Scalar Expansion Research Articles

Bulk viscous string cloud with strange quark matter in Brans-Dicke theory

Plane symmetric cosmologies with strange quark matter attached to the string cloud with bulk viscous fluid are studied in the context of Brans-Dicke theory. For the determinate solution, we have considered the geometric string (ρ = ρ s ) and the sum of the energy density and tension density of viscous string dust sources vanishes (ρ + ρ s = 0). Further we have considered the deceleration parameter to be constant and shear scalar proportional to the expansion scalar. We found that the universe models maintain anisotropic nature throughout the evolution and they correspond to accelerated expanding universe.

Some exact solutions of magnetized viscous model in string cosmology

In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.

Shear-free axially symmetric dissipative fluids

We study the general properties of axially symmetric dissipative configurations under the shear-free condition. The link between the magnetic part of the Weyl tensor and the vorticity, as well as the role of the dissipative fluxes, are clearly exhibited. As a particular case we examine the geodesic fluid. In this latter case, the magnetic part of the Weyl tensor always vanishes, suggesting that no gravitational radiation is produced during the evolution. Also (for the geodesic case), in the absence of dissipation, the system evolves towards a FRW spacetime if the expansion scalar is positive.

Thermal expansion inC2/cpyroxenes: a review and new high-temperature structural data for a pyroxene of composition (Na0.53Ca0.47)(Al0.53Fe0.47)Si2O6(Jd53Hd47)

AbstractSingle-crystal X-ray data collection was performedin situatT= 300 and 700°C on a sample synthesized along the jadeite–hedenbergite series. The structural data, together with those of a previous investigation of a crystal of the same composition, were compared to those of the endmembers. The evolution of the displacement parameters with temperature shows significant residuals for the O1, O2 and O3 oxygen atT= 0 K, most significantly in the O1, which were interpreted as an indication of positional disorder.Volume thermal expansion and axial deformation ellipsoids were calculated for the above sample together with those of a series ofC2/cpyroxenes. Pyroxenes with a divalent M2 cation, Ca, Fe and Mg have a greater expansion than those with a monovalent M2, like Na and Li; the Na pyroxene endmembers with Al, Cr and Fe were observed to show greater expansion than corresponding Li ones.The greater axial expansion is found along thebaxis, except in LiCrSi2O6; the changes along thebaxis are related to the volume thermal expansion. The axial orientation and anisotropy of the two axes onto the (010) plane is different in Na, Li and Ca-Mg-Fe pyroxenes, but the overall expansion onto the (010) plane, given by the sum of the scalar expansion along the two axes on (010), is very similar in pyroxenes.The deformation along thebaxis with temperature and composition is driven by the deformation along b of the octahedral M1 chain; most important is the contribution from the O1−O1 shared edge between M1 octahedra in the same octahedral chain.

Magnetized Viscous Fluid Anisotropic Models in String Cosmology

We study the evolution of a homogeneous and anisotropic Bianchi type VI0 cosmological model in the presence of magnetic field and viscous fluid together with a cloud of cosmic strings in general relativity. Since Viscous fluid and magnetic field have cosmological origin, it is interesting to discuss the effects of viscous fluid and magnetic field on the expansion history of the universe in early and later stages of evolution in string cosmol- ogy. Exact solutions of the field equations are obtained using the equation of state for a cloud of strings. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. The two string models, namely, geometrical(Nambu string) and Takabayasi (p-string) string models are discussed with magnetized and non-magnetized viscous fluid by taking certain physical conditions. We also examine numerically the effects of bulk viscosity and magnetic field on potential in each string model. We find that magnetic field and viscous fluid play important role during the early evolution of the universe. We observe that the viscous term affects the evolution much rapid as compare to magnetic field. The presence of viscous term prevents the universe to be empty. The other physical and geometrical aspects of each string model are also discussed in detail.

Kantowski–Sachs bulk viscous string cosmological model in Brans–Dicke theory of gravitation

In this paper, we investigate spatially homogenous and anisotropic Kantowski–Sachs cosmological model in Brans–Dicke (Phys. Rev. 124:925, 1961) scalar–tensor theory of gravitation in the presence of bulk viscous fluid containing one dimensional cosmic strings. To find a determinate solution of the highly non-linear field equations we use the special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983). We also use (i) the barotropic equation of state for the pressure and density. (ii) the trace free energy momentum tensor of the fluid and (iii) shear scalar is proportional to scalar expansion. Some physical and kinematical properties of the model obtained are, also, discussed.

Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology

We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann–Lemaître–Robertson–Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar–Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann–Lemaître–Robertson–Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.

Kaluza-Klein dark energy cosmological model in scale Co-variant Theory of Gravitation

A five dimensional Kaluza-Klein dark energy model with variable EoS parameter is investigated in the scale co-variant theory of gravitation proposed by Canuto et al. (in Phys. Rev. 39:429, 1977) in a five dimensional Kaluza-Klein space-time in the presence of perfect fluid source. Using the special law of variation for Hubble’s parameter proposed by Berman (in Nuovo Cimento B 74:183, 1983), we have obtained a determinate solution which represents a dark energy cosmological model in the theory. We have also used the result that the scalar expansion is proportional to shear scalar of the space-time. It is observed that the EoS parameter, skewness parameter in the model turn out to be functions of cosmic time. Some physical and Kinematical properties of the model are also discussed.

Bianchi type-III bulk viscous string cosmological model in Brans-Dicke theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-III space-time is considered in the framework of a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961) in the presence of bulk viscous fluid containing one dimensional cosmic strings. We have found a determinate solution of the field equations using the plausible physical conditions (i) a barotropic equation state for the pressure and density, (ii) special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B74:182, 1983), (iii) shear scalar is proportional to scalar expansion and (iv) the trace of the energy tensor of the fluid vanishes. We have also assumed that bulk viscous pressure is proportional to energy density. Some physical and kinematical properties of the model are, also, discussed.

Bianchi type-V bulk viscous string cosmological model in Saez-Ballester scalar-tensor theory of gravitation

In this paper, a spatially homogeneous and anisotropic Bianchi type-V cosmological model is considered in a scalar-tensor theory of gravitation proposed by Saez and Ballester (in Phys. Lett. A 113:467, 1986) when the source for energy momentum tensor is a bulk viscous fluid containing one dimensional cosmic strings. The field equations being highly non-linear, we obtain a determinate solution using the plausible physical conditions (i) the scalar of expansion of the space-time is proportional to shear scalar (ii) the baratropic equation of state for pressure and density and (iii) the bulk viscous pressure is proportional to the energy density. It is interesting to observe that cosmic strings do not survive in this model. Some physical and kinematical properties of the model are also discussed.

Stability of viscous fluid in Bianchi type-VI model with cosmological constant

In this paper, we investigate Bianchi type-$VI$ cosmological model for the universe filled with dark energy and viscous fluid in the presence of cosmological constant. Also, we show accelerating expansion of the universe by drawing volume scale, pressure and energy density versus cosmic time. In order to solve the Einstein field equations, we assume the expansion scalar is proportional to a component of the shear tensor. Therefore, we obtain the directional scale factors and show the EOS parameter crosses over phantom divided-line.

The dual Padé families of iterations for the matrix [formula omitted]th root and the matrix [formula omitted]-sector function

In this paper we consider the Padé family of iterations [B. Laszkiewicz, K. Ziȩtak, A Padé family of iterations for the matrix sector function and the matrix pth root, Numer. Linear Algebra Appl. 16 (2009) 951–970] and a new dual Padé family of iterations for computing the principal pth root of a matrix, including the Newton and Halley methods as particular cases. We prove convergence of iterations of these families in certain regions. We also propose a new dual Padé family of iterations for computing the matrix p-sector function and we determine a certain region of convergence. For this purpose we study properties of the Padé approximants to the function (1−z)−1/p.We show a connection of the series expansion with respect to B of the iterates, generated by iterations of the dual Padé family for computing the matrix pth root (I−B)1/p, with binomial scalar expansion of (1−b)1/p.

Bianchi-I Universe with Decaying Vacuum Energy Density and Time Varying Gravitational Constant

Anisotropic Locally Rotationally Symmetric Bianchi-I (LRSBI) cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Our calculations for the Supernova constraints concerning the luminosity distance provide reasonable results.

On the conformal version of Schwarzschild – de Sitter spacetime

An imperfect cosmic fluid with energy flux is analyzed. Even though its energy density ρ is positive, the pressure p = −ρ due to the fact that the metric is asymptotically de Sitter. The kinematical quantities for a nongeodesic congruence are computed. The scalar expansion is time independent but divergent at the singularity r = 2m. Far from the central mass m and for a cosmic time t̄ << H−1, the heat flux q does not depend on Newton's constant G.

Anisotropic Einstein-aether cosmological models

We investigate a class of spatially anisotropic cosmological models in Einstein-aether theory with a scalar field in which the self-interaction potential depends on the timelike aether vector field through the expansion and shear scalars. We derive the evolution equations in terms of expansion-normalized variables, which reduce to a dynamical system. We study the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions, and find that there are always ranges of values of the parameters of the models for which there exists an inflationary attractor.

Weighed scalar averaging in LTB dust models: part I. Statistical fluctuations and gravitational entropy

We introduce a weighed scalar average formalism (‘q-average’) for the study of the theoretical properties and the dynamics of spherically symmetric Lemaître–Tolman–Bondi (LTB) dust models. The ‘q-scalars’ that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the q-average convey the effects of inhomogeneity through the ratio of curvature and kinematic invariants and the magnitude of radial gradients. All curvature and kinematic proper tensors that characterize the models are expressible as irreducible algebraic expansions on the metric and 4-velocity, whose coefficients are the q-scalars and their linear and quadratic local fluctuation. All invariant contractions of these tensors are quadratic fluctuations, whose q-averages are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. We explore the application of this formalism to a definition of a gravitational entropy functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302–14). We show that a positive entropy production follows from a negative correlation between fluctuations of the density and Hubble scalar, providing a brief outline on its fulfilment in various LTB models and regions. While the q-average formalism is specially suited for LTB (and Szekeres) models, it may provide a valuable theoretical insight into the properties of scalar averaging in inhomogeneous spacetimes in general.

Anisotropic Bulk Viscous String Cosmological Model in a Scalar-Tensor Theory of Gravitation

Spatially homogeneous, anisotropic, and tilted Bianchi type-VI0model is investigated in a new scalar-tensor theory of gravitation proposed by Saez and Ballester (1986) when the source for energy momentum tensor is a bulk viscous fluid containing one-dimensional cosmic strings. Exact solution of the highly nonlinear field equations is obtained using the following plausible physical conditions: (i) scalar expansion of the space-time which is proportional to the shear scalar, (ii) the barotropic equations of state for pressure and energy density, and (iii) a special law of variation for Hubble’s parameter proposed by Berman (1983). Some physical and kinematical properties of the model are also discussed.

Viscosity-induced crossing of the phantom divide in the dark cosmic fluid

Choosing various natural forms for the equation-of-state parameter w and the bulk viscosity \zeta, we discuss how it is possible for a dark energy fluid to slide from the quintessence region across the divide w=-1 into the phantom region, and thus into a Big Rip future singularity. Different analytic forms for \zeta, as powers of the scalar expansion, are suggested and compared with experiments.

EVOLUTION OF EXPANSION-FREE SELF-GRAVITATING FLUIDS AND PLANE SYMMETRY

We investigate some analytical models of the plane symmetric distribution of anisotropic fluid with vanishing expansion scalar. Darmois junction conditions, on both the internal and external hypersurfaces, are given. A relationship between the Weyl tensor and the matter variables is developed. We explore four families of solutions under expansion-free condition some of which indicate the presence of thin shell, while some others satisfy junction conditions. It is shown that the Skripkin model is incompatible with junction conditions in the plane symmetry.

String cosmology with magnetized bulk viscous fluid in Bianchi I universe

The objective of the present paper is to study an anisotropic Bianchi-I cosmological model filled with bulk viscous fluid and magnetic field in string cosmology. The magnetic field is due to an electric current produced along the x-axis. The expansion in the model is considered to be proportional to one of the components of the shear tensor. We obtain two different quadrature forms of volume scale factor by considering two different relations between bulk viscosity and expansion scalar. We discuss the behavior of the classical potential with respect to the volume scale factor in the presence or absence of magnetic field and bulk viscosity in each case. We observe the role of bulk viscosity on the classical potential and also on the choices of bulk viscous pressure. By introduction of magnetic field or bulk viscosity or both into the model it results in changes in the potential as well as in volume scale factors. The physical and geometrical aspects of the solutions are discussed in detail.