Abstract:
In this paper we calculate the particle creation as seen by a stationary observer in an anisotropic universe. By using an observer and geometry dependent time to quantise a massive scalar field we show that a discrete energy spectrum shift occurs. The length scale associated with the geometry provides the energy scale by which the spectrum is shifted. The $\beta(p,q)$ coefficient for the Bogolubov transformation calculated is proportional to a series of delta functions whose argument contains $p$ and $q$ and half multiples of the root of the curvature.

Abstract:
We study the realisation of supersymmetric discrete flavour symmetry models to the thermal history of our universe. We focus on the evolution of the pseudo moduli field among the flavons by taking into account finite temperature corrections. We show that the pseudo moduli flavon dominates the energy density of our universe and this domination makes crucially difficult to realise the flavour symmetry models in our universe. We also discuss possible extensions of the supersymmetric discrete flavour symmetry models which can ensure the consistency of the models with the thermal history of our universe. Finally, we show an extension to realise the thermal inflation by the flavon domination.

Abstract:
The Mirror Matter or Exact Parity Model sees every standard particle, including the physical neutral Higgs boson, paired with a parity partner. The unbroken parity symmetry forces the mass eigenstate Higgs bosons to be maximal mixtures of the ordinary and mirror Higgs bosons. Each of these mass eigenstates will therefore decay 50% of the time into invisible mirror particles, providing a clear and interesting signature for the Large Hadron Collider (LHC) which could thus establish the existence of the mirror world. However, for this effect to be observable the mass difference between the two eigenstates must be sufficiently large. In this paper, we study cosmological constraints from Big Bang Nucleosynthesis on the mass difference parameter. We find that the temperature of the radiation dominated (RD) phase of the universe should never have exceeded a few 10's of GeV if the mass difference is to be observable at the LHC. Chaotic inflation with very inefficient reheating provides an example of how such a cosmology could arise. We conclude that the LHC could thus discover the mirror world and simultaneously establish an upper bound on the temperature of the RD phase of the universe.

Abstract:
We discuss a model for a universe with discrete matter content instead of the continuous perfect fluid taken in FRW models. We show how the redshift in such a universe deviates from the corresponding one in an FRW cosmology. This illustrates the fact that averaging the matter content in a universe and then evolving it in time, is not the same as evolving a universe with discrete matter content. The main reason for such deviation is the fact that the photons in such a universe mainly travel in an empty space rather than the continuous perfect fluid in FRW geometry.

Abstract:
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat spatial sections, these multiple images can be accommodated within any of the six classes of compact orientable 3-dimensional flat space forms. Moreover, the discovery of two more triples of multiple images in the neighbourhood of the first one, would allow the determination of the topology of the Universe, and in most cases the determination of its size.

Abstract:
In this paper a new proof is given for the supermodularity of information content. Using the decomposability of the information content an algorithm is given for discovering the Markov network graph structure endowed by the pairwise Markov property of a given probability distribution. A discrete probability distribution is given for which the equivalence of Hammersley-Clifford theorem is fulfilled although some of the possible vector realizations are taken on with zero probability. Our algorithm for discovering the pairwise Markov network is illustrated on this example, too.

Abstract:
We investigate the possibility of using the ratio between the 2-10 keV flux and the [Ne V]3426 emission line flux (X/NeV) as a diagnostic diagram to discover heavily obscured, possibly Compton-Thick Active Galactic Nuclei (AGN) up to z~1.5. First, we calibrate a relation between X/NeV and the cold absorbing column density N_H using a sample of 74 bright, nearby Seyferts with both X-ray and [Ne V] data available in the literature. Similarly to what is found for the X-ray to [O III]5007 flux ratio (X/OIII), we found that the X/NeV ratio decreases towards large column densities. Essentially all local Seyferts with X/NeV values below 15 are found to be Compton-Thick objects. Second, we apply this diagnostic diagram to different samples of distant obscured and unobscured QSOs in the SDSS: blue, unobscured, type-1 QSOs in the redshift range z=[0.1-1.5] show X/NeV values typical of unobscured Seyfert 1s in the local Universe. Conversely, SDSS type-2 QSOs at z~0.5 classified either as Compton-Thick or Compton-Thin on the basis of their X/OIII ratio, would have been mostly classified in the same way based on the X/NeV ratio. We apply the X/NeV diagnostic diagram to 9 SDSS obscured QSOs in the redshift range z=[0.85-1.31], selected by means of their prominent [Ne V]3426 line and observed with Chandra ACIS-S for 10ks each. Based on the X/NeV ratio, complemented by X-ray spectral analysis, 2 objects appear good Compton-Thick QSO candidates, 4 objects appear as Compton-Thin QSOs, while 3 have an ambiguous classification. When excluding from the sample broad lined QSOs with a red continuum and thus considering only genuine narrow-line objects, the efficiency in selecting Compton-Thick QSOs through the [Ne V] line is about 50% (with large errors, though), more similar to what is achieved with [O III] selection. [abridged]

Abstract:
The geometric structure of Friedmann universe in the discrete space time is researched. It is proved that the dust matter which forms the Friedmann universe is not distributed on the Friedmann spacetime points. The geodesic motion equations of test particles are derived, and the effects of clock and frequency shift are revealed.

Abstract:
A quantum model of universe is constructed in which values of dimensionless coupling constants of the fundamental interactions (including the cosmological constant) are determined via certain topological invariants of manifolds forming finite ensembles of 3D Seifert fibrations. The characteristic values of the coupling constants are explicitly calculated as the set of rational numbers (up to the factor $2\pi$) on the basis of a hypothesis that these values are proportional to the mean relative fluctuations of discrete volumes of manifolds in these ensembles. The discrete volumes are calculated using the standard Alexandroff procedure of constructing $T_0$-discrete spaces realized as nerves corresponding to characteristic canonical triangulations which are compatible with the Milnor representation of Seifert fibered homology spheres being the building material of all used 3D manifolds. Moreover, the determination of all involved homology spheres is based on the first nine prime numbers ($p_1=2, >..., p_9=23$). The obtained hierarchy of coupling constants at the present evolution stage of universe well reproduces the actual hierarchy of the experimentally observed dimensionless low-energy coupling constants.

Abstract:
We summarize results of the 1996 Snowmass workshop on future prospects for discovering dynamical electroweak symmetry breaking, compositeness, and anomalous couplings of quarks at colliders. We present the mass reach of the Tevatron to a color singlet or octet technirho, and to a topgluon or topcolor Z' from topcolor assisted technicolor. We explore the sensitivity of the Tevatron, LHC, NLC, and VLHC to contact interactions and excited fermions. Finally we investigate the possibility of seeing anomalous couplings of quarks at the Tevatron and LHC.