7 research outputs found
Bianchi I model in terms of nonstandard loop quantum cosmology: Quantum dynamics
We analyze the quantum Bianchi I model in the setting of the nonstandard loop
quantum cosmology. Elementary observables are used to quantize the volume
operator. The spectrum of the volume operator is bounded from below and
discrete. The discreteness may imply a foamy structure of spacetime at
semiclassical level. The results are described in terms of a free parameter
specifying loop geometry to be determined in astro-cosmo observations. An
evolution of the quantum model is generated by the so-called true Hamiltonian,
which enables an introduction of a time parameter valued in the set of all real
numbers.Comment: 18 pages, version accepted for publication by Class. Quant. Gra
Simple model of big-crunch/big-bang transition
We present classical and quantum dynamics of a test particle in the
compactified Milne space. Background spacetime includes one compact space
dimension undergoing contraction to a point followed by expansion. Quantization
consists in finding a self-adjoint representation of the algebra of particle
observables. Our model offers some insight into the nature of the cosmic
singularity.Comment: 17 pages, no figures, RevTeX4, accepted for publication in Class.
Quantum Gra
Turning Big Bang into Big Bounce: I. Classical Dynamics
The big bounce (BB) transition within a flat Friedmann-Robertson-Walker model
is analyzed in the setting of loop geometry underlying the loop cosmology. We
solve the constraint of the theory at the classical level to identify physical
phase space and find the Lie algebra of the Dirac observables. We express
energy density of matter and geometrical functions in terms of the observables.
It is the modification of classical theory by the loop geometry that is
responsible for BB. The classical energy scale specific to BB depends on a
parameter that should be fixed either by cosmological data or determined
theoretically at quantum level, otherwise the energy scale stays unknown.Comment: 14 pages, 1 figure, version accepted for publication in Physical
Review
Dirac quantization of membrane in time dependent orbifold
We present quantum theory of a membrane propagating in the vicinity of a time
dependent orbifold singularity. The dynamics of a membrane, with the parameters
space topology of a torus, winding uniformly around compact dimension of the
embedding spacetime is mathematically equivalent to the dynamics of a closed
string in a flat FRW spacetime. The construction of the physical Hilbert space
of a membrane makes use of the kernel space of self-adjoint constraint
operators. It is a subspace of the representation space of the constraints
algebra. There exist non-trivial quantum states of a membrane evolving across
the singularity.Comment: 16 pages, no figures, version accepted for publication in Journal of
High Energy Physic
Turning big bang into big bounce: II. Quantum dynamics
We analyze the big bounce transition of the quantum FRW model in the setting
of the nonstandard loop quantum cosmology (LQC). Elementary observables are
used to quantize composite observables. The spectrum of the energy density
operator is bounded and continuous. The spectrum of the volume operator is
bounded from below and discrete. It has equally distant levels defining a
quantum of the volume. The discreteness may imply a foamy structure of
spacetime at semiclassical level which may be detected in astro-cosmo
observations. The nonstandard LQC method has a free parameter that should be
fixed in some way to specify the big bounce transition.Comment: 14 pages, no figures, version accepted for publication in Class.
Quant. Gra