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1. Krzysztof Głód, Szymon Sikora, Sebastian J. Szybka Example of crosspolarized standing gravitational waves Phys. Rev. D: Part. Fields , vol. 106, p. 124022 (2022). [abstract] [preprint] [journal] [download]  Abstract: We use a cosmological counterpart of the cylindrical Halilsoy solution to illustrate properties of crosspolarized standing gravitational waves.  2. Szymon Sikora, Krzysztof Głód Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude The European Physical Journal C, vol. 81, p. 208 (2021). [abstract] [preprint] [journal]  Abstract: We construct an approximate solution to the
cosmological perturbation theory around Einstein–de Sitter
background up to the fourthorder perturbations. This could
be done with the help of the specific symmetry condition
imposed on the metric, from which follows that the model
density forms an infinite, cubic lattice. To verify the convergence of the perturbative construction, we express the resulting metric as a polynomial in the perturbative parameter and calculate the exact Einstein tensor. In our model, it seems
that physical quantities averaged over large scales overlap
with the respective Einstein–de Sitter prediction, while local
observables could differ significantly from their background
counterparts. As an example, we analyze the behavior of the local measurements of the Hubble constant and compare them with the Hubble constant of the homogeneous background model. A difference between these quantities is important in the context of a current Hubble tension problem.  3. Szymon Sikora, Krzysztof Głód Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities Phys. Rev. D: Part. Fields , vol. 99, p. 083512 (2019). [abstract] [preprint] [journal]  Abstract: We constructed a simple cosmological model which approximates the Einsteinde Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter λ, we are able to achieve large values of the density contrast. With a metric explicitly given, many model properties can be calculated in a straightforward way which is interesting in the context of the current discussion concerning the averaging of the inhomogeneities and their backreaction in cosmology. Although the Einsteinde Sitter model can be thought of as the model average, the light propagation differs from that of Einsteinde Sitter. The angular diameter distanceredshift relation is affected by the presence of inhomogeneities and depends on the observer’s position. The model construction scheme enables some generalizations in the future, so the present work is a step toward more realistic cosmological model described by a relatively simple analytical metric.  4. Sikora S., Bratek Ł., Jałocha J., Kutschera M. The influence of the velocity dispersion on the velocitydensity relation in the disk model of the galaxy Acta Phys. Pol., B , vol. 48, p. 2071 (2017). [abstract] [journal]  Abstract: Taking the velocity dispersion term into account in the Jeans equation describing the disk model, counterintuitively allows to reduce the local masstolight ratio at the outskirts of flattened galaxies, and stop the unbound growth of mass function. This is possible thanks to a more intertwined relation between the gravitational potential and the rotation curve than for spheroidal systems. This effect is illustrated on the example of
galaxy UGC 6446 by finding iteratively the column mass density from the rotation curve supplemented with an isotropic velocity dispersion profile in the disk plane. Along with galactic magnetic fields, this effect would allow to reduce the local masstolight ratio at the galactic outskirts.  5. Szymon Sikora, Krzysztof Głód Example of an inhomogeneous cosmological model in the context of backreaction Phys. Rev. D: Part. Fields , vol. 95, p. 063517 (2017). [abstract] [preprint] [journal]  Abstract: In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein–de Sitter background with periodically distributed dust overdensities. The model construction enables application of the GreenWald averaging scheme and the Buchert averaging technique simultaneously. We compare the angular diameter distance function of the considered model to the angular diameter distances corresponding to the average spacetimes given by the GreenWald and the Buchert frameworks respectively.  6. Jałocha J., Bratek Ł., Pękala J., Sikora S., Kutschera M. Magnetic flux density from the relative circular motion of stars and partially ionized gas in the Galaxy midplane vicinity Astrophys J. , vol. 833, p. 174 (2016). [abstract] [preprint] [journal]  Abstract: Observations suggest a slower stellar rotation relative to gas rotation in the outer part of the Milky Way Galaxy. This difference could be attributed to an interaction with the interstellar magnetic field. In a simple model, fields of order 10 micro Gauss are then required, consistently with the observed values. This coincidence suggests a tool for estimating magnetic fields in spiral galaxies. A NorthSouth asymmetry in the rotation of gas in the Galaxy could be of magnetic origin too.  
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