187 research outputs found
Quantum cosmology and late-time singularities
The development of dark energy models has stimulated interest to cosmological
singularities, which differ from the traditional Big Bang and Big Crunch
singularities. We review a broad class of phenomena connected with soft
cosmological singularities in classical and quantum cosmology. We discuss the
classification of singularities from the geometrical point of view and from the
point of view of the behaviour of finite size objects, crossing such
singularities. We discuss in some detail quantum and classical cosmology of
models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus
dust), of models based on the Born-Infeld-type fields and of the model of a
scalar field with a potential inversely proportional to the field itself. We
dwell also on the phenomenon of the phantom divide line crossing in the scalar
field models with cusped potentials. Then we discuss the Friedmann equations
modified by quantum corrections to the effective action of the models under
considerations and the influence of such modification on the nature and the
existence of soft singularities. We review also quantum cosmology of models,
where the initial quantum state of the universe is presented by the density
matrix (mixed state). Finally, we discuss the exotic singularities arising in
the brane-world cosmological models.Comment: final version, published in Classical and Quantum Gravity as a
topical revie
The problem of singularities and chaos in cosmology
We consider different aspects of the problem of cosmological singularity such
as the BKL oscillatory approach to the singularity, the new features of the
cosmological dynamics in the neighbourhood of the singularity in
multidimensional and superstring cosmological models and their connections with
such a modern branch of mathematics as infinite-dimensional Lie algebras. The
chaoticity of the oscillatory approach to the cosmological singularity is also
discussed. The Conclusion contains some thoughts about the past and the future
of the Universe in the light of the oscillatory approach to the Big Bang and
the Big Crunch cosmological singularities.Comment: 17 page
Chameleon Cosmology Model Describing the Phantom Divide Line Crossing
An exact solution describing the evolution of the type Bang-to-Rip with the
phantom divide line crossing is constructed in the Chameleon cosmology model,
based on two independent functions of the scalar field.Comment: 9 page
Cosmological Landscape and Euclidean Quantum Gravity
Quantum creation of the universe is described by the {\em density matrix}
defined by the Euclidean path integral. This yields an ensemble of universes --
a cosmological landscape -- in a mixed quasi-thermal state which is shown to be
dynamically more preferable than the pure quantum state of the Hartle-Hawking
type. The latter is suppressed by the infinitely large positive action of its
instanton, generated by the conformal anomaly of quantum matter. The
Hartle-Hawking instantons can be regarded as posing initial conditions for
Starobinsky solutions of the anomaly driven deSitter expansion, which are thus
dynamically eliminated by infrared effects of quantum gravity. The resulting
landscape of hot universes treated within the cosmological bootstrap (the
self-consistent back reaction of quantum matter) turns out to be limited to a
bounded range of the cosmological constant, which rules out a well-known
infrared catastrophe of the vanishing cosmological constant and suggests an
ultimate solution to the problem of unboundedness of the cosmological action in
Euclidean quantum gravity.Comment: 6 pages, to be published in the Special issue of J. Phys. A dedicated
to the Quantum Theories and Renormalization Group in Gravity and Cosmology
(IRGAC 2006, Barcelona, Spain, 11-15 July 2006
Selection rules for the Wheeler-DeWitt equation in quantum cosmology
Selection of physically meaningful solutions of the Wheeler-DeWitt equation
for the wavefunction in quantum cosmology, can be attained by a reduction of
the theory to the sector of true physical degrees of freedom and their
canonical quantization. The resulting physical wavefunction unitarily evolving
in the time variable introduced within this reduction can then be raised to the
level of the cosmological wavefunction in superspace of 3-metrics. We apply
this technique in several simple minisuperspace models and discuss both at
classical and quantum level physical reduction in {\em extrinsic} time -- the
time variable determined in terms of extrinsic curvature. Only this extrinsic
time gauge can be consistently used in vicinity of turning points and bounces
where the scale factor reaches extremum. Since the 3-metric scale factor is
canonically dual to extrinsic time variable, the transition from the physical
wavefunction to the wavefunction in superspace represents a kind of the
generalized Fourier transform. This transformation selects square integrable
solutions of the Wheeler-DeWitt equation, which guarantee Hermiticity of
canonical operators of the Dirac quantization scheme. Semiclassically this
means that wavefunctions are represented by oscillating waves in classically
allowed domains of superspace and exponentially fall off in classically
forbidden (underbarrier) regions. This is explicitly demonstrated in flat FRW
model with a scalar field having a constant negative potential and for the case
of phantom scalar field with a positive potential. The FRW model of a scalar
field with a vanishing potential does not lead to selection rules for solutions
of the Wheeler-DeWitt equation, but this does not violate Hermiticity
properties, because all these solutions are anyway of plane wave type and
describe cosmological dynamics without turning points and bounces.Comment: final version, to appear in Physical Review
Darkness without dark matter and energy -- generalized unimodular gravity
We suggest a Lorentz non-invariant generalization of the unimodular gravity
theory, which is classically equivalent to general relativity with a locally
inert (devoid of local degrees of freedom) perfect fluid having an equation of
state with a constant parameter . For the range of near this dark
fluid can play the role of dark energy, while for this dark dust admits
spatial inhomogeneities and can be interpreted as dark matter. We discuss
possible implications of this model in the cosmological initial conditions
problem. In particular, this is the extension of known microcanonical density
matrix predictions for the initial quantum state of the closed cosmology to the
case of spatially open Universe, based on the imitation of the spatial
curvature by the dark fluid density. We also briefly discuss quantization of
this model necessarily involving the method of gauge systems with reducible
constraints and the effect of this method on the treatment of recently
suggested mechanism of vacuum energy sequestering.Comment: 11 pages, final version, to be published in Physics Letters
Many-worlds interpretation of quantum theory, mesoscopic anthropic principle and biological evolution
We suggest to combine the Anthropic Principle with the Many-Worlds
Interpretation of Quantum Theory. Realizing the multiplicity of worlds it
provides an opportunity of explanation of some important events which are
assumed to be extremely improbable. The Mesoscopic Anthropic Principle
suggested here is aimed to explain appearance of such events which are
necessary for emergence of Life and Mind. It is complementary to the
Cosmological Anthropic Principle explaining the fine tuning of fundamental
constants. We briefly discuss various possible applications of the Mesoscopic
Anthropic Principle including the Solar Eclipses and assembling of complex
molecules. Besides, we address the problem of Time's Arrow in the framework of
the Many-Worlds Interpretation. We suggest the recipe for disentangling of
quantities defined by fundamental physical laws and by an anthropic selection.
The main emphasis is made on the problem of the biological evolution.Comment: 34 pages, submitted to NeuroQuantology, Special Issue on Everett's
Interpretation. arXiv admin note: substantial text overlap with
arXiv:0705.249
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