34 research outputs found
New higher-order transition in causal dynamical triangulations
We reinvestigate the recently discovered bifurcation phase transition in
Causal Dynamical Triangulations (CDT) and provide further evidence that it is a
higher order transition. We also investigate the impact of introducing matter
in the form of massless scalar fields to CDT. We discuss the impact of scalar
fields on the measured spatial volumes and fluctuation profiles in addition to
analysing how the scalar fields influence the position of the bifurcation
transition.Comment: 15 pages, 11 figures. Conforms with version accepted for publication
in Phys. Rev.
Cosmic voids and filaments from quantum gravity
Using computer simulations we study the geometry of a typical quantum
universe, i.e. the geometry one might expect before a possible period of
inflation. We display it using coordinates defined by means of four classical
scalar fields satisfying the Laplace equation with non-trivial boundary
conditions. The field configurations reveal cosmic web structures surprisingly
similar to the ones observed in the present-day Universe. Inflation might make
these structures relevant for our Universe.Comment: 4 pages, 2 figure
The transfer matrix in four-dimensional CDT
The Causal Dynamical Triangulation model of quantum gravity (CDT) has a
transfer matrix, relating spatial geometries at adjacent (discrete lattice)
times. The transfer matrix uniquely determines the theory. We show that the
measurements of the scale factor of the (CDT) universe are well described by an
effective transfer matrix where the matrix elements are labeled only by the
scale factor. Using computer simulations we determine the effective transfer
matrix elements and show how they relate to an effective minisuperspace action
at all scales.Comment: 32 pages, 19 figure
Statutory Interpretation as Argumentation
This chapter proposes a dialectical approach to legal interpretation, consisting of three dimensions: a formalization of the canons of interpretation in terms of argumentation schemes; a dialectical classification of interpretive schemes; and a logical and computational model for comparing the arguments pro and contra an interpretation. The traditional interpretive maxims or canons used in both common and civil law are translated into defeasible patterns of arguments, which can be evaluated through sets of corresponding critical questions. These interpretive argumentation schemes are classified in general categories and a distinction is drawn between schemes supporting and rebutting an interpretation. This framework allows conceiving statutory interpretation as a dialectical procedure consisting in weighing arguments pro and contra an interpretation. This procedure is formalized and represented computationally through tools from formal argumentation systems
Recent results in CDT quantum gravity
Contains fulltext :
181406.pdf (publisher's version ) (Open Access
Topology induced first-order phase transitions in lattice quantum gravity
Causal Dynamical Triangulations (CDT) is a lattice formulation of quantum
gravity, suitable for Monte-Carlo simulations which have been used to study the
phase diagram of the model. It has four phases characterized by different
dominant geometries, denoted phase , , and . In this article we
analyse the and the {phase} transitions in the case where the
topology of space is that of the three-torus. This completes the phase diagram
of CDT for such a spatial topology. We observe that the order of a phase
transition of spacetime geometries can depend on the topology of spacetime
Matter-driven change of spacetime topology
Using Monte-Carlo computer simulations, we study the impact of matter fields
on the geometry of a typical quantum universe in the CDT model of lattice
quantum gravity. The quantum universe has the size of a few Planck lengths and
the spatial topology of a three-torus. The matter fields are multi-component
scalar fields taking values in a torus with circumference in each
spatial direction, which acts as a new parameter in the CDT model. Changing
, we observe a phase transition caused by the scalar field. This
discovery may have important consequences for quantum universes with
non-trivial topology, since the phase transition can change the topology to a
simply connected one.Comment: 5 pages, 5 figure
Towards an UV fixed point in CDT gravity
Contains fulltext :
205961.pdf (publisher's version ) (Open Access