Plane-symmetric inhomogeneous Brans-Dicke cosmology with an equation of state p=γρp=\gamma \rho

We present a new exact solution in Brans-Dicke theory. The solution describes inhomogeneous plane-symmetric perfect fluid cosmological model with an equation of state $p=\gamma \rho$. Some main properties of the solution are discussed.Comment: 6 pages, Late

Cosmological dynamics of exponential gravity

We present a detailed investigation of the cosmological dynamics based on $\exp (-R/{\Lambda})$ gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite and asymptotic regimes. The results show that cosmic histories exist which admit a double de-Sitter phase which could be useful for describing the early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure

Some Late-time Asymptotics of General Scalar-Tensor Cosmologies

We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p=-rho vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be approach to a de Sitter spacetime at large 4-volumes the coupling function, omega(phi), which defines the scalar-tensor theory, must diverge faster than |phi_infty-phi|^(-1+epsilon) for all epsilon>0 as phi rightarrow phi_infty 0 for large values of the time. Thus, for a given theory, specified by omega(phi), there must exist some phi_infty in (0,infty) such that omega -> infty and omega' / omega^(2+epsilon) -> 0 as phi -> 0 phi_infty in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation `constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of ``Boltzmann brains'' at late cosmological times can be avoided in scalar-tensor theories, including Brans-Dicke theory, in which phi -> infty and omega ~ o(\phi^(1/2)) at asymptotically late times.Comment: 14 page

Dynamical System Approach to Cosmological Models with a Varying Speed of Light

Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for models with a time dependent equation of state. The solutions are analyzed on two-dimensional phase space in the variables $(x, \dot{x})$ where $x$ is a function of a scale factor $a$. Then we show how the horizon problem may be solved on some evolutional paths. It is shown that the models with negative curvature overcome the horizon and flatness problems. The presented method of reduction can be adopted to the analysis of dynamics of the universe with the general form of the equation of state $p=\gamma(a)\epsilon$. This is demonstrated using as an example the dynamics of VSL models filled with a non-interacting fluid. We demonstrate a new type of evolution near the initial singularity caused by a varying speed of light. The singularity-free oscillating universes are also admitted for positive cosmological constant. We consider a quantum VSL FRW closed model with radiation and show that the highest tunnelling rate occurs for a constant velocity of light if $c(a) \propto a^n$ and $-1 < n \le 0$. It is also proved that the considered class of models is structurally unstable for the case of $n < 0$.Comment: 18 pages, 5 figures, RevTeX4; final version to appear in PR

Research in interactive scene analysis

Cooperative (man-machine) scene analysis techniques were developed whereby humans can provide a computer with guidance when completely automated processing is infeasible. An interactive approach promises significant near-term payoffs in analyzing various types of high volume satellite imagery, as well as vehicle-based imagery used in robot planetary exploration. This report summarizes the work accomplished over the duration of the project and describes in detail three major accomplishments: (1) the interactive design of texture classifiers; (2) a new approach for integrating the segmentation and interpretation phases of scene analysis; and (3) the application of interactive scene analysis techniques to cartography

The Power of General Relativity

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to $R^{1+\delta}$. This scale-free extension reduces to general relativity when $\delta \to 0$. In order to constrain generalisations of general relativity of this power class we analyse the behaviour of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires $\delta >0$ or $\delta <-1/4$. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound $-0.017<\delta <0.0012.$ We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter--radiation equality will be shifted by $\sim 1$ for a value of $\delta \sim 0.0005.$ We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound $\delta =2.7\pm 4.5\times 10^{-19}$ assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound $0\leq \delta <7.2\times 10^{-19}$ on theories of this type.Comment: 26 pages and 5 figures. Published versio

On the Possibility of Anisotropic Curvature in Cosmology

In addition to shear and vorticity a homogeneous background may also exhibit anisotropic curvature. Here a class of spacetimes is shown to exist where the anisotropy is solely of the latter type, and the shear-free condition is supported by a canonical, massless 2-form field. Such spacetimes possess a preferred direction in the sky and at the same time a CMB which is isotropic at the background level. A distortion of the luminosity distances is derived and used to test the model against the CMB and supernovae (using the Union catalog), and it is concluded that the latter exhibit a higher-than-expected dependence on angular position. It is shown that future surveys could detect a possible preferred direction by observing ~ 20 / (\Omega_{k0}^2) supernovae over the whole sky.Comment: Extended SNe analysis and corrected some CMB results. Text also extended and references added. 8 pages, 5 figure

Cosmology in three dimensions: steps towards the general solution

We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the 3-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3-d cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3-d spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with non-zero (and zero) cosmological constant and generalise known solutions of Kriele and the 3-d counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3-d cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2+1 spacetimes.Comment: 35 pages, 2 figure

The Dominant Balance at Cosmological Singularities

We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity.Comment: 13 pages, to appear in the Proceedings of the Greek Relativity Meeting NEB12, June 29-July 2, 2006, Nauplia, Greec

Gradient expansion(s) and dark energy

Motivated by recent claims stating that the acceleration of the present Universe is due to fluctuations with wavelength larger than the Hubble radius, we present a general analysis of various perturbative solutions of fully inhomogeneous Einstein equations supplemented by a perfect fluid. The equivalence of formally different gradient expansions is demonstrated. If the barotropic index vanishes, the deceleration parameter is always positive semi-definite.Comment: 17 pages, no figure