Excited states of a string in a time dependent orbifold

We present analytical results on the propagation of a classical string in non-zero modes through the singularity of the compactified Milne space. We restrict our analysis to a string winding around the compact dimension of spacetime. The compact dimension undergoes contraction to a point followed by re-expansion. We demonstrate that the classical dynamics of the string in excited states is non-singular in the entire spacetime.Comment: Version accepted for publication in Class. Quantum Gra

Propagation of a string across the cosmological singularity

Our results concern the transition of a quantum string through the singularity of the compactified Milne (CM) space. We restrict our analysis to the string winding around the compact dimension (CD) of spacetime. The CD undergoes contraction to a point followed by re-expansion. We demonstrate that both classical and quantum dynamics of considered string are well defined. Most of presently available calculations strongly suggest that the singularity of a time dependent orbifold is useless as a model of the cosmological singularity. We believe that our results bring, to some extent, this claim into question.Comment: 9 pages, 2 figures, revtex4; version accepted for publication in Class. Quantum Gra

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

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

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

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

Reduced phase space approach to Kasner universe and the problem of time in quantum theory

We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of Dirac observables and an internal clock. We obtain the physical Hilbert space, which is the carrier space of the self-adjoint representation of the Dirac observables. Then we discuss the problem of time. We demonstrate that the inclusion of evolution in a gravitational system, at classical level as well as at quantum level, leads respectively to canonically and unitarily inequivalent theories. The example of Hubble operator in two different clock variables and with two distinct spectra is given.Comment: 24 page

Singularity resolution depends on the clock

We study the quantum cosmology of a flat Friedmann–Lemaître–Robertson–Walker Universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the action, as in unimodular gravity. We study two versions of the quantum theory: the first is based on a time coordinate conjugate to the radiation/dark energy matter component, i.e., conformal time (for radiation) or unimodular time. As shown by Gryb and Thébault, this quantum theory achieves a type of singularity resolution; we illustrate this and other properties of this theory. The theory is then contrasted with a second type of quantisation in which the logarithm of the scale factor serves as time, which has been studied in the context of the 'perfect bounce' for quantum cosmology. Unlike the first quantum theory, the second one contains semiclassical states that follow classical trajectories and evolve into the singularity without obstruction, thus showing no singularity resolution. We discuss how a complex scale factor best describes the semiclassical dynamics. This cosmological model serves as an illustration of the problem of time in quantum cosmology

Detection of maturity and ligament injury using magic angle directional imaging

Purpose: To investigate whether magnetic field–related anisotropies of collagen may be correlated with postmortem findings in animal models. Methods: Optimized scan planning and new MRI data‐processing methods were proposed and analyzed using Monte Carlo simulations. Six caprine and 10 canine knees were scanned at various orientations to the main magnetic field. Image intensities in segmented voxels were used to compute the orientation vectors of the collagen fibers. Vector field and tractography plots were computed. The Alignment Index was defined as a measure of orientation distribution. The knees were subsequently assessed by a specialist orthopedic veterinarian, who gave a pathological diagnosis after having dissected and photographed the joints. Results: Using 50% less scans than reported previously can lead to robust calculation of fiber orientations in the presence of noise, with much higher accuracy. The 6 caprine knees were found to range from very immature ( 3 years). Mature specimens exhibited significantly more aligned collagen fibers in their patella tendons compared with the immature ones. In 2 of the 10 canine knees scanned, partial cranial caudal ligament tears were identified from MRI and subsequently confirmed with encouragingly high consistency of tractography, Alignment Index, and dissection results. Conclusion: This method can be used to detect injury such as partial ligament tears, and to visualize maturity‐related changes in the collagen structure of tendons. It can provide the basis for new, noninvasive diagnostic tools in combination with new scanner configurations that allow less‐restricted field orientations