RESEARCH GROUP

MATHEMATICAL STRUCTURES OF THE UNIVERSE

#### Selected publications

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 7. Zdzislaw A. Golda, Andrzej WoszczynaA field theory approach to cosmological density perturbationsPhys. Lett. A , vol. 310, pp. 357-362 (2003). [abstract] [preprint] [journal] Abstract:Adiabatic perturbations propagate in the expanding universe like scalar massless fields in some effective Robertson-Walker space-time. 8. Zdzislaw A. Golda, Andrzej WoszczynaAcoustics of early universe. I. Flat versus open universe modelsClass. Quant. Grav., vol. 18, pp. 543-554 (2001). [abstract] [preprint] [journal] Abstract:A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $\omega_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the perturbations spectrum is discussed 9. Zdzislaw A. Golda, Andrzej WoszczynaAcoustics of early universe. II. Lifshitz vs. gauge-invariant theoriesJ. Math. Phys., vol. 42, pp. 856-862 (2001). [abstract] [preprint] [journal] Abstract:Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character. 10. Grazyna Siemieniec-Ozieblo, Andrzej WoszczynaOrder reduction in semiclassical cosmologyPhys. Rev. D, vol. 59, p. 083504 (1999). [abstract] [preprint] [journal] Abstract:We investigate the Robertson-Walker cosmology with Lagrangian $R+\alpha_1\hbar R^2+\alpha_2\hbar R^{\mu\nu}R_{\mu\nu} +L_{rad}$ where $L_{rad}$ means classical source with traceless energy-momentum tensor. We weaken the self-consistence condition (L. Parker, J. Z. Simon, Phys. Rev. {D47}(1993),{1339}). Quantum corrections are expressed as contributions to the effective equation of state. We show that the empty space-time is stable within the class of radiation-filled expanding universes with no order reduction of the field equations. 11. David H Lyth, Andrzej WoszczynaLarge scale perturbations in the open universePhys. Rev. D, vol. 52, pp. 3338-3357 (1995). [abstract] [preprint] [journal] Abstract:When considering perturbations in an open (Omega<1) universe, cosmologists retain only sub-curvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than -1 in units of the curvature scale, in contrast with the super-curvature modes whose eigenvalue is between -1 and 0). Mathematicians have known for almost half a century that all modes must be included to generate the most general HOMOGENEOUS GAUSSIAN RANDOM FIELD, despite the fact that any square integrable FUNCTION can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. The mathematics is here explained in a language accessible to physicists. Then it is pointed out that if the perturbations originate as a vacuum fluctuation of a scalar field there will be no super-curvature modes in nature. Finally the effect on the cmb of any super-curvature contribution is considered, which generalizes to Omega<1 the analysis given by Grishchuk and Zeldovich in 1978. A formula is given, which is used to estimate the effect. In contrast with the case Omega=1, the effect contributes to all multipoles, not just to the quadrupole. It is important to find out whether it has the same l dependence as the data, by evaluating the formula numerically. 12. Andrzej Woszczyna A dynamical systems approach to the cosmological structure formation - Newtonian universe Mon. Not. R.A.S., vol. 225, p. 701 (1992). [journal] Abstract:Abstract
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