| [1] |
A. Agnese and R. Festa.
Clues to discretization on the cosmic scale.
Physics Letters A, 227:165, 1997. BibTeX entry, PDF |
| [2] |
Spiros Cotsakis.
Cosmological singularities, 2002.
To be published in the Springer LNP Proceedings of the First Aegean
Summer School of Cosmology held on Samos, Greece, in September 21-29, 2001. BibTeX entry, Available here, Compressed PS
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the mathematical notion of a cosmology is described in some detail and issues related to the range of validity of general relativity are also discussed.
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| [3] |
Maria Vittoria Garzelli and Carlo Giunti.
Bayesian view of solar neutrino oscillations.
Journal of High Energy Physics, 2001(12):017, 2001. BibTeX entry, Available here, PDF
We present the results of a bayesian analysis of solar neutrino data in terms of ν e &to;νμ,τ and ν e &to;ν s oscillations, where ν s is a sterile neutrino. We perform a Rates Analysis of the rates of solar neutrino experiments, including the first SNO CC result, and spectral data of the CHOOZ experiment, and a Global Analysis that takes into account also the Super-Kamiokande day and night electron energy spectra. We show that the bayesian analysis of solar neutrino data does not suffer any problem from the inclusion of the numerous bins of the CHOOZ and Super-Kamiokande electron energy spectra and allows to reach the same conclusions on the favored type of neutrino transitions and on the determination of the most favored values of the oscillation parameters in both the Rates and Global Analysis. Our bayesian analysis shows that ν e &to;ν s transitions are strongly disfavored with respect to ν e &to;νμ,τ transitions. In the case of ν e &to;νμ,τ oscillations, the Large Mixing Angle region is favored by the data (86&percent; probability), the LOW region has some small chance (13&percent; probability), the Vacuum Oscillation region is almost excluded (1&percent; probability) and the Small Mixing Angle region is practically excluded (0.01&percent; probability). We calculate also the marginal posterior probability distributions for tan2 ϑ and Δ m 2 in the case of ν e &to;νμ,τ oscillations and we show that the data imply large mixing almost with certainty and large values of Δ m 2 are favored (2 × 10−6 eV2 < Δ m 2 < 10−3 eV2 with 86&percent; probability). We present also the results of a standard least-squares analysis of solar neutrino data and we show that the standard goodness of fit test is not able to reject pure ν e &to;ν s transitions. The likelihood ratio test, which is insensitive to the number of bins of the CHOOZ and Super-Kamiokande energy spectra, allows to reject pure ν e &to;ν s transitions in favor of ν e &to;νμ,τ transitions only in the Global Analysis.
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| [4] |
J.Thorwart J.J.Halliwell.
Life in an energy eigenstate: Decoherent histories analysis of a
model timeless universe, 2002.
Report-no: IC/TP/1-02/13. BibTeX entry, Available here, Compressed PS
Inspired by quantum cosmology, in which the wave function of the universe is annihilated by the total Hamiltonian, we consider the internal dynamics of a simple particle system in an energy eigenstate. Such a system does not possess a uniquely defined time parameter and all physical questions about it must be posed without reference to time. We consider in particular the question, what is the probability that the system's trajectory passes through a set of regions of configuration space without reference to time? We first consider the classical case, where the answer has a variety of forms in terms of a phase space probability distribution function. We then consider the quantum case, and we analyze this question using the decoherent histories approach to quantum theory, adapted to questions which do not involve time. When the histories are decoherent, the probabilities approximately coincide with the classical case, with the phase space probability distribution replaced by the Wigner function of the quantum state. For some initial states, decoherence requires an environment, and we compute the required influence functional and examine some of its properties. Special attention is given to the inner product used in the construction (the induced or Rieffel inner product), the construction of class operators describing the histories, and the extent to which reparametrization invariance is respected. Our results indicate that simple systems without an explicit time parameter may be quantized using the decoherent histories approach, and the expected classical limit extracted. The results support, for simple models, the usual heuristic proposals for the probability distribution function associated with a semiclassical wave function satisfying the Wheeler-DeWitt equation.
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