19 research outputs found
Network geometry with flavor: From complexity to quantum geometry
Here we introduce the Network Geometry with Flavor (NGF)
describing simplicial complexes defined in arbitrary dimension and evolving
by a non-equilibrium dynamics. The NGF can generate discrete geometries of
different nature, ranging from chains and higher dimensional manifolds to
scale-free networks with small-world properties, scale-free degree distribution
and non-trivial community structure. The NGF admits as limiting cases both the
Bianconi-Barab\'asi model for complex networks the stochastic Apollonian
network, and the recently introduced model for Complex Quantum Network
Manifolds. The thermodynamic properties of NGF reveal that NGF obeys a
generalized area law opening a new scenario for formulating its coarse-grained
limit. The structure of NGF is strongly dependent on the dimensionality . We
also show that NGF admits a quantum mechanical description in terms of
associated quantum network states. Quantum network states are evolving by a
Markovian dynamics and a quantum network state at time encodes all possible
NGF evolutions up to time . Interestingly the NGF remains fully classical
but its statistical properties reveal the relation to its quantum mechanical
description. In fact the -dimensional faces of the NGF have generalized
degrees that follow either the Fermi-Dirac, Boltzmann or Bose-Einstein
statistics depending on the flavor and the dimensions and .Comment: (37 pages, 4 figures
Functional Multiplex PageRank
(7 pages, 5 figures)(7 pages, 5 figures)(7 pages, 5 figures
Further evidence for asymptotic safety of quantum gravity
The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture
One Loop Beta Functions in Topologically Massive Gravity
We calculate the running of the three coupling constants in cosmological,
topologically massive 3d gravity. We find that \nu, the dimensionless
coefficient of the Chern-Simons term, has vanishing beta function. The flow of
the cosmological constant and Newton's constant depends on \nu, and for any
positive \nu there exist both a trivial and a nontrivial fixed point.Comment: 44 pages, 16 figure
Modified Dispersion Relations from the Renormalization Group of Gravity
We show that the running of gravitational couplings, together with a suitable
identification of the renormalization group scale can give rise to modified
dispersion relations for massive particles. This result seems to be compatible
with both the frameworks of effective field theory with Lorentz invariance
violation and deformed special relativity. The phenomenological consequences
depend on which of the frameworks is assumed. We discuss the nature and
strength of the available constraints for both cases and show that in the case
of Lorentz invariance violation, the theory would be strongly constrained.Comment: revtex4, 9 pages, updated to match published versio
Determination of the Fundamental Scale of Gravity and the Number of Space-time Dimensions from High Energetic Particle Interactions
Within the ADD-model, we elaborate an idea by Vacavant and Hinchliffe and
show quantitatively how to determine the fundamental scale of TeV-gravity and
the number of compactified extra dimensions from data at LHC. We demonstrate
that the ADD-model leads to strong correlations between the missing in
gravitons at different center of mass energies. This correlation puts strong
constraints on this model for extra dimensions, if probed at TeV
and TeV at LHC.Comment: 3 pages, 2 figure
Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
We investigate the future evolution of the dark energy universe in modified
gravities including gravity, string-inspired scalar-Gauss-Bonnet and
modified Gauss-Bonnet ones, and ideal fluid with the inhomogeneous equation of
state (EoS). Modified Friedmann-Robertson-Walker (FRW) dynamics for all these
theories may be presented in universal form by using the effective ideal fluid
with an inhomogeneous EoS without specifying its explicit form. We construct
several examples of the modified gravity which produces accelerating
cosmologies ending at the finite-time future singularity of all four known
types by applying the reconstruction program. Some scenarios to resolve the
finite-time future singularity are presented. Among these scenarios, the most
natural one is related with additional modification of the gravitational action
in the early universe. In addition, late-time cosmology in the non-minimal
Maxwell-Einstein theory is considered. We investigate the forms of the
non-minimal gravitational coupling which generates the finite-time future
singularities and the general conditions for this coupling in order that the
finite-time future singularities cannot emerge. Furthermore, it is shown that
the non-minimal gravitational coupling can remove the finite-time future
singularities or make the singularity stronger (or weaker) in modified gravity.Comment: 25 pages, no figure, title changed, accepted in JCA
Renormalization Group Flow in Scalar-Tensor Theories. II
We study the UV behaviour of actions including integer powers of scalar
curvature and even powers of scalar fields with Functional Renormalization
Group techniques. We find UV fixed points where the gravitational couplings
have non-trivial values while the matter ones are Gaussian. We prove several
properties of the linearized flow at such a fixed point in arbitrary dimensions
in the one-loop approximation and find recursive relations among the critical
exponents. We illustrate these results in explicit calculations in for
actions including up to four powers of scalar curvature and two powers of the
scalar field. In this setting we notice that the same recursive properties
among the critical exponents, which were proven at one-loop order, still hold,
in such a way that the UV critical surface is found to be five dimensional. We
then search for the same type of fixed point in a scalar theory with minimal
coupling to gravity in including up to eight powers of scalar curvature.
Assuming that the recursive properties of the critical exponents still hold,
one would conclude that the UV critical surface of these theories is five
dimensional.Comment: 14 pages. v.2: Minor changes, some references adde