In this work, we revisit the shear-free conjecture of general relativity and show the violation of the well-known shear-free condition for perfect-fluid spacetimes. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe below, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.
In this paper, we consider a universe dominated by the extended Chaplygin gas which recently proposed as the last version of Chaplygin gas models. Here, we only consider the second order term which recovers quadratic barotropic fluid equation of state. The density perturbations analyzed in both relativistic and Newtonian regimes and show that the model is stable without any phase transition and critical point. We confirmed stability of the model using thermodynamics point of view.
We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi type I geometry, with a generalized Chaplygin gas as matter source. The generalized Chaplygin gas, which interpolates between a high density relativistic era and a non-relativistic matter phase, is a popular dark energy candidate. For a Bianchi type I space-time brane filled with a cosmological fluid obeying the generalized Chaplygin equation of state the general solution of the gravitational field equations can be expressed in an exact parametric form,…
We study the fate of density perturbations in an Universe dominate by the Chaplygin gas, which exhibit negative pressure. We show that it is possible to obtain the value for the density contrast observed in large scale structure of the Universe by fixing a free parameter in the equation of state of this gas. The negative character of pressure must be significant only very recently.
The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begin…
The generalized Chaplygin gas, which interpolates between a high density relativistic era and a non-relativistic matter phase, is a popular dark energy candidate. We consider a generalization of the Chaplygin gas model, by assuming the presence of a bulk viscous type dissipative term in the effective thermodynamic pressure of the gas. The dissipative effects are described by using the truncated Israel-Stewart model, with the bulk viscosity coefficient and the relaxation time functions of the energy density only. The corresponding cosmological dynamics of the bulk viscous Chaplygin gas dominate…
Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with a modified Chaplygin gas model. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts are also computed; the results are in relatively good agreement with current observational data.
The evolution of a Universe modelled as a mixture of a Chaplygin gas and radiation is determined by taking into account irreversible processes. This mixture could interpolate periods of a radiation dominated, a matter dominated and a cosmological constant dominated Universe. The results of a Universe modelled by this mixture are compared with the results of a mixture whose constituents are radiation and quintessence. Among other results it is shown that: (a) for both models there exists a period of a past deceleration with a present acceleration; (b) the slope of the acceleration of the Univer…
In this paper, we study in Friedmann-Robertson-Walker universe the interaction between the viscous generalized Chaplygin gas with $f(R,T)$ gravity, which is an arbitrary function of the Ricci scalar $R$ and the trace $T$ of the energy-momentum tensor. Assuming that the contents of universe is dominated by a generalized Chaplygin gas and dark energy, we obtained the modified Friedmann equations and also the time dependent energy density and pressure of dark energy due to the shear and bulk viscosities for three interacting models depending on an input parameter $Q$. Within the simple form of sc…
The evolution of a universe modelled as a mixture of generalised Chaplygin gas and ordinary matter field is studied for a Robertson Walker type of spacetime. This model could interpolate periods of a radiation dominated, matter dominated and a cosmological constant dominated universe. Depending on the arbitrary constants appearing in our theory the instant of flip changes. Interestingly we also get a bouncing model when the signature of one of the constants changes. The velocity of sound may become imaginary under certain situations pointing to a perturbative state and consequently the possibi…
We employ the generalized Chaplygin gas of interacting dark energy to obtain the equation of state for the generalized Chaplygin gas energy density in non-flat universe. By choosing a negative value for $B$ we see that $w_{\rm Λ}^{eff}< -1$, that corresponds to a universe dominated by phantom dark energy.
Einstein Gravitational Field Equations (EFE) of Chaplygin gas dominated Bianchi-type models are obtained by using metric approximation. The solutions of equations for a special case, namely Bianchi I model which is a generalization of isotropic Friedmann-Robertson-Walker (FRW) cosmology, are obtained. The early and late behaviours of some kinematic parameters in model are presented in graphically.
We consider an anisotropic brane-world model with Bianchi type I and V geometry, without mirror symmetry or any form of junction conditions. The generalized Chaplygin gas, which interpolates between a high density relativistic era and a non-relativistic matter phase, is a popular candidate for the present accelerated expansion of the universe. Considering the generalized Chaplygin gas as a geometrical dark energy, we obtain the general solutions in an exact parametric form for both Bianchi type I and V space-times. Finally, we study the behavior of the observationally important parameters such…
Spherically symmetric dark energy structures are investigated in the framework of a generalized Chaplygin gas (GCG), which has an equation of state of the form $P = - A/ρ^α} $. We also study these in a modified GCG equation of state, which includes a matter term, i.e. $P = σ^{2} ρ- A/ρ^α$. The results of the latter are then compared with some observational data on low-surface-brightness galaxies which are supposed to be dominated by dark matter.
We consider the scenario emerging from the dynamics of a generalized $d$-brane in a $(d+1, 1)$ spacetime. The equation of state describing this system is given in terms of the energy density, $ρ$, and pressure, $p$, by the relationship $p = - A/ρ^α$, where $A$ is a positive constant and $0 < α\le 1$. We discuss the conditions under which homogeneity arises and show that this equation of state describes the evolution of a universe evolving from a phase dominated by non-relativistic matter to a phase dominated by a cosmological constant via an intermediate period where the effective equation of …
Motivated by recent developments in particle physics and cosmology, there has been growing interest in an unified description of dark matter and dark energy scenarios. In this paper we explore observational constraints from age estimates of high-$z$ objects on cosmological models dominated by an exotic fluid with equation of state $p = -A/ρ^α$ (the so-called generalized Chaplygin gas) which has the interesting feature of interpolating between non-relativistic matter and negative-pressure dark energy regimes. As a general result we find that, if the age estimates of these objects are correct, t…
Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. We consider the hypothesis that the transition to the accelerated period involves a quantum mechanical process. Three physically admissible cases are possible. In particular, we identify a minisuperspace configuration with two Lorentzian sectors, separated by a classically forbidden region. The Hartle-Hawking and Vilenkin wave functions are computed, together with the transition amplitudes towards the accelerating epoc…
The Chaplygin gas model, characterized by an equation of state of the type $p = - \frac{A}ρ$ emerges naturally from the Nambu-Goto action of string theory. This fluid representation can be recast under the form of a tachyonic field given by a Born-Infeld type Lagrangian. At the same time, the Chaplygin gas equation of state can be obtained from a self-interacting scalar field. We show that, from the point of view of the supernova type Ia data, the three representations (fluid, tachyonic, scalar field) lead to the same results. However, concerning the matter power spectra, while the fluid and t…
Integrability conditions arising from general irrotational fluid-flow considerations of a universe dominated by cosmic dark fluids will be investigated under special assumptions on the nature of the spacetime shear. Special emphasis will be placed on linearized perturbations of quasi-Newtonian and anti-Newtonian spacetimes, whereby the conditions for the existence and consistent evolution of such spacetimes in the presence of the Chaplygin gas fluid model will be derived and discussed.
We propose a phenomenological model for the early universe where there is a smooth transition between an early "quintessence" phase and a radiation dominated era. The matter content is modelled by an appropriately modified Chaplygin gas for the early universe. We constrain the model observationally by mapping the primordial power spectrum of the scalar perturbations to the latest data of WMAP7. We compute as well the spectrum of the primordial gravitational waves as would be measured today. We show that the high frequencies region of the spectrum depends on the free parameter of the model and …
A Universe containing uniform magnetic fields, strings, or domain walls is shown to have an ellipsoidal expansion. This case has motivations from observational cosmology especially the anomaly concerning the low quadrupole amplitude compared to the best-fit $Λ$CDM prediction in Planck data. It is shown that a Universe with eccentricity at decoupling of order $10^{-2}$ can reduce the quadrupole amplitude without affecting higher multipoles of the angular power spectrum of the temperature anisotropy. We study the evolution of ellipsoidal Universes using dynamical system techniques for the first …
We investigate the linear growth function for the large scale structures of the universe considering modified Chaplygin gas as dark energy. Taking into account observational growth data for a given range of redshift from the Wiggle-Z measurements and rms mass fluctuations from Ly-$α$ measurements we numerically analyze cosmological models to constrain the parameters of the MCG. The observational data of Hubble parameter with redshift ($Z$) is also considered. The Wang-Steinhardt ansatz for growth index $γ$ and growth function $f$ (defined as $f=Ω_{m}^γ (a)$) are considered for the numerical an…
The growth of large scale structure is studied in a universe containing both cold dark matter (CDM) and generalized Chaplygin gas (GCg). GCg is assumed to contribute only to the background evolution of the universe while the CDM component collapses and forms structures. We present some new analytical as well as numerical results for linear and non-linear growth in such model. The model passes the standard cosmological distance test without the need of a cosmological constant (LCDM). But we find that the scenario is severely constrained by current observations of large scale structure. Any smal…
In this paper we consider a cosmological model whose main components are a scalar field and a generalized Chaplygin gas. We obtain an exact solution for a flat arbitrary potential. This solution have the right dust limit when the Chaplygin parameter $A\rightarrow 0$. We use the dynamical systems approach in order to describe the cosmological evolution of the mixture for an exponential self-interacting scalar field potential. We study the scalar field with an arbitrary self-interacting potential using the "Method of $f$-devisers." Our results are illustrated for the special case of a coshlike p…
We investigate a model of interacting dark matter and dark energy given by a modified holographic Ricci cutoff in a spatially flat Friedmann-Robertson-Walker (FRW) space-time. We consider a nonlinear interaction consisting of a significant rational function of the total energy density and its first derivative homogeneous of degree one and show that the effective one-fluid obeys the equation of state of a relaxed Chaplygin gas. So that, the universe is dominated by pressureless dark matter at early times and undergoes an accelerated expansion in the far future driven by a strong negative pressu…
Higher-Dimensional Cosmology in the Framework of Generalized Chaplygin Gas: An Approximation Method
Netaji Nagar Day College（奈塔吉·纳加尔日学院）；Relativity and Cosmology Research Centre, Jadavpur University（贾达普大学相对论与宇宙学研究中心）；New Alipore College (Retd.)（新阿里波尔学院（退休））；Department of Physics, University of North Bengal（北孟加拉大学物理系）
We investigate the late time acceleration with a Chaplygin type of gas in spherically symmetric inhomogeneous model. At the early phase we get Einstien-deSitter type of solution generalised to inhomogeneous spacetime. But at late stage of the evolution our solutions admit the accelerating nature of the universe. For a large scale factor our model behaves like a ?CDM model. We calculate the deceleration parameter for this anisotropic model, which, unlike its homogeneous counterpart, shows that the flip is not syn- chronous occurring early at the outer shells. This is in line with other physical…
The type Ia supernovae observational data are used to estimate the parameters of a cosmological model with cold dark matter and the Chaplygin gas. The Chaplygin gas model depends essentially on four parameters: the Hubble constant, the velocity of the sound of the Chaplygin gas, the curvature of the Universe and the fraction density of the Chaplygin gas and the cold dark matter. The Bayesian parameter estimation yields $H_0 = 62.1^{+3.3}_{-3.4} km/Mpc.s$, $Ω_{k0} = -0.84^{+1.51}_{-1.23}$, $Ω_{m0} = 0.0^{+0.82}_{-0.0}$, $% Ω_{c0} = 1.40^{1.15}_{-1.16}$, $\bar{A} = c_s^2 = 0.93^{+0.07}_{-0.21} c…
The standard model of cosmology is investigated using time dependent cosmological constant $Λ$ and Newton's gravitational constant $G$. The total energy content is described by the modified Chaplygin gas equation of state. It is found that the time dependent constants coupled with the modified Chaplygin gas interpolate between the earlier matter to the later dark energy dominated phase of the universe. We also achieve a convergence of parameter $ω\to-1$, with minute fluctuations, showing an evolving $ω$. Thus our model fairly alleviates the cosmic coincidence problem which demands $ω=-1$ at pr…
The type Ia supernovae (SNe Ia) observational data are used to estimate the parameters of a cosmological model with cold dark matter and the generalized Chaplygin gas model (GCGM). The GCGM depends essentially on five parameters: the Hubble constant, the parameter $\bar{A}$ related to the velocity of the sound, the equation of state parameter $α$, the curvature of the Universe and the fraction density of the generalized Chaplygin gas (or the cold dark matter). The parameter $α$ is allowed to take negative values and to be greater than 1. The Bayesian parameter estimation yields $α= - 0.86^{+6.…
The generalized second law of gravitational thermodynamics is examined in scenarios where the dark energy dominates the cosmic expansion. For quintessence and phantom fields this law is fulfilled but it may fail when the dark energy is in the form of a Chaplygin gas. However, if a black hole is allowed in the picture, the law can be violated if the field is of phantom type.
The universal lower bound of the ratio of shear viscosity to entropy density is suggested by the string theory and gauge duality for any matter. We examined the ratio of shear viscosity to entropy density for viscous accretion flow towards a central gravitating object in the presence of dark energy. The ratio appears close to the universal lower bound for certain optically thin, hot accretion flows as they are embedded by strong magnetic field. Dark energy is a kind of exotic matter which has negative pressure. So dark energy creates repulsive force between the accreting particles, which indic…
Dynamical systems analysis of a cosmological model with interacting Umami Chaplygin fluid in adiabatic particle creation mechanism: Some bouncing features
Flat FRW perfect fluid cosmologies can be reproduced as particular solutions of suitable field theoretical models. Here we investigate the stability of perfect fluid model trajectories with respect to sets of trajectories of the corresponding field models having generic initial conditions. It is shown that the trajectories of barotropic perfect fluid models and those of the Chaplygin gas model are stable. The total probability to reach the Chaplygin gas regime early enough to achieve a matter dominated stage having a realistic duration is calculated for a scalar field model assuming a natural …
Classical models for dark energy can exhibit a variety of singularities, many of which occur for scale factors much bigger than the Planck length. We address here the issue whether some of these singularities, the big freeze and the big demarrage, can be avoided in quantum cosmology. We use the framework of quantum geometrodynamics. We restrict our attention to a class of models whose matter content can be described by a generalized Chaplygin gas and be represented by a scalar field with an appropriate potential. Employing the DeWitt criterium that the wave function be zero at the classical si…
We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when $d = 0$. We have drawn the best fit graph using the data obtained by the differential age method (CC) and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in …
In this paper we show that a \emph{one-to-one} correspondence exists between any dark energy model and an equivalent (from a cosmological point of view, in the absence of perturbations) quartessence model in which dark matter and dark energy are described by a single perfect fluid. We further show that if the density fluctuations are small, the evolution of the sound speed squared, $c_s^2$, is fully coupled to the evolution of the scale factor and that the transition from the dark matter to the dark energy dominated epoch is faster (slower) than in a standard $Λ$CDM model if $c_s^2 > 0$ ($c_s^…
Anisotropic stress contributions to the gravitational field can arise from magnetic fields, collisionless relativistic particles, hydrodynamic shear viscosity, gravitational waves, skew axion fields in low-energy string cosmologies, or topological defects. We investigate the effects of such stresses on cosmological evolution, and in particular on the dissipation of shear anisotropy. We generalize some previous results that were given for homogeneous anisotropic universes, by including small inhomogeneity in the universe. This generalization is facilitated by a covariant approach. We find that …
The currently accelerated expansion of our Universe is unarguably one of the most intriguing problems in today's physics research. Two realistic non-minimal torsion-matter coupling $f(T)$ models have been established and studied in our previous papers [Phys. Rev. D92, 104038(2015) and Eur. Phys. J. C77, 504(2017)] aiming to explain this "dark energy" problem. In this paper, we study the generalized power-law torsion-matter coupling $f(T)$ model. Dynamical system analysis shows that the three expansion phases of the Universe, i.e. the radiation dominated era, the matter dominated era and the da…
Using the spherically symmetric inhomogeneous Lemaitre-Tolman-Bondi dust solution, we study how the shear and the backreaction depend on the sharpness of the spatial transition between voids and walls and on the size of the voids. The voids considered here are regions with matter density Omega ~ 0 and expansion rate Ht ~ 1, while the walls are regions with matter density Omega ~ 1 and expansion rate Ht ~ 2/3. The results indicate that both the volume-average shear and the variance of the expansion rate grow proportional to the sharpness of the transition and diverge in the limit of a step func…
