Gurzadyan's Problem 5 and improvement of softenings for cosmological simulations using the PP method

This paper is devoted to different modifications of two standard softenings of the gravitational attraction (namely the Plummer and Hernquist softenings), which are commonly used in cosmological simulations based on the particle-particle (PP) method, and their comparison. It is demonstrated that some of the proposed alternatives lead to almost the same accuracy as in the case of the pure Newtonian interaction, even despite the fact that the force resolution is allowed to equal half the minimum interparticle distance. The revealed way of precision improvement gives an opportunity to succeed in solving Gurzadyan's Problem 5 and bring modern computer codes up to a higher standard.Comment: 8 pages, 1 figur

Significance of tension for gravitating masses in Kaluza-Klein models

In this letter, we consider the six-dimensional Kaluza-Klein models with spherical compactification of the internal space. Here, we investigate the case of bare gravitating compact objects with the dustlike equation of state $\hat p_0=0$ in the external (our) space and an arbitrary equation of state $\hat p_1=\Omega \hat\varepsilon$ in the internal space, where $\hat \varepsilon$ is the energy density of the source. This gravitating mass is spherically symmetric in the external space and uniformly smeared over the internal space. In the weak field approximation, the conformal variations of the internal space volume generate the admixture of the Yukawa potential to the usual Newton's gravitational potential. For sufficiently large Yukawa masses, such admixture is negligible and the metric coefficients of the external spacetime coincide with the corresponding expressions of General Relativity. Then, these models satisfy the classical gravitational tests. However, we show that gravitating masses acquire effective relativistic pressure in the external space. Such pressure contradicts the observations of compact astrophysical objects (e.g., the Sun). The equality $\Omega =-1/2$ (i.e. tension) is the only possibility to preserve the dustlike equation of state in the external space. Therefore, in spite of agreement with the gravitational experiments for an arbitrary value of $\Omega$, tension ($\Omega=-1/2$) plays a crucial role for the considered models.Comment: 8 pages, no figure

Problematic aspects of Kaluza-Klein excitations in multidimensional models with Einstein internal spaces

We consider Kaluza-Klein (KK) models where internal spaces are compact Einstein spaces. These spaces are stabilized by background matter (e.g., monopole form-fields). We perturb this background by a compact matter source (e.g., the system of gravitating masses) with the zero pressure in the external/our space and an arbitrary pressure in the internal space. We show that the Einstein equations are compatible only if the matter source is smeared over the internal space and perturbed metric components do not depend on coordinates of extra dimensions. The latter means the absence of KK modes corresponding to the metric fluctuations. Maybe, the absence of KK particles in LHC experiments is explained by such mechanism.Comment: 10 pages, no figure

Scalar perturbations in cosmological models with dark energy - dark matter interaction

Scalar cosmological perturbations are investigated in the framework of a model with interacting dark energy and dark matter. In addition to these constituents, the inhomogeneous Universe is supposed to be filled with the standard noninteracting constituents corresponding to the conventional $\Lambda$CDM model. The interaction term is chosen in the form of a linear combination of dark sector energy densities with evolving coefficients. The methods of discrete cosmology are applied, and strong theoretical constraints on the parameters of the model are derived. A brief comparison with observational data is performed.Comment: 10 pages, no figure