Universe Models with Negative Bulk Viscosity

The concept of negative temperatures has occasionally been used in connection with quantum systems. A recent example of this sort is reported in the paper of S. Braun et al. [Science 339,52 (2013)], where an attractively interacting ensemble of ultracold atoms is investigated experimentally and found to correspond to a negative-temperature system since the entropy decreases with increasing energy at the high end of the energy spectrum. As the authors suggest, it would be of interest to investigate whether a suitable generalization of standard cosmological theory could be helpful, in order to elucidate the observed accelerated expansion of the universe usually explained in terms of a positive tensile stress (negative pressure). In the present note we take up this basic idea and investigate a generalization of the standard viscous cosmological theory, not by admitting negative temperatures but instead by letting the bulk viscosity take negative values. Evidently, such an approach breaks standard thermodynamics, but may actually be regarded to lead to the same kind of bizarre consequences as the standard approach of admitting the equation-of-state parameter w to be less than -1. In universe models dominated by negative viscosity we find that the fluid's entropy decreases with time, as one would expect. Moreover, we find that the fluid transition from the quintessence region into the phantom region (thus passing the phantom divide w=-1) can actually be reversed. Also in generalizations of the LCDM-universe models with a fluid having negative bulk viscosity we find that the viscosity decreases the expansion of the universe.Comment: 7 pages latex, no figures, published electronically in Astrophys. Space Sc

On the Global Navigation Satellite Systems and Relativity

GNSS, or more precisely GNSS-2, is an abbreviation for Glob al Navigation Satellite Systems – Second generation, and serves as a generic name for the class of modern global sa tellite based radio navigation systems. GNSS-2 consists mainly of the four major Global Navigation Satellite Systems known as: GPS (U.S.), GLONASS (Russia), Galileo (EU) and Bei-Dou-2 (China). All these global radio navigation systems are based on the same navigation principle, i.e. utilizing ultra- stable clocks in satellites to determine the user position by independent measurements of the transit time of electromagnetic signals transmitted from satellites in orbit, so-called Radio Navigation Satellite Services (RNSS). The typical performance of these global radio navigation systems is to provide absolute positioning to an observer on the surface of the Earth within the precision of 5-10 meter. However, this precision can be improved utilizing state of the art processing techniques such as Precise Point Positioning (PPP), currently demonstrating absolute positioning of 5-10 centimeters utilizing only one receiver. To achieve this astonishing precision in terms of absolute position, the rate of time as measured on the clock in the satellite must be known to better than a few nanoseconds. Since the satellites are constantly moving with respect to the observer and are also located at highly different gravitational potentials, effects predicted by both the Special- and General theories of Relativity must be considered in order to achieve the desired accuracy in the observed transit times. These systems are in fact one of the very few man made systems, outside of particle accelerators, that experience significant relativistic effects

Experimental limits to the density of dark matter in the solar system

On the scales of galaxies and beyond there is evidence for unseen dark matter. In this paper we find the experimental limits to the density of dark matter bound in the solar system by studying its effect upon planetary motion.Comment: 9 pages, REVTeX, no figure

Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory

John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases: 1. A static, spherically symmetric space; and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe models. We find the general, exact solution of Nash’s field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE) in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satisfying way of including energy momentum into the theory has yet to be found.publishedVersio

The Principle of Relativity and Inertial Dragging

Machs principle and the principle of relativity have been discussed by H. I. Hartman and C. Nissim-Sabat in this journal. Several phenomena were said to violate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenon of inertial dragging been invoked, and no calculation have been offered by either side to substantiate their claims. Here I discuss the possible validity of the principle of relativity for rotating motion within the context of the general theory of relativity, and point out the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculations to demonstrate how these points come out as consequences of the general theory of relativityComment: 17 page

Viscous Cosmology for Early- and Late-Time Universe

From a hydrodynamicist's point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (excluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy-Verlinde formula is affected by viscosity.Comment: 71 pages, Invited Review for Int.J.Mod.Phys.

Entropy of gravitationally collapsing matter in FRW universe models

We look at a gas of dust and investigate how its entropy evolves with time under a spherically symmetric gravitational collapse. We treat the problem perturbatively and find that the classical thermodynamic entropy does actually increase to first order when one allows for gravitational potential energy to be transferred to thermal energy during the collapse. Thus, in this situation there is no need to resort to the introduction of an intrinsic gravitational entropy in order to satisfy the second law of thermodynamics.Comment: 9 pages, 4 figures. Major changes from previous version. We consider only thermodynamic entropy in this version. Published in PR