6 research outputs found
An optimal series expansion of the multiparameter fractional Brownian motion
We derive a series expansion for the multiparameter fractional Brownian
motion. The derived expansion is proven to be rate optimal.Comment: 21 pages, no figures, final version, to appear in Journal of
Theoretical Probabilit
About Lorentz invariance in a discrete quantum setting
A common misconception is that Lorentz invariance is inconsistent with a
discrete spacetime structure and a minimal length: under Lorentz contraction, a
Planck length ruler would be seen as smaller by a boosted observer. We argue
that in the context of quantum gravity, the distance between two points becomes
an operator and show through a toy model, inspired by Loop Quantum Gravity,
that the notion of a quantum of geometry and of discrete spectra of geometric
operators, is not inconsistent with Lorentz invariance. The main feature of the
model is that a state of definite length for a given observer turns into a
superposition of eigenstates of the length operator when seen by a boosted
observer. More generally, we discuss the issue of actually measuring distances
taking into account the limitations imposed by quantum gravity considerations
and we analyze the notion of distance and the phenomenon of Lorentz contraction
in the framework of ``deformed (or doubly) special relativity'' (DSR), which
tentatively provides an effective description of quantum gravity around a flat
background. In order to do this we study the Hilbert space structure of DSR,
and study various quantum geometric operators acting on it and analyze their
spectral properties. We also discuss the notion of spacetime point in DSR in
terms of coherent states. We show how the way Lorentz invariance is preserved
in this context is analogous to that in the toy model.Comment: 25 pages, RevTe
Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons
The stability of cosmological event and Cauchy horizons of spacetimes
associated with plane symmetric domain walls are studied. It is found that both
horizons are not stable against perturbations of null fluids and massless
scalar fields; they are turned into curvature singularities. These
singularities are light-like and strong in the sense that both the tidal forces
and distortions acting on test particles become unbounded when theses
singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques
Cosmological evolution of general scalar fields in a brane-world cosmology
We study the cosmology of a general scalar field and barotropic fluid during
the early stage of a brane-world where the Friedmann constraint is dominated by
the square of the energy density. Assuming both the scalar field and fluid are
confined to the brane, we find a range of behaviour depending on the form of
the potential. Generalising an approach developed for a standard Friedmann
cosmology, in \cite{delaMacorra:1999ff}, we show that the potential dependence
can be described through a parameter , where is the 5-dimensional Planck mass, is
the Hubble parameter and . For the case where
asymptotes to zero, we show that the solution exhibits stable
inflationary behaviour. On the other hand if it approaches a finite constant,
then . For
asymptotically, we find examples where it does so both with and without
oscillating. In the latter case, the barotropic fluid dominates the scalar
filed asymptotically. Finally we point out an interesting duality which leads
to identical evolution equations in the high energy dominated regime
and the low energy dominated regime.Comment: 10 pages, 3 figure