geometrical constraints, the
theory admits a continuum limit with a non-trivial phase structure parametrized
by the homotopy types of the class of manifolds considered. The results
obtained qualitatively coincide, when specialized to dimension two, with those
of two-dimensional quantum gravity models based on random triangulations of
surfaces.Comment: 13 page
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