Quantum vacuum fluctuations and dark energy

It is shown that the curvature of space-time induced by vacuum fluctuations of quantum fields should be proportional to the square of Newton’s constant G. This offers a possible explanation for the success of the formula ρ∼ Gm ⁶ c ² h ⁻⁴, ρ being the dark energy density and m a typical mass of elementary particles.     

Dynamics of Kantowski-Sachs universe with magnetized anisotropic Dark Energy

Kantowski-Sachs cosmological model in the presence of magnetized anisotropic dark energy is investigated. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS p=ωρ and a uniform magnetic field of energy density ρ _B . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar. The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model as well as anisotropic fluid does not approach isotropy through the evolution of the universe.     

Bianchi type-II space-times with constant deceleration parameter in self creation cosmology

The properties of locally rotationally symmetric Bianchi type-II perfect fluid space-times are analyzed in Barber’s second self-creation theory by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. By assuming the equation of state p=γ ρ, many new solutions are obtained for different era—Zel’dovich, radiation, vacuum and vacuum energy dominated. The solutions with power-law and exponential expansion are discussed. A detailed study of geometrical and physical parameters is carried out. The nature of singularity is also clarified in each case.     

Stability of strange dwarfs. I. Static criterion for stability. Statement of the problem

This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M _0core /M _⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ _c and the energy density ρ _tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ _c and ρ _tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M ₀ (total baryon number) of the quark core and different masses of the crust. In each series, ρ _tr ranges from the value for white dwarfs to ρ _drip = 4.3∙10¹¹ g/cm³, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ _tr . Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009).     

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Bianchi type-I cosmological models for binary mixture of perfect fluid and dark energy

We consider a self consistent system of Bianchi Type-I cosmology and Binary Mixture of perfect fluid and dark energy. The perfect fluid is taken to be obeying equations of state p _PF =γρ _PF with γ∈[0,1]. The dark energy is considered to be obeying a quintessence-like equation of state where the dark energy obeys equation of state p _DE =ωρ _DE where ω∈[−1,0]. Exact solutions to the corresponding Einstein field equations are obtained. Some special cases are discussed and studied. Further more power law models and exponential models are investigated.     

The cyclical reversible transitions of the universe’s evolution

In this work we propose cyclical reversible transitions as the scenario in which the universe evolves, through a series consisting of reversible expansion, temporary stability, and contraction. Our model is based on the comparison between local and global time-dependent densities {ρ ₀(τ ₀),ρ(τ)} instead of the critical density ρ _c, local and global time-dependent Hubble parameters {H ₀(τ ₀),H(τ)}, and the variations {Δρ(τ),ΔH(τ)} due to cosmological chaotic fluctuations, which are generally ignored in certain oscillating models. By taking into account all these factors, a rate equation in the form of (H ₀/H)² ∝(ρ ₀/ρ) has been established, and from it we derive some others, to provide a mechanism that is responsible for the cyclical reversible transitions. Also, the problems of singularities, black hole overproduction, and the second law of thermodynamics arising in oscillating universe models are conceptually resolved.     

Five dimensional universe model with variable cosmological term Λ and a big bounce

We assume the four dimensional induced matter of the 5D Ricci flat bouncing cosmological solution contains a perfect fluid. The big bounce singularity of simple 5D cosmological model is studied with the cosmological term Λ=α ρ and Λ=β H ² where α and β are constants and ρ and H are respectively energy density and Hubble parameter. This big bounce singularity is found to be an event horizon at which the scale factor and mass density of the universe are finite, while the pressure is infinite.      

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

Some magnetized bulk viscous string cosmological models in?General Relativity

Some Bianchi type-I viscous fluid string cosmological models with magnetic field are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density ξ(t)=ξ ₀ ρ ^m , where ξ ₀ and m are constants. To get a determinate model, we assume conditions ρ=(1+ω)λ, where ρ is rest energy density, ω a positive constant and λ the string tension density and expansion θ is proportional to eigen value σ ₁¹ of the shear tensor σ _j ⁱ . The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is discussed.      

Time dependent viscous string cloud cosmological models

Bianchi type-I string cosmological models are studied in Saez-Ballester theory of gravitation when the source for the energy momentum tensor is a viscous string cloud coupled to gravitational field. The bulk viscosity is assumed to vary with time and is related to the scalar expansion. The relationship between the proper energy density ρ and string tension density λ are investigated from two different cosmological models.     

Brans-Dicke Quantum Cosmology

By solving a Wheeler-De Witt ‘extended’ equation in the Brans-Dicke theory, we have found that the probability distribution predicts: i) An initial value for the Brans-Dicke scalar field φ ∼ ρ^1/2_VAC in the beginning of the inflation, where ρ_VAC is the vacuum density energy (this gives a planck mass ∼ ρ^1/4_VAC) ii) Large values for the Brans-Dicke parameter w. On the other hand it is shown that by taking into account the dynamical behaviour of φ and the matter scalar field σ we can formulate a ‘creation boundary condition’ where in the ‘beginning’ of the Universe (R =0, ‘nothing’ for some authors) we have a dynamical σ already ‘created’. This could be the energetic mechanism which makes Universe tunnels the potential barrier to evolve classically after. Besides we have found the possibility of a cosmological uncertainty principle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi Type-1 vacuum models in modified theory of general relativity

In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.     

A class of regular and well behaved charge analogue of?Kuchowicz’s relativistic super-dense star model

We obtain a well behaved class of charge analogues of neutral superdense star model due to Kuchowicz, by using a particular electric field, which involves a parameter K and vanishes when K=0. The members of this class are seen to satisfy the various physical conditions e.g. c ² ρ≥3p≥0, dp/dr<0, dρ/dr<0, along with the velocity of sound, dp/c ² dρ<1 and the adiabatic index ((p+c ² ρ)/p)(dp/(c ² dρ))>1, for the interval 0<K<1 with the maximum mass 6.8374M _Θ and the radius 23.4679 km with the central red shift Z _c =0.75364. In the interval, 0<K≤0.1179, the velocity of sound and the ratio p/c ² ρ are found monotonically decreasing towards the pressure free interface, which presents a relevant model for massive star like Neutron star or pulsar with the maximum mass as 4.1474M _Θ and the radius 20.5481 km with the central red shift Z _c =0.6654.     

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)² < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc ², (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c ², when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq_· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ _⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 10¹⁴ gm cm^-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R ² by −R² in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ² > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres. This revised version was published online in July 2006 with corrections to the Cover Date.     

Plane symmetric cosmological models with perfect fluid and dark energy

We consider a self-consistent system of Plane symmetric cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein’s field equations are obtained as a quadrature. The cases of Zeldovich Universe, Dust Universe and Radiation Universe and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.     

XLVIII. The density of white dwarf stars

The density of the white dwarf stars is reconsidered from the point of view of the theory of the poly tropic gas spheres, and gives for themean density of a white dwarf (under ideal conditions) the formula ρ=2.162 × 10⁶ × (M/⊙)². The above formula is derived on considerations which are a much nearer approximation to the conditionsactually existent in a white dwarf than the previous calculations of Stoner based on uniform density distribution in the star and which gave for the limiting density the formula ρ=3.977 × 10⁶ × (M/⊙)².     

Dark matter-systematics of its distribution

The dynamical masses of dwarf-spheroidals, spiral and elliptical galaxies, dwarf irregular binaries, groups of galaxies and clusters are shown to lie in a band about the M ∼ ρR³ line. The value of ρ is approximately the same as that estimated for unseen matter in the solar neighbourhood. The clusters themselves lie about theM ∼ R ^-3 line derived for a self-gravitating neutrino gas; their masses are distributed around the maximum Jeans-mass, M_Jmax. corresponding to m_v - 10 eV in an expanding universe. The present day length scales of clusters and the dispersion in the velocities observed within them are understood in terms of a 100-fold expansion subsequent to the initial growth of the fluctuations at M_Jmax. These systematics on theR-M plane imply that the initial condensations in the expanding universe are on the scale of the rich clusters of galaxies, these condensations were triggered dominantly by the gravitation of the neutrinos and the constant density of al systems arises naturally due to the embedding of these systems in the large scale neutrino condensations. If the neutrino density falls off asr ^-2 beyond the cluster edge till the distributions from different clusters overlap, then the mean density of the neutrinos approximately equals the closure density of the universe.     

Some new exact solutions with finite central parameters and?uniform radial motion of sound

We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I₁) is studied extensively. The solution (I₁) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M _Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ _b =2×10¹⁴ g/cm³, the maximum mass of Neutron star comes out to be 1.34 M _Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.     

Tidal interactions in binary stellar systems

The tidal interactions in binary stellar systems are studied under the assumption that the orbital motion of the binary is negligible in comparison with the stellar motion. By integrating over time the tidal forces acting on the stars, the energy changes are derived. These are used to obtain simple analytical expressions for the rates of disruption and merging. This method gives appropriate value for the Roche density ρ_r and it is found that the disruption rate of a satellite of density ρ changes drastically at ρ ρ_R A comparison is made with earlier results obtained under the simplifying assumption that stellar motion is negligible in comparison with the orbital motion of the binary and its implications are discussed.