Abstract: A mathematical model of the cosmological evolution of statistical systems of scalarly charged particles with Higgs scalar interaction is formulated and investigated. Examples are given of numerical modeling of such systems, revealing their very remarkable properties, in particular, the formation of paired bursts of cosmological acceleration. PubDate: 2020-10-01

Abstract: A new model is constructed for the Big Bang and the expansion of the Universe, based on a description of a spread of a finite mass of ideal (nonviscous and non-heat-conducting) gas from a point (“initial hot singularity”) to empty space in the framework of general and special relativity (GR and SR). That is, the expansion began inside the sphere with the gravitational radius of the Universe. At first sight, such a spread, like a spread of the singularity of a black hole, is impossible. However, a fundamental difference is that a black hole results from a collapse of a massive star after complete burning of its thermonuclear fuel. Therefore, although at a collapse the temperature, pressure and density grow infinitely, this growth is such that the gravitational forces in the course of compression are always larger than the resisting high pressure. Everything is the opposite at a spread of the initial hot singularity because of the huge (at the beginning of the spread) energy and pressure of all kinds of massless (with zero rest mass) and massive particles and antiparticles, under a negligible contribution of the excess (over antibaryons and positrons) baryons and electrons. In the process of spreading, the situation changes, and the energy of the atoms formed by these baryons and electrons becomes dominant. PubDate: 2020-10-01

Abstract: We study the early inflationary phase of the universe driven by noncanonical scalar field models using an exponential potential. The noncanonical scalar field models are represented by Lagrangian densities containing square and square-root kinetic corrections to the canonical Lagrangian density. We investigate the Lie symmetry of the homogeneous scalar field equations obtained from noncanonical Lagrangian densities and find only a one-parameter Lie point symmetry for both canonical and noncanonical scalar field equations. We use the Lie symmetry generator to obtain an exact analytical group-invariant solution of the homogeneous scalar field equations from an invariant curve condition. The solutions obtained are consistent and satisfy the Friedmann equations subject to constraint conditions on the potential parameter \(\lambda\) for the canonical case and on the parameter \(\mu\) for the noncanonical case. In this scenario, we obtain the values of various inflationary parameters and make useful checks on the observational constraints on the parameters from Planck data by imposing a set of bounds on the parameters \(\lambda\) and \(\mu\) . The results for the scalar spectral index ( \(n_{S}\) ) and the tensor-to-scalar ratio ( \(r\) ) are presented in the \((n_{S},r)\) plane in the background of Planck-2015 and Planck-2018 data for noncanonical cases and are in good agreement with cosmological observations. For theoretical completeness of the noncanonical models, we verify that the noncanonical models under consideration are free from ghosts and Laplacian instabilities. We also treat the noncanonical scalar field model equations for two power-law (kinetic) corrections by the dynamical system theory. We provide useful checks on the stability of the critical points for both cases and show that the group-invariant analytical noncanonical inflation solutions are stable attractors in phase space. PubDate: 2020-10-01

Abstract: It is known than the inclusion of spatial curvature can modify the evolution of matter perturbations and affect the Large Scale Structure (LSS) formation. We quantify the effects of the nonzero spatial curvature in terms of LSS formation for a cosmological model with a running vacuum energy density and a warm dark matter component. The evolution of density perturbations and the modified shape of their power spectrum are constructed and analyzed. PubDate: 2020-10-01

Abstract: We propose a possibility of qualitatively taking into account the mutual influence of two gravitationally interacting null strings (thin tubes of a massless scalar field) on the motion of each of them. It is shown that it is possible to implement a self-consistent motion of two null strings in which their mutual gravitational influence leads to vibrations of each string inside a bounded spatial region. Such systems of gravitationally interacting null strings can be considered as primary particles in a null string gas with a nonzero rest mass. Gravitationally interacting primary particles can combine into more complex formations, “macro” objects. A peculiar feature of such “macro” formations in the null string gas is the fundamental impossibility of having a completely formed structure (in the null string gas, there are inevitable processes leading to a random (dynamic) change in the number of null strings that gravitationally belong to the “macro” object). By averaging various spatial distributions of “macro” formations over time, it is possible to introduce the concepts of “substance” and “interaction fields” in the null string gas. PubDate: 2020-10-01

Abstract: We use the dynamical system method in order to investigate the dynamics of a non-minimally coupled tachyon field within induced gravity on the brane in a holographic cosmological context. Assuming an exponential potential and a monomial form of the nonminimal coupling function, we construct the phase space of the model. Two possible cases, namely, the minimal and nonminimal coupling, are investigated. Using dynamical systems tools, it is found that the model can describe an attractor solution which corresponds to the inflationary era in the non-minimal coupling case. PubDate: 2020-10-01

Abstract: We investigate the Universe at the late stage of its evolution and inside the cell of uniformity, 150–370 Mpc. We consider the Universe to be filled at these scales with dustlike matter, a minimally coupled Galileon field and radiation. We use the mechanical approach. Therefore, the peculiar velocities of the inhomogeneities as well as the fluctuations of other perfect fluids can be considered nonrelativistic. Such fluids are said to be coupled because they are concentrated around the inhomogeneities. We investigate the conditions under which the physical Galileon field, i.e., the field compatible with the results of the latest gravitational wave experiments GW150914, GW151226, GW170104, GW170814, GW170817 and GW170608, can become coupled. We know that at the background level coupled scalar fields behave as two-component perfect fluids: one which mimics a network of frustrated cosmic strings and another one which corresponds to an effective cosmological constant. We found as well a correction for the Galileon field, which behaves like a matter component. PubDate: 2020-10-01

Abstract: We present the second-order post-Newtonian solution for the quasi-Keplerian motion in the Schwarzschild space-time under the Wagoner-Will-Epstein-Haugan representation. Detailed derivations are provided for readers’ convenience. PubDate: 2020-10-01

Abstract: The shell theorem, proved by Newton in his Principia (1687), states that the net force exerted by a uniform spherical shell on a body located anywhere inside it is zero, as long as the force is proportional to the inverse square of the distance between the interacting bodies. This null result remains valid whenever the interaction depends only on the distance between the bodies, but not on their relative motion. In this work, I develop a direct closed-form evaluation of the integral of the elements of force to show that Weber-like interactions, which take into account the relative motion between the body and the shell, yield a nonzero force opposite to the acceleration of the body with respect to the shell, whatever be its position and velocity. For gravitational interactions, this nonzero force is relevant in cosmology since it can be identified with the force of inertia, as caused by the celestial sphere (i.e., the set of distant stars), which allows for a full mathematical implementation of Mach’s principle. PubDate: 2020-10-01

Abstract: To estimate the influence of “dark energy” on Keplerian orbits, we solve the general-relativistic equations of motion of a test particle in the field of a pointlike mass embedded in the cosmological background formed by the cosmological constant with realistic cosmological Robertson–Walker asymptotics at infinity. It is found that under certain relations between three crucial parameters of the problem—the initial radius of the orbit, the Schwarzschild and de Sitter radii—a specific secular perturbation caused by \(\Lambda\) -term becomes significant, i.e., can reach the rate of the standard Hubble flow. This fact is interesting both by itself and may have important consequences for the long-term dynamics of planets and stellar binary systems. PubDate: 2020-10-01

Abstract: \(f(R,T)\) gravity is a widely used extended theory of gravity introduced by Harko et al., which is a straightforward generalization of \(f(R)\) gravity. The action in this extended theory of gravity incorporates well-motivated functional forms of the Ricci scalar \(R\) and the trace of the energy momentum tensor \(T\) . The present manuscript aims at constraining the most widely used \(f(R,T)\) gravity model of the form \(f(R+2\lambda T)\) to understand its coherency and applicability in cosmology. We communicate here a novel method to find a lower bound on the model parameter \(\lambda\gtrsim-1.9\times 10^{-8}\) through the equation relating the cosmological constant ( \(\Lambda\) ) and the critical density of the universe ( \(\rho_{\textrm{cr}}\) ). PubDate: 2020-07-01

Abstract: The reduced vacuum Hamiltonian equations of conformal geometrodynamics of compact manifolds in extrinsic time are written. This is achieved by generalizing the theorem of implicit function derivative to the functional analysis. Under the assumption that constant curvature slicing takes place, York’s field time becomes the global time. PubDate: 2020-07-01

Abstract: We review and present full details of the Feynman diagram based and the heat-kernel method based calculations of the simplest nonlocal form factors in the one-loop contributions of a massive scalar field. The paper has pedagogical and introductory purposes and is intended to help the reader in better understanding the existing literature on the subject. The functional calculations are based on the solution by Avramidi and Barvinsky and Vilkovisky for the heat kernel and are performed in curved space-time. One of the important points is that the main structure of nonlocalities is the same as in the flat background. PubDate: 2020-07-01

Abstract: We study the evolution of the universe by assuming an integrated model, which involves interacting dark energy and the holographic principle with the Hubble scale as an IR cutoff. First we determine the interaction rate at which matter is converting to dark energy. At the next step, we evaluate the equation of state parameter which describes the nature of dark energy. Our result predicts that the present state of the universe is dominated by quintessence type dark energy, and it will become phantom dominated in the near future. Again, our analysis successfully addresses the problem of present accelerated expansion of the universe and softens the coincidence problem. We also find that the universe was previously undergoing a decelerated phase of expansion and a transition from deceleration to acceleration should have occurred at a time \(t_{q=0}=0.732t_{0}\) , where \(t_{0}\) is the present age of the universe. Finally, we discuss the evolution of black holes in this environment. PubDate: 2020-07-01

Abstract: Spinning equations of Finslerian gravity, the counterpart of the Mathisson-Papapetrou spinning equations of motion are obtained. Two approaches of Finslerian geometries are formulated and discussed, the Cartan-Rund and Finsler-Cartan ones, as well as their corresponding spinning equations. The significance of the nonlinear connection and its relevance on spinning equations is noticed, and their deviations are examined. PubDate: 2020-07-01

Abstract: We study the accretion of dark matter and dark energy onto \((n+2)\) -dimensional Morris–Thorne wormholes. The wormhole mass and its rate of change have been written in the background of the \((n+2)\) -dimensional Friedmann-Robertson-Walker (FRW) model of the Universe. We have assumed the candidates of dark energy in the form of entropy-corrected holographic dark energy (ECHDE) and entropy-corrected new agegraphic dark energy (ECNADE) with its logarithmic and power-law versions. For these different dark energy models, the wormhole mass has been calculated in terms of the redshift when dark matter and the above types of dark energies accrete onto the wormhole. For this purpose, we have taken two classes of scale factors, where in class I the scale factor describes a future singularity while class II follows from an initial singularity. We graphically present the nature of the wormhole mass in different dimensions (4D, 5D, 6D) for ECHDE and ECNADE accretion. In the class I scale factor, we observe that the wormhole mass increases during the evolution of the Universe in both ECHDE and ECNADE models in both the power-law and logarithmic versions. Also, with the class II scale factor, we see that the wormhole mass decreases during the evolution of the Universe for ECHDE in both power-law and logarithmic versions, and for ECNADE with power law models, while the wormhole mass increases during the evolution of the Universe for ECNADE in its logarithmic version. PubDate: 2020-07-01

Abstract: Cosmological density perturbations governed by Newtonian and MONDian force laws scenarios for the period from matter domination to recombination have been investigated. Particularly, we find solutions for the density contrast equations obtained for both cases with respect to a homogeneous spatially flat Friedman-Lemaître-Robertson-Walker (FLRW) background using the Lie symmetry approach. Numerical solutions of the density contrast equations for both cases also have been provided in order to study the evolution of the density contrast. For the Newtonian case we find a limiting mass that dictates whether the growth of the density contrast is possible or not. Interestingly, in the Newtonian case, physical growth of the density contrast is not possible since the horizon mass is smaller than the limiting mass. On the other hand, growth of the density contrast is possible depending on the initial condition and the fluctuation mass of the MOND-dominated region despite the radiation pressure that leads to future structure formation. PubDate: 2020-07-01

Abstract: We construct a noncommutative gauge theory for the deformed metric corresponding to the modified structure of a gravitational field in the case of noncommutative Yukawa–Schwarzschild space-time. The thermodynamic properties and corrections t o the gravitational force on the horizon of a noncommutative Yukawa–Schwarzschild black hole are analyzed. PubDate: 2020-07-01

Abstract: It was suggested in our previous paper [Yu.V. Dumin, Grav. Cosmol. 25, 169 (2019)] that the cosmological Dark Energy might be mediated by the time–energy uncertainty relation in the Mandelstam–Tamm form, which is appropriate for the long-term evolution of quantum systems. The amount of such Dark Energy gradually decays with time, and the corresponding scale factor of the Universe increases by a “quasi-exponential” law (namely, the exponent is proportional to of the square root of time) throughout the entire cosmological evolution. While such a universal behavior looks quite appealing, an important question arises: Does the quasi-exponential expansion resolve the major problems of the early Universe in the same way as the standard inflationary scenario' In the present paper, we elucidate this issue by analyzing the causal structure of the space–time following from this model. It is found that the observed region of the Universe (the past light cone) covers a single causally connected domain developing from the Planck times (the future light cone). Consequently, there should be no appreciable inhomogeneity and anisotropy in the early Universe, creation of the topological defects will be suppressed, etc. From this point of view, the uncertainty-mediated Dark Energy can serve as a reasonable alternative to the standard (exponential) inflationary scenario. PubDate: 2020-07-01

Abstract: An axially symmetric nonvacuum solution of the Einstein field equations, regular everywhere and free from curvature divergence is presented. The matter-energy content is a the pure radiation field satisfying the energy conditions, and the metric is of type N in the Petrov classification scheme. The space-time develops circular closed timelike curves everywhere outside a finite region of space i.e., beyond a null curve. Furthermore, the physical interpretation of the solution based on the study of the equations of geodesic deviation is presented. Finally, the von Zeipel cylinders with respect to the Zero Angular Momentum Observers (ZAMOs) is discussed. In addition, circular null and timelike geodesic of pace-time are also presented. PubDate: 2020-07-01