1. A. Woszczyna, W. Czaja, K. Głód, Z. A. Golda, R. A. Kycia, A. Odrzywołek, P. Plaszczyk, L. M. Sokołowski, S. J. Szybka ccgrg: The symbolic tensor analysis package with tools for general relativity Wolfram Library Archive, vol. 8848 (2014). [abstract] [journal] 
Abstract: Riemann and Weyl curvature, covariant derivative, Lie derivative, the first and the second fundamental form on hypersurfaces, as well as basic notions of relativistic hydrodynamics (expansion, vorticity, shear) are predefined functions of the package. New tensors are easy to define. Instructions, basic examples, and some more advanced examples are attached to the package. Characteristic feature of the ccgrg package is the specific coupling between the functional programming and the ParkerChristensen index convention. This causes that no particular tools to rising/lowering tensor indices neither to the tensor contractions are needed. Tensor formulas are written in the form close to that of classical textbooks in GRG, with the only difference that the summation symbol appears explicitly. Tensors are functions, not matrixes, and their components are evaluated lazily. This means that only these components which are indispensable to realize the final task are computed. The memoization technique prevents repetitive evaluation of the same quantities. This saves both, time and memory. 
2. Wojciech Czaja, Zdzislaw A. Golda, Andrzej Woszczyna The acoustic wave equation in the expanding universe. SachsWolfe theorem The Mathematica Journal, vol. 13 (2011). [abstract] [journal] [cdf] 
Abstract: This article considers the acoustic field propagating in the radiationdominated universe of arbitrary space curvature. The field equations are reduced to the d’Alembert equation in an auxiliary static RobertsonWalker spacetime and dispersion relations are discussed.
*supported by the grant from The John Templeton Foundation 
3. Marek Demianski, Zdzislaw A. Golda, Andrzej Woszczyna Evolution of density perturbations in a realistic universe Gen. Rel. Grav., vol. 37, pp. 20632082 (2005). [abstract] [preprint] [journal] 
Abstract: Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matterenergy content of the universe is now dominated by dark energy and dark matter we present the general solution of the equation that describes the evolution of density perturbations in the linear approximation. It turns out that as in the standard CDM model the density perturbations grow very slowly during the radiation dominated epoch and their amplitude increases by a factor of about 4000 in the matter and later dark energy dominated epoch of expansion of the universe.

4. Zdzisław A. Golda, Andrzej Woszczyna, Karolina Zawada Canonical gaugeinvariant variables Acta Phys. Pol., B , vol. B36, p. 2133 (2005). [abstract] [preprint] [journal] 
Abstract: Under an appropriate change of the perturbation variable LifshitzKhalatnikov propagation equations for the scalar perturbation reduce to d'Alembert equation. The change of variables is based on the Darboux transform 
5. G. SiemieniecOzieblo, A. Woszczyna Acoustic instabilities at the transition from the radiationdominated to the matterdominated universe Astron. Astrophys. , vol. 419, pp. 801810 (2004). [abstract] [preprint] [journal] 
Abstract: The transition from acoustic noise in the radiationdominated universe to the density structures in the matter dominated epoch is considered. The initial state is a stochastic field of sound waves moving in different directions. The construction of the initial state is compatible with the hyperbolic type of propagation equation for density perturbations, and parallel to the theory of stochastic background of gravitational waves. Instantaneous transition between the cosmological epochs is assumed, and DarmoisIsrael joining conditions are applied to match solutions for sound waves with growing or decaying modes at the decoupling. As a result a substantial amplification of the low scale structures is obtained.

6. Z. Golda, A.Woszczyna Dispersion of density waves in the early universe with positive cosmological constant Class. Quantum Grav., vol. 20, p. 277 (2003). [abstract] [preprint] [journal] 
Abstract: Density perturbations in the flat (K=0) RobertsonWalker universe with radiation ($p=\epsilon/3$) and positive cosmological constant ($\Lambda>0$) are investigated. The phenomenon of anomalous dispersion of acoustic waves on $\Lambda$ is discussed.
