734 research outputs found
Diffusion in quantum geometry
The change of the effective dimension of spacetime with the probed scale is a
universal phenomenon shared by independent models of quantum gravity. Using
tools of probability theory and multifractal geometry, we show how dimensional
flow is controlled by a multiscale fractional diffusion equation, and
physically interpreted as a composite stochastic process. The simplest example
is a fractional telegraph process, describing quantum spacetimes with a
spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4
towards the infrared. The general profile of the spectral dimension of the
recently introduced multifractional spaces is constructed for the first time.Comment: 5 pages, 1 figure. v2: title slightly changed, discussion improve
Stability of multi-field cosmological solutions
We explore the stability properties of multi-field solutions of assisted
inflation type, where several fields collectively evolve to the same
configuration. In the case of noninteracting fields, we show that the condition
for such solutions to be stable is less restrictive than that required for
tracking in quintessence models. Our results, which do not rely on the
slow-roll approximation, further indicate that to linear order in homogeneous
perturbations the fields are in fact unaware of each other's existence. We end
by generalizing our results to some cases of interacting fields and to other
background solutions and dynamics, including the high-energy braneworld.Comment: 6 pages; v2: typos corrected, version accepted by PR
2-point functions in quantum cosmology
We discuss the path-integral formulation of quantum cosmology with a massless
scalar field as a sum-over-histories, with particular reference to loop quantum
cosmology. Exploiting the analogy with the relativistic particle, we give a
complete overview of the possible two-point functions, deriving vertex
expansions and composition laws they satisfy. We clarify the tie between
definitions using a group averaging procedure and those in a deparametrised
framework. We draw some conclusions about the physics of a single quantum
universe and multiverse field theories where the role of these sectors and the
inner product are reinterpreted.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in
Journal of Physics: Conference Series (JPCS
Degeneracy of consistency equations in braneworld inflation
In a Randall-Sundrum type II inflationary scenario we compute perturbation
amplitudes and spectral indices up to next-to-lowest order in the slow-roll
parameters, starting from the well-known lowest-order result for a de Sitter
brane. Using two different prescriptions for the tensor amplitude, we show that
the braneworld consistency equations are not degenerate with respect to the
standard relations and we explore their observational consequences. It is then
shown that, while the degeneracy between high- and low-energy regimes can come
from suitable values of the cosmological observables, exact functional matching
between consistency expressions is plausibly discarded. This result is then
extended to the Gauss-Bonnet case.Comment: 16 pages, 3 figures. v3: major revision. Changed title, updated
references, rearranged material, new prescription for the tensor spectrum,
new figures, extended and more robust conclusion
Fractal universe and quantum gravity
We propose a field theory which lives in fractal spacetime and is argued to
be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and
causal. The system flows from an ultraviolet fixed point, where spacetime has
Hausdorff dimension 2, to an infrared limit coinciding with a standard
four-dimensional field theory. Classically, the fractal world where fields live
exchanges energy momentum with the bulk with integer topological dimension.
However, the total energy momentum is conserved. We consider the dynamics and
the propagator of a scalar field. Implications for quantum gravity, cosmology,
and the cosmological constant are discussed.Comment: 4 pages. v2: typos corrected; v3: discussion improved, intuitive
introduction added, matches the published versio
2-point functions in quantum cosmology
We discuss the path-integral formulation of quantum cosmology with a massless
scalar field as a sum-over-histories, with particular reference to loop quantum
cosmology. Exploiting the analogy with the relativistic particle, we give a
complete overview of the possible two-point functions, deriving vertex
expansions and composition laws they satisfy. We clarify the tie between
definitions using a group averaging procedure and those in a deparametrised
framework. We draw some conclusions about the physics of a single quantum
universe and multiverse field theories where the role of these sectors and the
inner product are reinterpreted.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in
Journal of Physics: Conference Series (JPCS
2-point functions in quantum cosmology
We discuss the path-integral formulation of quantum cosmology with a massless
scalar field as a sum-over-histories, with particular reference to loop quantum
cosmology. Exploiting the analogy with the relativistic particle, we give a
complete overview of the possible two-point functions, deriving vertex
expansions and composition laws they satisfy. We clarify the tie between
definitions using a group averaging procedure and those in a deparametrised
framework. We draw some conclusions about the physics of a single quantum
universe and multiverse field theories where the role of these sectors and the
inner product are reinterpreted.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in
Journal of Physics: Conference Series (JPCS
On topological charged braneworld black holes
We study a class of topological black hole solutions in RSII braneworld
scenario in the presence of a localized Maxwell field on the brane. Such a
black hole can carry two types of charge, one arising from the extra dimension,
the tidal charge, and the other one from a localized gauge field confined to
the brane. We find that the localized charge on the brane modifies the bulk
geometry and in particular the bulk Weyl tensor. The bulk geometry does not
depend on different topologies of the horizons. We present the temperature and
entropy expressions associated with the event horizon of the braneworld black
hole and by using the first law of black hole thermodynamics we calculate the
mass of the black hole.Comment: 9 pages, references added, to appear in MPL
Primordial perturbations from slow-roll inflation on a brane
In this paper we quantise scalar perturbations in a Randall-Sundrum-type
model of inflation where the inflaton field is confined to a single brane
embedded in five-dimensional anti-de Sitter space-time. In the high energy
regime, small-scale inflaton fluctuations are strongly coupled to metric
perturbations in the bulk and gravitational back-reaction has a dramatic effect
on the behaviour of inflaton perturbations on sub-horizon scales. This is in
contrast to the standard four-dimensional result where gravitational
back-reaction can be neglected on small scales. Nevertheless, this does not
give rise to significant particle production, and the correction to the power
spectrum of the curvature perturbations on super-horizon scales is shown to be
suppressed by a slow-roll parameter. We calculate the complete first order
slow-roll corrections to the spectrum of primordial curvature perturbations.Comment: 23 pages, 10 figure
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