2,769 research outputs found
The Power of General Relativity
We study the cosmological and weak-field properties of theories of gravity
derived by extending general relativity by means of a Lagrangian proportional
to . This scale-free extension reduces to general relativity when
. In order to constrain generalisations of general relativity of
this power class we analyse the behaviour of the perfect-fluid Friedmann
universes and isolate the physically relevant models of zero curvature. A
stable matter-dominated period of evolution requires or . The stable attractors of the evolution are found. By considering the
synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the
bound We evaluate the effect on the power spectrum of
clustering via the shift in the epoch of matter-radiation equality. The horizon
size at matter--radiation equality will be shifted by for a value of
We study the stable extensions of the Schwarzschild
solution in these theories and calculate the timelike and null geodesics. No
significant bounds arise from null geodesic effects but the perihelion
precession observations lead to the strong bound assuming that Mercury follows a timelike geodesic. The combination of
these observational constraints leads to the overall bound on theories of this type.Comment: 26 pages and 5 figures. Published versio
Fractals and Scars on a Compact Octagon
A finite universe naturally supports chaotic classical motion. An ordered
fractal emerges from the chaotic dynamics which we characterize in full for a
compact 2-dimensional octagon. In the classical to quantum transition, the
underlying fractal can persist in the form of scars, ridges of enhanced
amplitude in the semiclassical wave function. Although the scarring is weak on
the octagon, we suggest possible subtle implications of fractals and scars in a
finite universe.Comment: 6 pages, 3 figs, LaTeX fil
New Isotropic and Anisotropic Sudden Singularities
We show the existence of an infinite family of finite-time singularities in
isotropically expanding universes which obey the weak, strong, and dominant
energy conditions. We show what new type of energy condition is needed to
exclude them ab initio. We also determine the conditions under which
finite-time future singularities can arise in a wide class of anisotropic
cosmological models. New types of finite-time singularity are possible which
are characterised by divergences in the time-rate of change of the
anisotropic-pressure tensor. We investigate the conditions for the formation of
finite-time singularities in a Bianchi type universe with anisotropic
pressures and construct specific examples of anisotropic sudden singularities
in these universes.Comment: Typos corrected. Published versio
Magnetic Brane-worlds
We investigate brane-worlds with a pure magnetic field and a perfect fluid.
We extend earlier work to brane-worlds, and find new properties of the Bianchi
type I brane-world. We find new asymptotic behaviours on approach to the
singularity and classify the critical points of the dynamical phase space. It
is known that the Einstein equations for the magnetic Bianchi type I models are
in general oscillatory and are believed to be chaotic, but in the brane-world
model this chaotic behaviour does not seem to be possible.Comment: 21 pages, 3 ps figures; To appear in CQ
Gradient expansion(s) and dark energy
Motivated by recent claims stating that the acceleration of the present
Universe is due to fluctuations with wavelength larger than the Hubble radius,
we present a general analysis of various perturbative solutions of fully
inhomogeneous Einstein equations supplemented by a perfect fluid. The
equivalence of formally different gradient expansions is demonstrated. If the
barotropic index vanishes, the deceleration parameter is always positive
semi-definite.Comment: 17 pages, no figure
Vibration-powered sensing system for engine condition monitoring
Condition monitoring is becoming an established technique for managing the maintenance of machinery in transport applications. Vibration energy harvesting allows wireless systems to be powered without batteries, but most traditional generators have been designed to operate at fixed frequencies. The variety of engine speeds (and hence vibration frequencies) in transport applications therefore means that these are not usable. This paper describes the application-driven specification, design and implementation of a novel vibration-powered sensing system for condition monitoring of engines. This demonstrates that, through careful holistic design of the entire system, condition monitoring systems can be powered solely from machine vibration, managing their energy resources and transmitting sensed data wirelessly
The linearization method and new classes of exact solutions in cosmology
We develop a method for constructing exact cosmological solutions of the
Einstein equations based on representing them as a second-order linear
differential equation. In particular, the method allows using an arbitrary
known solution to construct a more general solution parameterized by a set of
3\textit{N} constants, where \textit{N} is an arbitrary natural number. The
large number of free parameters may prove useful for constructing a theoretical
model that agrees satisfactorily with the results of astronomical observations.
Cosmological solutions on the Randall-Sundrum brane have similar properties. We
show that three-parameter solutions in the general case already exhibit
inflationary regimes. In contrast to previously studied two-parameter
solutions, these three-parameter solutions can describe an exit from inflation
without a fine tuning of the parameters and also several consecutive
inflationary regimes.Comment: 7 page
The Dominant Balance at Cosmological Singularities
We define the notion of a finite-time singularity of a vector field and then
discuss a technique suitable for the asymptotic analysis of vector fields and
their integral curves in the neighborhood of such a singularity. Having in mind
the application of this method to cosmology, we also provide an analysis of the
time singularities of an isotropic universe filled with a perfect fluid in
general relativity.Comment: 13 pages, to appear in the Proceedings of the Greek Relativity
Meeting NEB12, June 29-July 2, 2006, Nauplia, Greec
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