Singularities in Bianchi cosmologies

We discuss how infinite density singularities may be shown to occur in Friedmann-Robertson-Walker universes and orthogonal spatially homogeneous universes, but how very different behaviours are possible in tilted homogeneous cosmologies. After considering various possibilities that arise in this case, we illustrate them by examining the behaviour of exact solutions of Einstein's equations for a homogeneous cosmology which is a locally rotationally symmetric tilted Bianchi type V universe. These universes - which can be arbitrarily similar to a Robertson-Walker universe at late times - show a variety of singular behaviours quite different from those in the ‘orthogonal’ case. In particular, there exist such universes in which two singularities occur at the early stages of the universe, but in which the density of matter is finite at all times.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Cosmological Consequences of an Inhomogeneous Space-Time

Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an inflationary era able to overcome problems of standard cosmological models.Here an inhomogeneous model is proposed which allows to obtain a Friedmann-Robertson-Walker behaviour far away from the inhomogeneities and it naturally describes structures formation.We also obtain that the cosmological term does not prevent structure formation, avoiding a fine tuning problem in initial conditions.The asymptotic exact solution have been calculated. A simple test with universe age prediction has been performed. A relation between the inhomogeneity, the breaking of time reversal, parity and the matter-antimatter asymmetry is briefly discussed.     

Evolution of the universe with flat extra dimensions

Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern that entails not only stable extra dimensions in the radiation-dominated era, thereby preserving essential predictions in the standard cosmology, but also the present accelerating expansion while satisfying the limit on the variation of Newtonian gravitational constant. In this natural evolution pattern the extra dimensions tend to be stabilized automatically without resorting to artificial mechanisms in both the radiation-dominated and the matter-dominated era, as a wonderful feature for building models with extra dimensions. In addition, the naturalness of this evolution pattern that guarantees the late-time accelerating expansion of a matter-dominated universe presents a solution to the coincidence problem: why the accelerating phase starts at the present epoch. The feasibility of this evolution pattern for describing our universe is discussed.     

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in Fathi et al. (Eur. Phys. J. C 76, 527 2016). In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.     

A Non-Singular Universe with Vacuum Energy

A model for the universe based on the back-reaction effects of quantum fields at finite temperature in the background of Robertson-Walker spacetime and in the presence of a non-zero cosmological constant is constructed. We discuss the vacuum regime in the light of the results obtained through previous studies of the back-reaction of massless quantum fields in the static Einstein universe, and we argue that an adiabatic vacuum state and thermal equilibrium is achieved throughout this regime. Critical density is maintained naturally from the very early stages as a consequence of back-reaction effect of the vacuum fluctuations of quantum fields. Results show that such a model can explain many features of the early universe as well as the present universe. The model is free from the basic problems of the standard Friedmann cosmology, and is non-singular but involves a continuous creation of energy at a rate proportional to the size of the universe, which is lower than that suggested by the steady-state cosmology.     

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.     

Time‐reparametrization invariance and Hamilton‐Jacobi approach to the cosmological σ‐model

The construction of physical models with local time‐reparametrization invariance is reviewed. Negative‐energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant formulation of the dynamics is used to develop a time and gauge invariant Hamilton‐Jacobi theory. This formalism is applied to solve for the cosmology of a homogeneous universe of the Friedmann‐Lemaître‐Robertson‐Walker type. After a discussion of empty universes, the FLRW theory is extended with homogeneous scalar fields generically described by a σ‐model on some scalar manifold. An explicit gauge‐invariant solution is constructed for the non‐linear O(N)‐models.     

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.     

Quantum effects on higher dimensional space-time

Particle production in an odd-dimensional homogeneous universe with small anisotropy is discussed by using the effective action method. The pair production is a completely non-local phenomenon in an odd-dimensional theory, in contrast to the case of the familiar four-dimensional space-time. The effect of the closedness of the extra-dimensional space, i.e., the Casimir effect, which seems to be important in the scenario of Kaluza-Klein cosmology, is also discussed in the case of five dimensions.     

Gravity,antimatter and the Dirac-Milne universe

We review the main arguments against antigravity, a different acceleration of antimatter relative to matter in a gravitational field, discussing and challenging Morrison’s, Good’s and Schiff’s arguments. Following Price, we show that, very surprisingly, the usual expression of the Equivalence Principle is violated by General Relativity when particles of negative mass are supposed to exist, which may provide a fundamental explanation of MOND phenomenology, obviating the need for Dark Matter. Motivated by the observation of repulsive gravity under the form of Dark Energy, and by the fact that our universe looks very similar to a coasting (neither decelerating nor accelerating) universe, we study the Dirac-Milne cosmology, a symmetric matter-antimatter cosmology where antiparticles have the same gravitational properties as holes in a semiconductor. Noting the similarities with our universe (age, SN1a luminosity distance, nucleosynthesis, CMB angular scale), we focus our attention on structure formation mechanisms, finding strong similarities with our universe. Additional tests of the Dirac-Milne cosmology are briefly reviewed, and we finally note that a crucial test of the Dirac-Milne cosmology will be soon realized at CERN next to the ELENA antiproton decelerator, possibly as early as fall 2018, with the AEgIS, ALPHA-g and Gbar antihydrogen gravity experiments.     

Cosmology in Massive Gravity

We argue that more cosmological solutions in massive gravity can be obtained if the metric tensor and the tensor Σμν defined by Stückelberg fields take the homogeneous and isotropic form.The standard cosmology with matter and radiation dominations in the past can be recovered and ΛCDM model is easily obtained.The dynamical evolution of the universe is modified at very early times.     

The problems of singularity particle horizon and flatness in quantum cosmology

Classical relativistic cosmology is known to have the space-time singularity as an inevitable feature. The standard big bang models have very small particle horizons in the early stages which make it difficult to understand the observed homogeneity in the universe. The relatively narrow range of the observed matter density in the neighbourhood of closure density requires highly fine tuning of the early universe. In this paper it is argued that these three problems can be satisfactorily resolved in quantum cosmology. It is shown that it is extremely unlikely that the universe evolved to the present state from quantum states with singularity and particle horizon. Similarly, it is shown that of all possible states the Robertson-Walker model of flat spatial sections is the most likely state for the universe to evolve out of a quantum fluctuation. To demonstrate these results a suitable formalism for quantum cosmology is first developed.     

Accelerated expansion of an anisotropic Brans–Dicke cosmology from nonlinear derivative interaction and Gauss–Bonnet invariant

The study of Brans–Dicke cosmology has attracted considerable attention in the recent years since it explains most of the important features of the progress of the universe. We discuss in this letter a homogeneous and anisotropic cosmological model in the framework of Brans–Dicke theory including together a non-linear derivative interaction which appears in theory with the Galilean shift symmetry, a Gauss–Bonnet invariant motivated from heterotic string theory which plays an important role in numerous alternatives cosmological frameworks, two scalar fields and their interactions to fit easier with universe history expansion. Several particular cases are studied and the properties related to scaling solutions and asymptotic behaviour are discussed in some details.     

New Solutions to Einstein's Equations in the Taub Universe and Their Accelerating Stage

Following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe.     

Growing inhomogeneities in cosmological Goldstone modes

We examine the evolution of initial inhomogeneities in a Goldstone field in an expanding Friedmann-Robertson-Walker universe. We find subhorizon inhomogeneities grow, relative to the homogeneous state. This stems not from growing fluctuations — which simply redshift — but from rapid ( a⁻⁶) decay of the homogeneous state. We show how Goldstone modes escape assumptions — some inapplicable, some ill-founded — underpinning conventional analyses of cosmological fluctuations. Finally, we reconcile our analysis to standard cosmology, noting that the Goldstone evolution is essentially decoupled and dynamical.     

Co-Existence of Modified Chaplygin Gas and Other Dark Energies in the Framework of Fractal Universe

In this work, we consider a non-flat universe in the framework of fractal cosmology. We have investigated the co-existence of different kinds of dark energy models such as tachyonic field, DBI-essence, hessence, k-essence, dilaton, quintessence with the modified Chaplygin gas (MCG) in fractal universe and obtained the statefinder parameters. The natures of the scalar fields and the concerned potentials have been analyzed by the correspondence scenario in the fractal universe.     

A 5D noncompact and non Ricci flat Kaluza–Klein Cosmology

A model universe is proposed in the framework of 5D noncompact Kaluza–Klein cosmology which is not Ricci flat. The 4D part as the Robertson–Walker metric is coupled to conventional perfect fluid, and its extra-dimensional part is coupled to a dark pressure through a scalar field. It is shown that neither early inflation nor current acceleration of the 4D universe would happen if the nonvacuum states of the scalar field would contribute to 4D cosmology.