<Emphasis Type="Italic">Bulk Scale Factor</Emphasis> at Very Early Universe

In this paper we propose a higher dimensional Cosmology based on FRW model and brane-world scenario. We consider the warp factor in the brane-world scenario as a scale factor in 5-dimensional generalized FRW metric, which is called as bulk scale factor, and obtain the evolution of it with space-like and time-like extra dimensions. It is then showed that, additional space-like dimensions can produce exponentially bulk scale factor under repulsive strong gravitational force in the empty universe at a very early stage.     

Alternative Inflationary Scenario Due to Compact Extra Dimensions

The main goal of this paper is to give an alternative interpretation of space-like and time-like extra dimensions as a primary factor for inflation in the early universe. We introduce the 5-dimensional perfect fluid and compare the energy-momentum tensor for the bulk scalar field with space-like and time-like extra dimensions. It is shown, that additional dimensions can imply to negative pressure in the slow roll regime in the early higher-dimensional world.     

Quintessential inflation from a variable cosmological constant in a 5D vacuum

We explore an effective 4D cosmological model for the universe where the variable cosmological constant governs its evolution and the pressure remains negative along all the expansion. This model is introduced from a 5D vacuum state where the (space-like) extra coordinate is considered as noncompact. The expansion is produced by the inflaton field, which is considered as nonminimally coupled to gravity. We conclude from experimental data that the coupling of the inflaton with gravity should be weak, but variable in different epochs of the evolution of the universe.     

The Hubble parameter in the early universe with viscous QCD matter and finite cosmological constant

The evolution of a flat, isotropic and homogeneous universe is studied. The background geometry in the early phases of the universe is conjectured to be filled with causal bulk viscous fluid and dark energy. The energy density relations obtained from the assumption of covariant conservation of energy‐momentum tensor of the background matter in the early universe are used to derive the basic equation for the Hubble parameter H. The viscous properties described by ultra‐relativistic equations of state and bulk viscosity taken from recent heavy‐ion collisions and lattice QCD calculations have been utilized to give an approximate solution of the field equations. The cosmological constant is conjectured to be related to the energy density of the vacuum. In this treatment, there is a clear evidence for singularity at vanishing cosmic time t indicating the dominant contribution from the dark energy. The time evolution of H seems to last for much longer time than the ideal case, where both cosmological constant and viscosity coefficient are entirely vanishing.     

The dynamical evolution of 3-space in a higher dimensional steady state universe

We investigate a class of cosmological solutions of Einstein’s field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject to two constraints that (i) the total volume scale factor of the universe is constant and (ii) the effective energy density is constant. We obtain various interesting new dynamics for the external space that yield a time varying deceleration parameter including oscillating cases when the flat/curved external and curved/flat internal spaces are considered. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the extra dimensions.     

Exact Causal Viscous Cosmologies

The general exact solution of the gravitational field equations for a homogeneous flat Friedmann-Robertson-Walker universe filled with a causal bulk viscous fluid with bulk viscosity coefficient proportional to the Hubble function is obtained in the framework of the full causal Israel-Stewart-Hiscock theory. The general solution of the field equations is represented in an exact closed parametric form and corresponds to a transition between two Minkowskian space-times connected by an inflationary period. The evolution of the temperature, entropy, deceleration parameter and bulk viscosity coefficient are considered in the general case. Particular solutions corresponding to a particular choice of parameters and leading to a non-inflationary evolution of the universe are presented too.     

Friedmann Cosmology with a Generalized Equation of State and Bulk Viscosity

The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state (endowed some deviation from the conventionally assuned cosmic perfect fluid model).We assume the bulk viscosity is a linear combination of two termsone is constant,and the other is proportional to the scalar expansion θ = 3a/a.The equation of state is described as p = (γ - 1)p p0,where p0 is a parameter.In this framework we demonstrate that this model can be used to explain the dark energy dominated universe,and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolutionno future singularity,big rip,or Type-Ⅲ singularity as presented in [S.Nojiri,S.D.Odintsov,and S.Tsujikawa,Phys.Rev.D 71 (2005) 063004].     

Viscous quark‐gluon plasma in the early universe

In the present work a study is given for the evolution of a flat, isotropic and homogeneous Universe, which is filled with a causal bulk viscous cosmological fluid. We describe the viscous properties by an ultra‐relativistic equation of state, and bulk viscosity coefficient obtained from recent lattice QCD calculations. The basic equation for the Hubble parameter is derived by using the energy equation obtained from the assumption of the covariant conservation of the energy‐momentum tensor of the matter in the Universe. By assuming a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density, we derive the evolution equation for the Hubble function. By using the equations of state from recent lattice QCD simulations and heavy‐ion collisions we obtain an approximate solution of the field equations. In this treatment for the viscous cosmology, no evidence for singularity is observed. For example, both the Hubble parameter and the scale factor are finite at t = 0, where t is the comoving time. Furthermore, their time evolution essentially differs from the one associated with non‐viscous and ideal gas. Also it is noticed that the thermodynamic quantities, like temperature, energy density and bulk pressure remain finite. Particular solutions are also considered in order to prove that the free parameter in this model does qualitatively influence the final results.     

Some Anisotropic Universes in the Presence of Imperfect Fluid Coupling with Spatial Curvature

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI₀-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinitely expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.     

Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum

Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.     

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.     

Evolving Horava cosmological horizons

Several sets of radially propagating null congruence generators are exploited in order to form 3-dimensional marginally trapped surfaces, referred to as black hole and cosmological apparent horizons in a Ho?ava universe. Based on this method, we deal with the characteristics of the 2-dimensional space-like spheres of symmetry and the peculiarities of having trapping horizons. Moreover, we apply this method in standard expanding and contracting FLRW cosmological models of a Ho?ava universe to investigate the conditions under which the extra parameters of the theory may lead to trapped/anti-trapped surfaces both in the future and in the past. We also include the cases of negative time, referred to as the finite past, and discuss the formation of anti-trapped surfaces inside the cosmological apparent horizons.     

Brane Formation and Cosmological Constraint on the Number of Extra Dimensions

Special relativity is generalized to extra dimensions and quantized energy levels of particles are obtained. By calculating the probability of particles' motion in extra dimensions at high temperature of the early universe, it is proposed that the branes may have not existed since the very beginning of the universe, but formed later. Meanwhile, before the formation, particles of the universe may have filled in the whole bulk, not just on the branes. This scenario differs from that in the standard big bang cosmology in which all particles are assumed to be in the 4D spacetime. So, in brane models, whether our universe began from a 4D big bang singularity is questionable. A cosmological constraint on the number of extra dimensions is also given which favors N ≥ 7.     

Bianchi Type-VI Anisotropic Dark Energy Model with Varying EoS Parameter

Within the scope of an anisotropic Bianchi type-VI cosmological model we have studied the evolution of the universe filled with perfect fluid and dark energy. To get the deterministic model of Universe, we assume that the shear scalar (σ) in the model is proportional to expansion scalar (?). This assumption allows only isotropic distribution of fluid. Exact solution to the corresponding equations are obtained. The EoS parameter for dark energy as well as deceleration parameter is found to be the time varying functions. Using the observational data qualitative picture of the evolution of the universe corresponding to different of its stages is given. The stability of the solutions obtained is also studied.     

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.     

Dark matter and cosmic acceleration from Wesson’s IMT

In the present work a procedure is build up, that allows obtaining dark matter (DM) and cosmic acceleration in our 4D universe embedded in a 5D manifold. Both, DM and the factor causing cosmic acceleration, as well ordinary matter are induced in the 4D space-time by a warped, but empty from matter, 5D bulk. The procedure is carried out in the framework of the Weyl–Dirac version (Israelit, Found Phys 35:1725, 2005; Israelit, Found Phys 35:1769, 2005) of Paul Wesson’s Induced Matter Theory (Wesson, Space-time matter, 1999) enriched by Rosen’s approach (Found Phys 12:213, 1982). Considering chaotically oriented Weyl vector fields, which exist in microscopic cells, we obtain cold dark matter (CDM) consisting of weylons, massive bosons having spin 1. Assuming homogeneity and isotropy at large scale we derive cosmological equations in which luminous matter, CDM and dark energy may be considered separately. Making in the given procedure use of present observational data one can develop a model of the Universe with conventional matter, DM and cosmic acceleration, induced by the 5D bulk.     

On the Adiabatic Expansion of the Visible Space in a Higher-Dimensional Cosmology

In the context of higher-dimensional cosmologies, with isotropic visible and internal space and multi-perfect fluid matter, we study the conditions under which adiabatic expansion of the visible external space is possible, when a time-dependent internal space is present. The analysis is based on a reinterpretation of the four-dimensional stress-energy tensor in the presence of the extra dimensions. This modifies the usual adiabatic energy conservation laws for the visible universe, leading to a new type of cosmological evolution which includes large-scale entropy production in four dimensions.     

Viscous phenomena and entropy production in the early universe

We calculate shear and bulk viscosity of the cosmological fluid for the early universe. Integrating the gravitational equations for isotropic models, we find that photon entropy increases by 0.11% due to the bulk viscosity in the lepton and plasma eras.     

Holographic dark energy in a cyclic universe

In this paper we study the cosmological evolution of the holographic dark energy in a cyclic universe, generalizing the model of holographic dark energy proposed by Li. The holographic dark energy with c<1 can realize a quintom behavior; namely, it evolves from a quintessence-like component to a phantom-like one. The holographic phantom energy density grows rapidly and dominates the late-time expanding phase, helping to realize a cyclic universe scenario in which the high energy regime is modified by the effects of quantum gravity, causing a turn-around (and a bounce) of the universe. The dynamical evolution of holographic dark energy in the regimes of low energy and high energy is governed by two differential equations, respectively. It is of importance to link the two regimes for this scenario. We propose a link condition giving rise to a complete picture of holographic evolution of a cyclic universe.