Перегляд за Автор "Canay, Ezgi"

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  • Ескіз
    Документ
    Effect of the Cubic Torus Topology on Cosmological Perturbations
    (2021) Eingorn, Maxim; Canay, Ezgi; Metcalf, Jacob M.; Brilenkov, Maksym; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр Иванович
    We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula, we express the Yukawa potentials via Ewald sums. We show that for the present Universe, both the bare summation of Yukawa potentials and the Yukawa-Ewald sums require smaller numbers of terms to yield the numerical values of the potential and the force up to desired accuracy. Nevertheless, the Yukawa formula is yet preferable owing to its much simpler structure.
  • Ескіз
    Документ
    Effects of nonlinearity of f (R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification
    (2020) Canay, Ezgi; Eingorn, Maxim; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр Иванович
    We study the effects associated with nonlinearity of f (R) gravity and of the background perfect fluid manifested in the Kaluza–Klein model with spherical compactification. The background space-time is perturbed by a massive gravitating source which is pressureless in the external space but has an arbitrary equation of state (EoS) parameter in the internal space. As characteristics of a nonlinear perfect fluid, the squared speeds of sound are not equal to the background EoS parameters in the external and internal spaces. In this setting, we find exact solutions to the linearized Einstein equations for the perturbed metric coefficients. For nonlinear models with f (R0) = 0, we show that these coefficients acquire correction terms in the form of two summed Yukawa potentials and that in the degenerated case, the solutions are reduced to a single Yukawa potential with some “corrupted” prefactor (in front of the exponential function), which, in addition to the standard 1/r term, contains a contribution independent of the three-dimensional distance r . In the linear f (R) = 0 model, we generalize the previous studies to the case of an arbitrary nonlinear perfect fluid. We also investigate the particular case of the nonlinear background perfect fluid with zero speed of sound in the external space and demonstrate that a non-trivial solution exists only in the case of f (R0) = 0.
  • Ескіз
    Документ
    Gravitational Interaction in the Chimney Lattice Universe †
    (2021) Eingorn, Maxim; McLaughlin II, Andrew; Canay, Ezgi; Brilenkov, Maksym; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр Иванович
    We investigate the influence of the chimney topology T T R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.
  • Ескіз
    Документ
    Scalar and vector perturbations in a universe with nonlinear perfect fluid
    (2021) Canay, Ezgi; Ruslan, Brilenkov; Eingorn, Maxim; Arapo˘glu, A. Savas; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр Иванович
    We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.