We demonstrate the scale invariance of the vacuum Bianchi type IX equations and use this to argue for the possibility of multifractal turbulence as a realisation of the suggestion by Belinski that there will be a fragmentation of local regions of inhomogeneous Mixmaster chaos on approach to an initial inhomogeneous cosmological singularity. Differences between the gravitational and hydrodynamical situations are outlined. Various potential obstacles to this picture of gravitational turbulence are discussed.
We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium solutions are analysed and the results are compared with the standard inflationary cosmological solutions and previously studied cosmological Einstein-Aether models.
In this paper, we will analyse the cosmological models in Einstein-aether gravity, which is a modified theory of gravity in which a time-like vector field breaks the Lorentz symmetry. We will use this formalism to analyse different cosmological models with different behavior of the scale factor. In this analysis, we will use a certain functional dependence of the dark energy on the Hubble parameter. It will be demonstrated that the aether vector field has a non-trivial effect on these cosmological models. We will also perform the \emph{Om} diagnostic in Einstein-aether gravity. Thus, we will f…
Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. In the Bose-Einstein Condensation model, dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present work, we study the Bose-Einstein Condensation process in a cosmological context, by assuming that this process can be described (at least approxima…
We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.
Einstein-Cartan theory is an extension of the standard formulation of General Relativity characterized by a non-vanishing torsion. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important at very high spin densities. In this work we analyze in detail the physics of Einstein-Cartan theory with Dirac and Maxwell fields minimally coupled to the spacetime torsion. This breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe. The resulting Dirac-like and Maxwell-like equat…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solut…
We consider the global cosmological evolution and the evolution of the density contrast in the Bose-Einstein condensate dark matter model, in the framework of a Post-Newtonian cosmological approach. In the Bose-Einstein model, dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state. For a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. The basic equation describing the evolution of the perturbations of the Bose-Einstein condensate is obtained, an…
We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of p…
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is preserved under the disformal transformation. We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation. Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame…
The so-called Einstein-Aether theory is General Relativity coupled (at second derivative order) to a dynamical unit time-like vector field (the aether). It is a Lorentz-violating theory, and gained much attention in the recent years. In the present work, we study the cosmological evolution of Einstein-Aether models with power-law-like potential, by using the method of dynamical system. In the case without matter, there are two attractors which correspond to an inflationary universe in the early epoch, or a de Sitter universe in the late time. In the case with matter but there is no interaction…
We proved that strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant could not support a nontrivial configuration of complex scalar fields. We considered the general case of the arbitrary number of U(1) gauge fields in the theory under consideration.
We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.
In the present work, we analyze the evolution of the scalar and tensorial perturbations and the quantities relevant for the physical description of the Universe, as the density contrast of the scalar perturbations and the gravitational waves energy density during the Bose-Einstein condensation of dark matter. The behavior of these parameters during the Bose-Einstein phase transition of dark matter is analyzed in details. To study the cosmological dynamics and evolution of scalar and tensorial perturbations in a Universe with and without cosmological constant we use both analytical and numerica…
The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discr…
We probe the pure Einstein's gravity contributions to the second-order density power spectrum. In the small-scale, we discover that the Einstein's gravity contribution is negligibly small. This guarantees that Newton's gravity is sufficient to handle the baryon acoustic oscillation scale. In the large scale, however, we discover that the Einstein's gravity contribution to the second-order power spectrum dominates the linear-order power spectrum. Thus, pure Einstein gravity contribution appearing in the third-order perturbation leads to an infrared divergence in the power spectrum.
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.
We construct models with the Gauss-Bonnet term multiplied to a function of the scalar field leading to inflationary scenario. The consideration is related with the slow-roll approximation. The cosmological attractor approach gives the spectral index of scalar perturbations which is in a good agreement with modern observation and allows variability for tensor-to-scalar ratio. We reconstruct models with variability of parameters which allow to reproduce cosmological attractor predictions for inflationary parameters in the leading order of $1/N$ approximation in the Einstein-Gauss-Bonnet gravity.
We prove that in the infinite speed-of-light limit (i.e., non-relativistic and subhorizon limits), the relativistic fully nonlinear cosmological perturbation equations in two gauge conditions, the zero-shear gauge and the uniform-expansion gauge, exactly reproduce the Newtonian hydrodynamic perturbation equations in the cosmological background; as a consequence, in the same two gauge conditions, the Newtonian hydrodynamic equations are exactly recovered in the Minkowsky background.
We propose to compute the action and global charges of the asymptotically anti-de Sitter solutions in Einstein-Gauss-Bonnet theory by adding boundary counterterms to the gravitational action. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension $d\leq 9$. We apply this tehnique for several different types of black objects. Apart from static and rotating black holes, we consider also Einstein-Gauss-Bonnet black string solutions with negative cosmological constant.
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in arXiv:0804.0009, hep-th/0406238 . The second class is constructed…
Even though we know that physical observations are frame independent, the frame dependence of cosmological perturbations is relatively subtle and has led to confusion in the past. In this paper we show that while the (unobservable) matter power spectrum is frame dependent, the observable number counts are not. We shall also determine how the frame dependence of the power spectrum depends on scale.
We present a novel homogeneous and geometrically flat exact solution of Einstein's General Relativity equations for an ideal fluid. The solution, which describes an expanding/contracting hypercylinder, fits well with the observational pillars upon which rely the standard FLRW cosmology and, furthermore, it can naturally solve some of its most outstanding problems.
Cosmological solutions of Einstein's equation for fluids with heat flow in a generalized Robertson-Walker metric are obtained, generalizing the results of Bergmann.
A new approach to the cosmological constant problem is proposed by modifying Einstein's theory of general relativity, using instead a scalar-tensor theory of gravitation. This theory of gravity crucially incorporates the concept of quantum symmetry breaking. The role of the cosmological constant $λ$ as a graviton mass in the weak-field limit is necessarily utilized. Because $λ$ takes on two values as a broken symmetry, so does the graviton mass -- one of which cannot be zero. Gravity now exhibits both long- and short-range forces, by introducing hadron bags into strong interaction physics usin…
One of the possible applications of macroscopic Einstein equations has been considered. So, the nonsingular isotropic and uniform cosmological model is built. The cosmological consequences of this model are agree with conclusions of standard hot model of the Universe.
We consider cosmological and black hole solutions in the Einstein and higher-derivative gravity in two dimensions where the theory is formulated first in $D$ dimensions. In the limit that $D$ tends to $2$ with simultaneous singular rescaling of the scalar curvature coupling constant as $1/(D-2)$, we get the novel Einstein and higher-derivative gravity. Due to non-trivial contribution of scalar curvature which is topological invariant in exactly two dimensions to gravitational equations in the two-dimensional limit one gets novel cosmological and black hole solutions.In particular, the de Sitte…
We construct non-stationary exact solutions to five dimensional Einstein-Maxwell-Chern-Simons theory with positive cosmological constant. The solutions are based on four-dimensional Atiyah-Hitchin space. In asymptotic regions, the solutions approach to Gibbons-Perry-Sorkin monopole solutions. On the other hand, near the four-dimensional bolt of Atiyah-Hitchin space, our solutions show a bolt structure in five dimensions. The c-function for the solutions shows monotonic increase in time, in agreement with the general expected behaviour of c-function in asymptotically dS spacetimes.
The Hamiltonian of any quantum cosmological model must obey some conditions in order to be self-adjoint, or to admit self-adjoint extensions. We will consider in this paper the self-adjoint character of the Hamiltonian resulting from the Brans-Dicke theory, both in Einstein and Jordan frames. In both cases we find the wave-function solutions in order to obtain concrete predictions for the evolution of the Universe. We show that the specific cosmological scenarios obtained depend very weakly on the conditions of having a self-adjoint operator. The problem of equivalence between Einstein and Jor…
We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D=10 or D=11 which is exactly the conditions for superstrings or M-theory. We obtain analytic solutions with generic initial conditions in the four dimensional Einstein frame and study the accelerating universe when both our space and the internal space have negative curvatures.
We categorize the global structure of spherically symmetric static solutions of Einstein SU(2) Yang Mills equations with positive cosmological constant that are smooth at the center of spherical symmetry.
The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a global classical solution in the future time direction. Some late time asymptotic properties are obtained as well.
In this paper, the dependence of the Einstein gravity with the cosmological constant as well as of this theory in the first-order formalism on the gauge and parametrization is been analyzed. The one-loop counterterms off the mass shell have been plainly calculated in arbitrary gauge and parametrization. The tensor package of analytic calculations, written in REDUCE, allowed all the calculations to be carried out. A method of renormalization group functions calculations off shell is discussed.
Adopting a simple ansatz, we find exact solutions to the Einstein-Maxwell-dilaton equations, which stand for the multi-black hole configuration with maximal charge in a cosmological metric and dilaton field background driven by a cosmological term.
We prove a global in time existence theorem for the initial values problem for the Einstein-Boltzmann system with cosmological constant and arbitrarily large initial data, in the spatially homogeneous case, in a Robertson-Walker space-time.
We present arguments for the existence of charged, rotating black holes with equal-magnitude angular momenta in an odd number of dimensions $D\geq 5$. These solutions posses a regular horizon of spherical topology and approach asymptotically the Anti-de Sitter spacetime background. We analyze their global charges, their gyromagnetic ratio and their horizon properties.
Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with positive curvature. In the case of the Universe consisting of massless particles the equation for R(t) is solved analytically.
We report on a new two-parameter class of cosmological solutions to the Einstein-Maxwell equations. The solutions have everywhere regular curvature invariants. We prove that the solutions are geodesically complete and globally hyperbolic.
In this paper we study the Einstein-Boltzmann system for Israel particles with a positive cosmological constant. We consider spatially homogeneous solutions of Bianchi types except IX and obtain future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system. The result shows that the solutions converge to the de Sitter solution at late times.
We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-aether theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.
The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated on the existence of a covariantly constant field. It turns out that even without fundamental Higgs fields and other physical matter, gravitational self-interactions can generate this mechanism if the cosmological constant is non-vanishing. This article identifies the order parameter, and clarifies how these Abelian instanton solutions are associated with a …
The general exact solution of the Einstein-Dirac equations with cosmological constant in the homogeneous Riemannian space of the Bianchi 1 type is obtained.
This thesis investigates a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a simple ϕ^2 potential in the Einstein frame and investigate the corresponding $f(R)$ in the former picture. Such approach yields plenty of new pieces of information, namely a self-terminating inflationary solution with a linear Lagrangian, a robust criterion for stability of such theories, a dynamical effective potential for the Ricci scalar $R$, the addition of a…
We prove a global in time existence theorem for the initial value problem for the Einstein-Boltzmann system, with positive cosmological constant and arbitrarily large initial data, in the spatially homogeneous case, in a Robertson-Walker space-time.
We consider static spherically symmetric solutions of the Einstein equations with cosmological constant coupled to the SU(2) Yang Mills equations. We prove that most solutions can be continued back to the origin of spherical symmetry and that the qualitative behavior of solutions near this origin does not depend on the value of the cosmological constant.
By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the two vacua with the same scale factor $a$, but opposite $\dot a$. The tunneling from one vacuum to the other provides a robust mechanism for bounce universes; it always occurs for systems with positive energy density. For suitable matter energy-momentum tensor we also construct cyclic universes. Cosmological solutions that resemble the classical time crystals c…
In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence problem of gravitational wave. Currently many works on gravitational wave source modeling use Bondi's result to do the analysis including the gravitational wave calculation in numerical relativity. Recently more and more observations imply that the Einstein equations should be modified with an nonzero cosmological constant. In this work we use Bondi's original method to treat the…
Rastall gravity is a modified gravity proposal that incorporates a non-conserved energy momentum tensor (EMT). We study the equivalence between Rastall gravity and general relativity, analyzing its consequences for an EMT of dark matter and dark energy. We find that the translation between the Rastall and Einstein interpretations modifies the equation of state for each component. For instance, cold dark matter can translate into warm dark matter. If the EMT components are allowed to interact, the translation also changes the type of interaction between the components.
We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $Λ$. These solutions approach asymptotically the anti-de Sitter spacetime and possess a regular event horizon. A discussion of the main properties of the solutions and the differences with respect to the asymptotically flat case is presented. The mass of these configurations is computed by using a counterterm method. We note that the $Λ=-3$ configurations have an higher dimensional interpretation in context of $d=11$ supergravity. The existen…
We study black hole solutions in the Einstein gravity with Gauss-Bonnet term, the dilaton and a positive "cosmological constant" in various dimensions. Physically meaningful black holes with a positive cosmological term are obtained only for those in static spacetime with $(D-2)$-dimensional hyperbolic space of negative curvature and $D>4$. We construct such black hole solutions of various masses numerically in $D=5,6$ and 10 dimensional spacetime and discuss their properties. In spite of the positive cosmological constant the spacetime approach anti-de Sitter spacetime asymptotically. The bla…
We suggest an interpretation of Einstein Equations of General Relativity at large scales in which the Cosmological constant is exactly zero in the limit of zero spacetime variations of fundamental constants. We argue that in a quasiclassical Universe such variation should be tiny which leads to a tiny value for the Dark Energy. Next, we suggest that the are two sources of the Dark Energy. The first is the variation in Newton's constant $G_N$. It is a form of Dark Energy in that it has negative pressure, but it differs from the Cosmological Constant by a negative contribution to the energy. The…
We study the phase space of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein-Gauss-Bonnet action with a cosmological constant. We show that all the physical solutions have anti-de Sitter asymptotic behavior.
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.
Numerical evidence for a cosmological version of the Bartnik-McKinnon family of particle-like solutions of the Einstein-Yang-Mills system is presented. Our solutions are also static, but space has the topology of a three-sphere. By adjusting the cosmological constant we found numerically a spherically symmetric solution which can be regarded as an excitation of the unique SO(4)-invariant solution. We expect that for each node number there exists such a solution without a cosmological horizon.
We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is equivalent to the Robertson-Walker metric of cosmology. This general solution shows interconnections among many 5D solutions, such as the solution in the braneworld scenario and the topological black hole with cosmological constant. If the 5D cosmological constant is positive, the metric periodically depends on the extra dimension. Thus we can compactify the e…
It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by…
We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate how to obtain the general solutions of the corresponding models in the Jordan frame.
The method of obtaining of Vlasov-type equations for systems of interacting massive charged particles from the general relativistic Einstein-Hilbert action is considered. An effective approach to synchronizing the proper times of various particles of a many-particle system is proposed. Based on the resulting expressions for the relativistic actions, an analysis of composite structure of cosmological term in Einstein's equations is performed.
