RESEARCH GROUP

MATHEMATICAL STRUCTURES OF THE UNIVERSE

Selected publications

 
   
   
   
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61. Andrzej Woszczyna
Dispersion of density waves in the Universe with positive cosmological constant
Conference report (2008).
[abstract] [Mathematica 5.2]

Abstract:
Marie Curie Host Fellowships for the Transfer of Knowledge (TOK) Project MTKD-CT-2005-029466: PARTICLE PHYSICS AND COSMOLOGY: THE INTERFACE, Fourth Workshop 13.02 - 16.02.2008, Warszawa

62. Sebastian J. Szybka
Chaos, Gravity and Wave Maps with Target SU(2)
Proceedings of the MG11 Meeting on General Relativity (2008).
[abstract] [journal]

Abstract:
We present the numerical evidence for chaotic solutions and fractal threshold behavior in the Einstein equations coupled to a wave map (with target SU(2)). This phenomenon is explained in terms of heteroclinic intersections.

63. Leszek M. Sokołowski
Metric gravity theories and cosmology: I. Physical interpretation and viability.
Class. Quantum Grav., vol. 24, pp. 3391-3411 (2007).
[abstract] [preprint]

Abstract:
We critically review some concepts underlying current applications of gravity theories with Lagrangians depending on the full Riemann tensor to cosmology. We argue that it is impossible to reconstruct the underlying Lagrangian from the observational data: the Robertson-Walker spacetime is so simple and "flexible" that any cosmic evolution may be fitted by infinite number of Lagrangians. Confrontation of a solution with the astronomical data is obstructed by the existence of many frames of dynamical variables and the fact that initial data for the gravitational triplet depend on which frame is minimally coupled to ordinary matter. Prior to any application it is necessary to establish physical contents and viability of a given gravity theory. A theory may be viable only if it has a stable ground state. We provide a method of checking the stability and show in eleven examples that it works effectively.

64. Leszek M. Sokołowski
Metric gravity theories and cosmology: II. Stability of a ground state in f(R) theories.
Class. Quantum Grav., vol. 24, pp. 3713-3734 (2007).
[abstract] [preprint]

Abstract:
A fundamental criterion of viability of any gravity theory is existence of a stable ground-state solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary.

65. Leszek Pysiak
Time Flow in a Noncommutative Regime
International Journal of Theoretical Physics, vol. 46, pp. 16-30 (2007).
[abstract] [journal] [download]

Abstract:
We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics, initiated in the paper (Heller et al. (2005) International Journal Theoretical Physics 44, 671). We construct the von Neumann algebra M of random operators on a groupoid, which now is not related to a finite group G, but is the pair groupoid of the Lorentzian frame bundle E over spacetime M. We consider the time flow on M depending on the state f . The state f defining the noncommutative dynamics is assumed to be normal and faithful. Then the pair (M, f)() is a noncommutative probabilistic space and f can also be interpreted as an equilibrium thermal state, satisfying the Kubo-Martin-Schwinger condition. We argue that both the “time flow” and thermodynamics have their common roots in the noncommutative unification of dynamics and probability.

66. M. Heller, Z. Odrzygóźdź, L. Pysiak, W. Sasin
Anatomy of Malicious Singularities
Journal of Mathematical Physics, vol. 48, pp. 092504-092511 (2007).

Abstract:
Abstract

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