Effect of the Cubic Torus Topology on Cosmological Perturbations

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.

Cosmological constant, axial anomalies and photon mass dynamos from chiral Fermionic torsion

Motivated by Palle’s investigation on the handness of chirality of vorticity in Einstein–Cartan cosmology [Entropy 5 (2014)], several aspects of chiral torsional handness in magnetogenesis and cosmology are presented. In the first one, we obtain torsion bounds from massive photons and axial anomalies. In the second, we deal with magnetogenesis from photon mass and in the third, we discuss chiral torsion degrees of freedom to obtain a torsion cosmological constant dependent solution. The torsion solution decays fast and implies a strong suppression of torsion at present universe. Our result contains the Poplawski [Phys. Lett. B (2010)] results in the case axial torsion vector associated to Einstein–Cartan fermionic sector matter and conformal anomalies of quarks. In the third example, a magnetic field bound from chiral torsionic dynamos is obtained as [Formula: see text]. In the non-minimal cosmological models, chiral dynamos are sourced by massive photons, London currents and chiral magnetic effect (CME). Chiral chemical potential is found to be mimic by torsion. Cosmological constant bound [Formula: see text] is found. At the early universe, the cosmological constant [Formula: see text] is obtained. Torsion used in the present universe is [Formula: see text]. In the last and fourth example, chiral anisotropic currents are obtained and magnetic helicity is shown to depend upon torsion when the chiral chemical potential is non-constant.

A probe of cosmological models in modified teleparallel gravity

In this paper, we have investigated the physical behavior of cosmological models in modified Teleparallel gravity with a general function [Formula: see text] where [Formula: see text] and [Formula: see text] are model parameters and [Formula: see text] is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. We have derived the deceleration parameter [Formula: see text] in terms of equation of state (EoS) parameter [Formula: see text] and Hubble parameter [Formula: see text]. We have investigated the variation of [Formula: see text] over the observed values of Hubble constant in various observations within the range of redshift [Formula: see text]. Also, we have studied effective energy density [Formula: see text], effective pressure [Formula: see text] and effective EoS parameter [Formula: see text]. We have observed that the second term of [Formula: see text] function behaves just like variable cosmological term [Formula: see text] ([Formula: see text]) at late-time universe and causes the acceleration in expansion and works just like dark energy candidates. Also, we have evaluated the age of the present universe for various stages of matter [Formula: see text] and various [Formula: see text] functions.

Cosmological models with a hybrid scale factor

In this paper, we present some cosmological models with a hybrid scale factor (HSF) in the framework of general relativity (GR). The HSF fosters an early deceleration as well as a late-time acceleration and mimics the present Universe. The dynamical aspects of different cosmological models with HSF in the presence of different matter fields have been discussed.

Gravitational Interaction in the Chimney Lattice Universe

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.

Lyra’s cosmology of homogeneous and isotropic universe in Brans–Dicke theory

In this paper, we investigate a scalar field Brans–Dicke cosmological model in Lyra’s geometry which is based on the modifications in a geometrical term as well as energy term of Einstein’s field equations. We have examined the validity of the proposed cosmological model on the observational scale by performing statistical analysis from the latest [Formula: see text] and SN Ia observational data. We find that the estimated values of Hubble’s constant and matter energy density parameter is in agreement with their corresponding values, obtained from recent observations of Wilkinson Microwave Anisotropy Probe (WMAP) and Plank collaboration. We also derived the deceleration parameter, age of the universe and jerk parameter in terms of red-shift and computed its present values. The dynamics of the deceleration parameter in the derived model of the universe show a signature flipping from positive to a negative value and also indicate that the present universe is in the accelerating phase.

Applying Friedmann models to describe the evolution of the Universe based on data from the SAI Supernovae Catalog

In the recent years thanks to the modern and sophisticated technologies the astronomers and astrophysicists were able to look deep into the Universe. This vast data poses some new problem to the cosmologists. One of the problems is to develop an adequate theory. Another one is to fit the theoretical results with the observational one. In this report within the scope of the isotropic and homogeneous Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological model we study the evolution of the Universe filled with dust or cosmological constant. The reason to consider this model is the present universe surprisingly homogeneous and isotropic in large scale. We also compare our results with the data from the SAI Supernovae Catalog. Since the observational data are given in terms of Hubble constant (????) and redshift (????) we rewrite the corresponding equations as a functions of ????. The task is to find the set of parameters for the mathematical model of an isotropic and homogeneous Universe that fits best with the astronomical data obtained from the study of supernovae: magnitude (????), redshift (????).