We study self-consistent cosmological solutions for an Einstein Universe in a graph-based induced gravity model. The graph-based field theory has been proposed by the present authors to generalize dimensional deconstruction. In this paper, we consider self-consistent Einstein equations for a ``graph theory space''. Especially, we demonstrate specific results for cycle graphs.
We study self-consistent cosmological solutions for an Einstein universe in a graph-based induced gravity model. Especially, we demonstrate specific results for cycle graphs.
This paper is an extended and more detailed version of arXiv:0812.0533. We tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the construction of the topological cocycles. All constructed cocycles lead to unitarily equivalent representations of the fundamental group of the circle (see…
Stochastic Einstein equations are considered when 3D space metric $γ_{ij}$ are stochastic functions. The probability density for the stochastic quantities is connected with the Perelman's entropy functional. As an example, the Friedman Universe is considered. It is shown that for the Friedman Universe the dynamical evolution is not changed. The connection between general relativity and Ricci flows is discussed.
The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically stable around a center equilibrium point. Thus, study of this solution is interesting because it supports non-singular emergent cosmological models in which the early universe oscillates indeterminately about an initial Einstein static solution and is thus past eternal.
We study self-consistent static solutions for an Einstein universe in a graph-based induced gravity. The one-loop quantum action is computed at finite temperature. In particular, we demonstrate specific results for the models based on cycle graphs.
We consider the existence and stability of the Einstein static universe under the Generalized Uncertainty Principle (GUP) effects. We show that this solution in the presence of perfect fluid with a minimal length is cyclically stable around a center equilibrium point. By taking linear homogeneous perturbations, we find that the scale factor of Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the GUP coupling parameter $α$. Thus, in the model by GUP effects, our universe can stay at the Einstein static state past-eternally, which means that the big…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an arbitrary function that denotes inhomogeneous number density of particles, are a generalization of Einstein's static universe. On some examples of explicit solutions, we discuss non-linear density contrast and deviation of the metric functions.
We investigate the stability of the Einstein static universe as a non-LRS Bianchi type IX solution of the Einstein equations in the presence of both non-tilted and tilted fluids. We find that the static universe is unstable to homogeneous perturbations of Bianchi type IX to the future and the past.
By rescaling the Gauss-Bonnet (GB) coupling constant $α\rightarrow α/(D-4)$ and considering the $D \rightarrow 4$ limit, the GB gravity gives rise to nontrivial modification of general relativity in four dimensions. In this work, we investigate the realization of the emergent universe scenario in the $4 D$ GB gravity. First, we obtain the Einstein static universe filled with a perfect fluid. Then, we show that both spatially closed and open universes can be stable against both homogeneous and inhomogeneous scalar perturbations simultaneously.
By considering the realization of the emergent universe scenario in Eddington-inspired Born-Infeld (EiBI) theory, we study the stability of the Einstein static universe filled with perfect fluid in EiBI theory against both the homogeneous and inhomogeneous scalar perturbations in this work. We find that in both the spatially flat and closed cases, the emergent universe scenario is no longer viable, since the Einstein static universe cannot be stable against both the homogeneous and inhomogeneous scalar perturbations simultaneously. However, the emergent universe scenario survives in the spatia…
The stability of Einstein static universe against homogeneous scalar perturbations in the context of braneworld scenario is investigated. The stability regions are obtained in terms of the constant geometric linear equation of state parameter $ω_{extr}=p_{extr}/ρ_{extr}$ and are studied for each evolutionary era of the universe. The results are discussed for the case of closed, open or flat universe in each era under the obtained restricting conditions. We also briefly investigate the stability against vector and tensor perturbations. Contrary to the classical general relativity, it is found t…
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe.
We suggest using Einstein's static universe metric for the metastable state after reheating, instead of the Friedman-Robertson-Walker spacetime. In this case strong static gravitational potential leads to the effective reduction of the Higgs vacuum expectation value, which is found to be compatible with the Standard Model first order electroweak phase transition conditions. Gravity could also increase the CP-violating effects for particles that cross the new phase bubble walls and thus is able to lead to the successful electroweak baryogenesis scenario.
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein static solution in presence of vacuum energy corresponding to conformally-invariant fields. We show that the presence of vacuum energy stabilizes this solution by changing it to a centre equilibrium point, which is cyclically stable. This allows non-singular emergent cosmological models to be constructed in which initially the universe oscillates indefinitely a…
Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan theory. The interplay between torsion and the cosmological constant is discussed. A possible way out of the cosmological constant's sign problem is suggested.
Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Lambda is unstable to homogeneous perturbations. We show that LQC modifications can lead to a centre of stability for a large enough positive value of Lambda.
It is argued that the solution space of the equation determining the class of $f(R)$ theories which admit an Einstein static universe should be broadened by including the algebraic roots.
Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries.
We show that there exists a critical point for the coupling constants in Einsteinian cubic gravity where the linearized equations on the maximally-symmetric vacuum vanish identically. We construct an exact isotropic bounce universe in the critical theory in four dimensions. The comoving time runs from minus infinity to plus infinity, yielding a smooth universe bouncing between two de Sitter vacua. In five dimensions we adopt numerical approach to construct a bounce solution, where a singularity occurred before the bounce takes place. We then construct exact anisotropic bounces that connect two…
In this letter we have considered the eigenvalues and eigenfunctions of relativistic massless scalar particle which conformally coupled to the background of Einstein universe. We found the eigenvalues and eigenfunctions exactly.
The gravitaional force produced by a point particle, like the sun, in the background of the static Einstein universe is studied. Both the approximate solution in the weak field limit and exact solution are obtained. The main properties of the solution are {\it i}) near the point particle, the metric approaches the Schwarzschild one and the radius of its singularity becomes larger than that of the Schwarzschild singularity, {\it ii}) far from the point particle, the metric approaches the static Einstein closed universe. The maximum length of the equator of the universe becomes smaller than that…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein Static Universe found in General Relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations.
We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity…
A family of cosmological models is considered which in a certain synchronized system of reference possess flat slices t = const. They are generated from the Einstein-de Sitter universe by a suitable transformation. Under physically reasonable presumptions these transformed models fulfil certain energy conditions.
A static Friedmann brane in a 5-dimensional bulk (Randall-Sundrum type scenario) can have a very different relation between the density, pressure, curvature and cosmological constant than in the case of the general relativistic Einstein static universe. In particular, static Friedmann branes with zero cosmological constant and 3-curvature, but satisfying rho>0 and rho+3p>0, are possible. Furthermore, we find static Friedmann branes in a bulk that satisfies the Einstein equations but is not Schwarzschild-anti de Sitter or its specializations. In the models with negative bulk cosmological consta…
This work analyzes the effects of quantization on a Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model with positive curvature and material content composed of a Bose-Einstein condensate, a radioactive fluid and a cosmological constant playing the role of the dark energy of the universe. The quantization of the model was performed using the finite difference method in the Crank-Nicolson scheme: solutions of the Wheeler-DeWitt equation are obtained, in the form of finite norm wave packets which are well defined in all space, even if the 3D-sphere is degenerate. The introduction of the Bose-Eins…
We study the cosmological models in which an extended Chaplygin gas universe is merged with the braneworld scenario. In particular, we examine the realization of Einstein static universe on the brane embedded in a non-constant curvature bulk space and perform a detailed perturbation analysis. We extract the stability conditions and find their impacts on the geometric equation of state parameter and the spatial curvature of the universe.
We report a symmetry property of the Einstein-Friedmann equations for spatially flat Friedmann-Lemaître-Robertson-Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a one-parameter Abelian group.
We present a brief overview of the stability analysis of the Einstein static universe in various modified theories of gravity, like f(R) gravity, Gauss-Bonnet or f(G) gravity, and Horava-Lifshitz gravity.
In this short paper we establish the definition of the Lie derivative of a second rank tensor in the context of teleparallel theory of gravity and also extend it for a general tensor of rank $p+q$. This definition is then used to find Killing vectors of the Einstein universe. It turns out that Killing vectors of the Einstein universe in the teleparallel theory are the same as in General Relativity.
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy originating from conformally-invariant fields is stable. Using the fix point method and taking linear homogeneous perturbations, we find that the scale factor of Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the coupling parameter $λ$ between the energy-momentum tensor and the gradient of Ricci scalar. Thus, …
We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, $δω_{g}(t)=-Cδa(t)$. We obtain neu…
We study the back-reaction effects of the finite-temperature scalar field and the photon field in the background of an Einstein universe. In each case we find a relation between the temperature of the universe and its radius. These relations exhibit a minimum radius below which no self-consistent solution for the Einstein field equation can be found. A maximum temperature marks the transition from the vacuum dominated era to the radiation dominated era. An interpretation to this behavior in terms of Bose-Einstein condensation in the case of the scalar field is given.
The effective gravitational mass as well as the energy and momentum distributions of a radiating charged particle in Einstein's universe are evaluated. The Moller's energy-momentum complex is employed for this computation. The spacetime under study is a generalization of Bonnor and Vaidya spacetime in the sense that the metric is described in the cosmological background of Einstein's universe in lieu of the flat background. Several spacetimes are limiting cases of the one considered here. Particularly for the Reissner-Nordstrom black hole background, our results are exactly the same with those…
A panoramic view, preceded by a short background of Newtonian mechanics and Maxwellian electrodynamics, is offered on the extent of how Einstein's space-time geometry, believed to be central to an understanding of the structure of the universe, is overshadowed by several hitherto unheard of features like dark matter and dark energy, that seem to be necessary, but by no means sufficient, for a more complete picture.
We study the Einstein static universe in the framework of Generalized Uncertainty Principle constructed by the Snyder non-commutative space. It is shown that the deformation parameter can induce an effective energy density subject to GUP which obeys the holographic principle (HP) and plays the role of a cosmological constant. Using the holographic feature of this effective energy density, we introduce natural IR and UV cut-offs which depend on the GUP based effective equation of state. Moreover, we propose a solution to the cosmological constant problem. This solution is based on the result th…
We study the stability of Einstein static Universe, with FLRW metric, by considering linear homogeneous perturbations in the kinetic coupled gravity. By taking linear homogeneous perturbations, we find that the stability of Einstein static Universe, in the kinetic coupled gravity with quadratic scalar field potential, for closed ($K=1$) isotropic and homogeneous FLRW Universe depends on the coupling parameters $κ$ and $\varepsilon$. Specifically, for $κ=L_P^2$ and $\varepsilon=1$ we find that the stability condition imposes the inequality $a_0>\sqrt{3}L_P$ on the initial size $a_0$ of the clos…
We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein condensate both experimentally and theoretically. The expansion redshifts long-wavelength excitations, as in an expanding universe. After expansion, energy in the radial mode leads to the production of bulk topological excitations -- solitons and vortices -- driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. These complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of "preheating" that may have…
In this paper we investigate the Bose-Einstein condensation of massive spin-1 particles in an Einstein universe. The system is considered under relativistic conditions taking into consideration the possibility of particle-antiparticle pair production. An exact expression for the charge density is obtained, then certain approximations are employed in order to obtain the solutions in closed form. A discussion of the approximations employed in this and other work is given. The effects of finite-size and spin-curvature coupling are emphasized.
Acceleration of the universe is obtained from a model of non-relativistic particles with a short-range attractive interaction, at low enough temperature to produce a Bose-Einstein condensate. Conditions are derived for negative-pressure behavior. In particular, we show that a phantom-accelerated regime at the beginning of the universe solves the horizon problem, consistently with nucleosynthesis.
We obtain a family of regular static, spherically symmetric solutions in Einstein--Cartan theory with an electromagnetic field and a nonminimally coupled scalar field with the correct sign of kinetic energy density. At different values of its parameters, the solution, being asemptotically flat at large values of the radial coordinate, describes (i) twice asemptotically flat symmetric wormholes, (ii) asymmetric wormholes with an AdS asymptotic at the "far end", (iii) regular black holes with an extremal horizon or two simple horizons, and (iv) black universes with a de Sitter asymptotic at the …
This paper explores stability of the Einstein universe against linear homogeneous perturbations in the background of $f(\mathcal{G},T)$ gravity. We construct static as well as perturbed field equations and investigate stability regions for the specific forms of generic function $f(\mathcal{G},T)$ corresponding to conserved as well as non-conserved energy-momentum tensor. We use the equation of state parameter to parameterize the stability regions. The graphical analysis shows that the suitable choice of parameters lead to stable regions of the Einstein universe.
We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.
We show how to derive several families of accelerating universe solutions to an Einstein-Aether gravity theory. These solutions provide possible descriptions of inflationary behaviour in the early universe and late-time cosmological acceleration.
This paper investigates the existence and stability of Einstein universe in the context of $f(R,T,Q)$ gravity, where $Q=R_{μν}T^{μν}$. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parameterize the stability regions corresponding to conserved as well as non-conserved energy-momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, the stable regions of the Einstein universe are obtain…
We analyze the stability of the Einstein static universe by considering homogeneous perturbations in the context of f(G) modified Gauss-Bonnet theories of gravity. By considering a generic form of f(G), the stability region of the Einstein static universe is parameterized by the linear equation of state parameter w=p/rho and the second derivative f"(G) of the Gauss-Bonnet term.
Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Hořava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition against the linear scalar perturbations is obtained. Using this general condition, it is shown that there is no stable Einstein static universe for the case of flat universe, $k=0$. For the the special case of large values of running parameter of HL gravity $ω$, in a positively curved universe $k>0$, the domination of the quintessence and phantom matter fields w…
We show that inflation and current cosmic acceleration can be generated by a metric-affine f(R) gravity formulated in the Einstein conformal frame, if the gravitational Lagrangian L(R) contains both positive and negative powers of the curvature scalar R. In this frame, we give the equations for the expansion of the homogeneous and isotropic matter-dominated universe in the case L(R)=R+{R^3}/{β^2}-{α^2}/{3R}, where αand βare constants. We also show that gravitational effects of matter in such a universe at very late stages of its expansion are weakened by a factor that tends to 3/4, and the ene…
The stability of an Einstein static universe in the DGP braneworld scenario is studied in this paper. Two separate branches denoted by $ε=\pm1$ of the DGP model are analyzed. Assuming the existence of a perfect fluid with a constant equation of state, $w$, in the universe, we find that, for the branch with $ε=1$, there is no a stable Einstein static solution, while, for the case with $ε=-1$, the Einstein static universe exists and it is stable when $-1<w<-1/3$. Thus, the universe can stay at this stable state past-eternally and may undergo a series of infinite, non-singular oscillations. There…
