Cosmological solutions with massive gravitons

We present solutions describing spatially closed, open, or flat cosmologies in the massive gravity theory within the recently proposed tetrad formulation. We find that the effect of the graviton mass is equivalent to introducing to the Einstein equations a matter source that can consist of several different matter types - a cosmological term, quintessence, gas of cosmic strings, and non-relativistic cold matter.     

Cosmological compactification in Kaluza-Klein model and time-dependent cosmological term

Einstein's equations for the generalized (4+D)-dimensional Robertson-Walker model are solved taking the conformally invariant action for the matter field. Compactification of this model is discussed and the compactification time/compactification mass scale for different values ofD is calculated. The resulting 4-dimensional action for gravity is obtained. It is found that a time-dependent cosmological constant is induced which is very large when the cosmic time is small and very small when the cosmic time is large.     

Cosmological solutions with charged black holes

We consider the problem of constructing cosmological solutions of the Einstein–Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct exact initial data for N charged black holes on a hypersphere. This corresponds to the maximum of expansion of a cosmological solution, and provides sufficient information for a unique evolution. We then consider the specific example of a universe that contains eight charged black holes, and show that the existence of non-zero electric charge reduces the scale of the cosmological region of the space. These solutions generalize the Majumdar–Papapetrou solutions away from the extremal limit of charged black holes, and provide what we believe to be some of the first relativistic calculations of the effects of electric charge on cosmological backreaction.     

Cosmological solutions in macroscopic gravity

In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the equations of macroscopic gravity for a spatially homogeneous and isotropic macroscopic space-time and find that the correlation tensor is of the form of a spatial curvature term. We briefly discuss the physical consequences of these results.     

Cosmological solutions in the brane-bulk system

In this work we find cosmological solutions in the brane-bulk system starting from a 5D line element which is a simple extension, for cosmological applications, of the pioneering Randall-Sundrum line element. From the knowledge of the bulk metric, assumed to have the form of plane waves propagating in the fifth dimension, we solve the corresponding 4D Einstein equations on the brane with a well defined energy-momentum tensor.Received: 24 November 2004, Revised: 24 January 2005, Published online: 16 March 2005PACS: 04.20.Jb, 04.50. + h     

Cosmological background solutions and cosmological backreactions

The cosmological backreaction proposal, which attempts to account for observations without a primary dark energy source in the stress-energy tensor, has been developed and discussed by means of different approaches. Here, we focus on the concept of cosmological background solutions in order to develop a framework to study different backreaction proposals.     

Cosmological solutions of a quadratic theory of gravity with torsion

Following the general approach of Hehl, and Hayashi and Shirafuji, we give the gravity equations for the lagrangian $\text{L}\text{=(}\text{e}\text{/2L}{}^2\text{)(F+}\text{1}\text{2}\text{×F}{}^2\text{) +}\text{L}{}_{\mathrm{M}}$. We have found the explicit Einstein-de Sitter solutions for a spinless dust. We have discussed in this case the singularity problem for the metric and for the torsion.     

Orbifold compactification and solutions of M-theory from Milne spaces

In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications , where Id is the identity matrix, is analyzed in detail. The spectrum of an eleven-dimensional field theory can be obtained with the help of the theory of harmonic functions in the fundamental domain of this group and it is associated with the cusp forms and the Eisenstein series. The supersymmetry surviving for supergravity solutions involving real hyperbolic space factors is briefly discussed.Received: 30 November 2004, Published online: 25 January 2005     

Cosmological solutions for the coupled Einstein-Yang-Mills-Higgs equations

The coupled system of Einstein-Yang-Mills-Higgs equations is solved numerically for a Robertson-Walker symmetric universe. The open universe must be excluded because, for this situation, the coupled system is unable to produce energy-momentum densityT in agreement with the Robertson-Walker symmetry. For the closed universe, inflation solutions do occur if an early re-collapse is avoided by suitable choice of the initial conditions. The energy exchange between the minimally coupled Higgs and Yang-Mills subsystems is very small so that the inflating power of the Higgs field cannot be disturbed by the presence of the Yang-Mills field. After the inflation phase the influence of the Yang-Mills field is completely negligible (cosmic no-hair theorem).     

Cosmological solutions in a spontaneously broken gauge theory

We consider solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically de Sitter space-time. The basic features of two classes of solutions are discussed, one of them corresponding to magnetic monopoles, the other one to sphalerons. We find that although the total mass within the cosmological horizon of these configurations is finite, their mass evaluated at timelike infinity generically diverges for most values of the cosmological constant. Also, no solutions exist in the absence of a Higgs potential.     

Cosmological solutions of time varying speed of light theories

We consider scalar–tensor theory for describing varying speed of light in a spatially flat FRW space–time. We find some exact solutions in the metric and Palatini formalisms. Also we examine the dynamics of this theory by dynamical system method assuming a ΛCDM background and we find some exact solutions by considering the character of critical points of the theory in both formalisms. We show that for any attractor the form of non-minimal coupling coefficient is quadratic in terms of the scalar field Ψ. Also we show that only attractors of the de Sitter era satisfy the horizon criteria.     

Cosmological singularities and analytical solutions in varying vacuum cosmologies

We investigate the dynamical features of a large family of running vacuum cosmologies for which \(\Lambda \) evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the stability of singular solutions which describe de-Sitter, radiation and matter dominated eras. We find several classes of \(\Lambda (H)\) cosmologies for which new analytical solutions are given in terms of Laurent expansions. Finally, we show that the Milne universe and the \(R_{h}=ct\) model can be seen as perturbations around a specific \(\Lambda (H)\) model, but this model is unstable.     

Nuclear Calabi-Yau space

In this note a Calabi-Yau manifold already found for⁹Li will be shown to carry an Euler number of six if Yang-Mills symmetry is broken. Not only does this specify the correct number of generations of quarks and leptons, but peaks on the manifold are associated with the lowest eigenvalues of aCP-invariant Dirac spin operatorC _[A].     

Viscous Cosmological Model with Variable Gravitational and Cosmological Constants

We have considered some cosmological solutions with variable gravitational and cosmological constants with bulk viscosity. It is found that the solutions are singularity free and the deceleration parameter is in general not a constant unless we assume perfect fluid with equation of state in the standard cosmologies. Moreover, the deceleration parameter is a function of the scale factor and changes sign with evolution, so our solution is a generalization of those obtained by Arbab I. Arbab. The introduction of viscosity not only free from singularity but also give the deceleration parameter a freedom to vary with scale factor. Thus, a viscous cosmological fluid gives a more general situation in the early universe.