16 research outputs found
Non-Linear Relativity in Position Space
We propose two methods for obtaining the dual of non-linear relativity as
previously formulated in momentum space. In the first we allow for the (dual)
position space to acquire a non-linear representation of the Lorentz group
independently of the chosen representation in momentum space. This requires a
non-linear definition for the invariant contraction between momentum and
position spaces. The second approach, instead, respects the linearity of the
invariant contraction. This fully fixes the dual of momentum space and dictates
a set of energy-dependent space-time Lorentz transformations. We discuss a
variety of physical implications that would distinguish these two strategies.
We also show how they point to two rather distinct formulations of theories of
gravity with an invariant energy and/or length scale.Comment: 7 pages, revised versio
Comments on "Note on varying speed of light theories"
In a recent note Ellis criticizes varying speed of light theories on the
grounds of a number of foundational issues. His reflections provide us with an
opportunity to clarify some fundamental matters pertaining to these theories
Bouncing Universes with Varying Constants
We investigate the behaviour of exact closed bouncing Friedmann universes in
theories with varying constants. We show that the simplest BSBM varying-alpha
theory leads to a bouncing universe. The value of alpha increases
monotonically, remaining approximately constant during most of each cycle, but
increasing significantly around each bounce. When dissipation is introduced we
show that in each new cycle the universe expands for longer and to a larger
size. We find a similar effect for closed bouncing universes in Brans-Dicke
theory, where also varies monotonically in time from cycle to cycle.
Similar behaviour occurs also in varying speed of light theories
Quantum symmetry, the cosmological constant and Planck scale phenomenology
We present a simple algebraic argument for the conclusion that the low energy
limit of a quantum theory of gravity must be a theory invariant, not under the
Poincare group, but under a deformation of it parameterized by a dimensional
parameter proportional to the Planck mass. Such deformations, called
kappa-Poincare algebras, imply modified energy-momentum relations of a type
that may be observable in near future experiments. Our argument applies in both
2+1 and 3+1 dimensions and assumes only 1) that the low energy limit of a
quantum theory of gravity must involve also a limit in which the cosmological
constant is taken very small with respect to the Planck scale and 2) that in
3+1 dimensions the physical energy and momenta of physical elementary particles
is related to symmetries of the full quantum gravity theory by appropriate
renormalization depending on Lambda l^2_{Planck}. The argument makes use of the
fact that the cosmological constant results in the symmetry algebra of quantum
gravity being quantum deformed, as a consequence when the limit \Lambda
l^2_{Planck} -> 0 is taken one finds a deformed Poincare invariance. We are
also able to isolate what information must be provided by the quantum theory in
order to determine which presentation of the kappa-Poincare algebra is relevant
for the physical symmetry generators and, hence, the exact form of the modified
energy-momentum relations. These arguments imply that Lorentz invariance is
modified as in proposals for doubly special relativity, rather than broken, in
theories of quantum gravity, so long as those theories behave smoothly in the
limit the cosmological constant is taken to be small.Comment: LaTex, 19 page
New varying speed of light theories
We review recent work on the possibility of a varying speed of light (VSL).
We start by discussing the physical meaning of a varying , dispelling the
myth that the constancy of is a matter of logical consistency. We then
summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz
invariance; bimetric theories (where the speeds of gravity and light are not
the same); locally Lorentz invariant VSL theories; theories exhibiting a color
dependent speed of light; varying induced by extra dimensions (e.g. in the
brane-world scenario); and field theories where VSL results from vacuum
polarization or CPT violation. We show how VSL scenarios may solve the
cosmological problems usually tackled by inflation, and also how they may
produce a scale-invariant spectrum of Gaussian fluctuations, capable of
explaining the WMAP data. We then review the connection between VSL and
theories of quantum gravity, showing how ``doubly special'' relativity has
emerged as a VSL effective model of quantum space-time, with observational
implications for ultra high energy cosmic rays and gamma ray bursts. Some
recent work on the physics of ``black'' holes and other compact objects in VSL
theories is also described, highlighting phenomena associated with spatial (as
opposed to temporal) variations in . Finally we describe the observational
status of the theory. The evidence is currently slim -- redshift dependence in
the atomic fine structure, anomalies with ultra high energy cosmic rays, and
(to a much lesser extent) the acceleration of the universe and the WMAP data.
The constraints (e.g. those arising from nucleosynthesis or geological bounds)
are tight, but not insurmountable. We conclude with the observational
predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio
Observable Effects of Scalar Fields and Varying Constants
We show by using the method of matched asymptotic expansions that a
sufficient condition can be derived which determines when a local experiment
will detect the cosmological variation of a scalar field which is driving the
spacetime variation of a supposed constant of Nature. We extend our earlier
analyses of this problem by including the possibility that the local region is
undergoing collapse inside a virialised structure, like a galaxy or galaxy
cluster. We show by direct calculation that the sufficient condition is met to
high precision in our own local region and we can therefore legitimately use
local observations to place constraints upon the variation of "constants" of
Nature on cosmological scales.Comment: Invited Festscrift Articl
Early Universe Dynamics in Semi-Classical Loop Quantum Cosmology
Within the framework of loop quantum cosmology, there exists a semi-classical
regime where spacetime may be approximated in terms of a continuous manifold,
but where the standard Friedmann equations of classical Einstein gravity
receive non-perturbative quantum corrections. An approximate, analytical
approach to studying cosmic dynamics in this regime is developed for both
spatially flat and positively-curved isotropic universes sourced by a
self-interacting scalar field. In the former case, a direct correspondence
between the classical and semi-classical field equations can be established
together with a scale factor duality that directly relates different expanding
and contracting universes. Some examples of non-singular, bouncing cosmologies
are presented together with a scaling, power-law solution.Comment: 14 pages, In Press, JCA