149 research outputs found
Bianchi type-II cosmological model: some remarks
Within the framework of Bianchi type-II (BII) cosmological model the behavior
of matter distribution has been considered. It is shown that the non-zero
off-diagonal component of Einstein tensor implies some severe restriction on
the choice of matter distribution. In particular for a locally rotationally
symmetric Bianchi type-II (LRS BII) space-time it is proved that the matter
distribution should be strictly isotropic if the corresponding matter field
possesses only non-zero diagonal components of the energy-momentum tensor.Comment: 3 page
Dynamical Vacuum in Quantum Cosmology
By regarding the vacuum as a perfect fluid with equation of state p=-rho, de
Sitter's cosmological model is quantized. Our treatment differs from previous
ones in that it endows the vacuum with dynamical degrees of freedom. Instead of
being postulated from the start, the cosmological constant arises from the
degrees of freedom of the vacuum regarded as a dynamical entity, and a time
variable can be naturally introduced. Taking the scale factor as the sole
degree of freedom of the gravitational field, stationary and wave-packet
solutions to the Wheeler-DeWitt equation are found. It turns out that states of
the Universe with a definite value of the cosmological constant do not exist.
For the wave packets investigated, quantum effects are noticeable only for
small values of the scale factor, a classical regime being attained at
asymptotically large times.Comment: Latex, 19 pages, to appear in Gen. Rel. Gra
Trace Anomaly and Backreaction of the Dynamical Casimir Effect
The Casimir energy for massless scalar field which satisfies priodic boundary
conditions in two-dimensional domain wall background is calculated by making
use of general properties of renormalized stress-tensor. The line element of
domain wall is time dependent, the trace anomaly which is the nonvanishing
for a conformally invariant field after renormalization,
represent the back reaction of the dynamical Casimir effect.Comment: 8 pages, no figures, typos corrected, discussion added, has been
accepted for the publication in GR
Casimir effect for scalar fields with Robin boundary conditions in Schwarzschild background
The stress tensor of a massless scalar field satisfying Robin boundary
conditions on two one-dimensional wall in two-dimensional Schwarzschild
background is calculated. We show that vacuum expectation value of stress
tensor can be obtained explicitly by Casimir effect, trace anomaly and Hawking
radiation.Comment: 10 pages, no figure
Spinors, Inflation, and Non-Singular Cyclic Cosmologies
We consider toy cosmological models in which a classical, homogeneous, spinor
field provides a dominant or sub-dominant contribution to the energy-momentum
tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a
field were to exist, appropriate choices of the spinor self-interaction would
generate a rich variety of behaviors, quite different from their widely studied
scalar field counterparts. We first discuss solutions that incorporate a stage
of cosmic inflation and estimate the primordial spectrum of density
perturbations seeded during such a stage. Inflation driven by a spinor field
turns out to be unappealing as it leads to a blue spectrum of perturbations and
requires considerable fine-tuning of parameters. We next find that, for simple,
quartic spinor self-interactions, non-singular cyclic cosmologies exist with
reasonable parameter choices. These solutions might eventually be incorporated
into a successful past- and future-eternal cosmological model free of
singularities. In an Appendix, we discuss the classical treatment of spinors
and argue that certain quantum systems might be approximated in terms of such
fields.Comment: 12 two-column pages, 3 figures; uses RevTeX
Monotonic functions in Bianchi models: Why they exist and how to find them
All rigorous and detailed dynamical results in Bianchi cosmology rest upon
the existence of a hierarchical structure of conserved quantities and monotonic
functions. In this paper we uncover the underlying general mechanism and derive
this hierarchical structure from the scale-automorphism group for an
illustrative example, vacuum and diagonal class A perfect fluid models. First,
kinematically, the scale-automorphism group leads to a reduced dynamical system
that consists of a hierarchy of scale-automorphism invariant sets. Second, we
show that, dynamically, the scale-automorphism group results in
scale-automorphism invariant monotone functions and conserved quantities that
restrict the flow of the reduced dynamical system.Comment: 26 pages, replaced to match published versio
Graph Theoretical Characteristics of EEG-Based Functional Brain Networks in Patients With Epilepsy: The Effect of Reference Choice and Volume Conduction
It is well-established that both volume conduction and the choice of recording reference (montage) affect the correlation measures obtained from scalp EEG, both in the time and frequency domains. As a result, a number of correlation measures have been proposed aiming to reduce these effects. In our previous work, we have showed that scalp-EEG based functional brain networks in patients with epilepsy exhibit clear periodic patterns at different time scales and that these patterns are strongly correlated to seizure onset, particularly at shorter time scales (around 3 and 5 h), which has important clinical implications. In the present work, we use the same long-duration clinical scalp EEG data (multiple days) to investigate the extent to which the aforementioned results are affected by the choice of reference choice and correlation measure, by considering several widely used montages as well as correlation metrics that are differentially sensitive to the effects of volume conduction. Specifically, we compare two standard and commonly used linear correlation measures, cross-correlation in the time domain, and coherence in the frequency domain, with measures that account for zero-lag correlations: corrected cross-correlation, imaginary coherence, phase lag index, and weighted phase lag index. We show that the graphs constructed with corrected cross-correlation and WPLI are more stable across different choices of reference. Also, we demonstrate that all the examined correlation measures revealed similar periodic patterns in the obtained graph measures when the bipolar and common reference (Cz) montage were used. This includes circadian-related periodicities (e.g., a clear increase in connectivity during sleep periods as compared to awake periods), as well as periodicities at shorter time scales (around 3 and 5 h). On the other hand, these results were affected to a large degree when the average reference montage was used in combination with standard cross-correlation, coherence, imaginary coherence, and PLI, which is likely due to the low number of electrodes and inadequate electrode coverage of the scalp. Finally, we demonstrate that the correlation between seizure onset and the brain network periodicities is preserved when corrected cross-correlation and WPLI were used for all the examined montages. This suggests that, even in the standard clinical setting of EEG recording in epilepsy where only a limited number of scalp EEG measurements are available, graph-theoretic quantification of periodic patterns using appropriate montage, and correlation measures corrected for volume conduction provides useful insights into seizure onset
Realizations of Real Low-Dimensional Lie Algebras
Using a new powerful technique based on the notion of megaideal, we construct
a complete set of inequivalent realizations of real Lie algebras of dimension
no greater than four in vector fields on a space of an arbitrary (finite)
number of variables. Our classification amends and essentially generalizes
earlier works on the subject.
Known results on classification of low-dimensional real Lie algebras, their
automorphisms, differentiations, ideals, subalgebras and realizations are
reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in
Appendix are correcte
Some remarks on Bianchi type-II, VIII and IX models
Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IX
spacetime it is shown that the off-diagonal components of the corresponding
metric impose severe restrictions on the components of the energy momentum
tensor in general. If the energy momentum tensor is considered to be diagonal
one, the spacetime, expect a partial case of BII, becomes locally rotationally
symmetric.Comment: 8 page
- …