In the context of brane cosmology, we investigate exact solution of the gravitational field equations in the Randall-Sundrum model for an anisotropic brane with Bianchi V geometry, with a generalized Chaplygin gas, which plays the role of dark energy and interacts with dark matter particles. Also, the behavior of the observationally important parameters like expansion and anisotropy is examined.
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.
This manuscript investigate the dark energy Bianchi type-I cosmological models in presence of generalized Chaplygin gas, variable gravitational and cosmological constants. In this manuscript, exact solutions of Einstein field equations are obtained under the assumption of time periodic varying deceleration parameter. The physical and dynamical behaviors of the models have been discussed with the help of graphical representations. Also we have discussed the stability and physical acceptability of the obtained solutions
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…
In this paper we construct modified cosmic Chaplygin gas which has viscosity. We use exponential function method to solve non-linear equation and obtain time-dependent dark energy density. Then discuss Hubble expansion parameter and scale factor and fix them by using observational data. We also investigate stability of this theory.
In this work, we consider F(R) alternative theories of gravity with an eye to Noether symmetry through the gauge theorem. For non-vacuum models, one finds Λ like gravity with energy density of Chaplygin Gas. We also obtain the effective equation of state parameter for corresponding cosmology and scale factor behavior with respect to cosmic time which show that the model provides viable EoS and scale factor with respect to observational data.
In this paper we discuss the inflationary universe in the context of a Chaplygin gas equation of state within the framework of the effective theory of loop quantum cosmology. Under the slow-roll approximation, we calculate the primordial perturbations for this model. We give the general expressions of the scalar spectral index, its running, and the tensor-to-scalar ratio, etc. For the chaotic inflation with a quadratic potential, using the WMAP 5-year results, we determine the parameters of the Chaplygin inflation model in loop quantum cosmology. The results are consistent with the WMAP observ…
The modified Chaplygin gas (MCG) cosmological model is derived by using the geometrothermodynamics (GTD) formalism. We show that the MCG corresponds to a system with internal thermodynamic interaction and describes the current accelerated expansion of the universe. Moreover, we also show that the MCG can be interpreted as a unified model for dark energy and dark matter that is perfectly consistent with the current SNe observations and CMB anisotropy measurements.
In this work, we focus on the collapse of a spherically symmetric perturbation, with a classical top-hat profile, to study the nonlinear evolution of only viscous modified Chaplygin gas (VMCG) perturbations in Einstein's gravity as well as in loop quantum Cosmology (LQC). In the perturbed region, we have investigated the natures of equation of state parameter, square speed of sound and another perturbed quantities. The results have been analyzed by numerical and graphical investigations.
In this paper, we study two different models of dark energy based on Chaplygin gas equation of state. The first model is the variable modified Chaplygin gas while the second one is the extended Chaplygin gas. Both models are considered in the framework of higher order $f(R)$ modified gravity. We also consider the case of time varying gravitational constant $G$ and $Λ$ for both models. We investigate some cosmological parameters such as the Hubble, the deceleration and the equation of state parameters. Then we showed that the model that we considered, extended Chaplygin gas with time-dependent …
We find exact solution of the Einstein equations in the context of the brane world scenario. We have supposed a {generalized chaplygin gas} equation of state for bulk. This study display a constant energy density and pressure for bulk in late time. It is shown that our assumptions impose a specific equation of state on brane. {In this work, we have obtained a decelerate universe in early time and late time.} In the end, it is shown that under some assumption we have equation of state of cosmological constant for bulk.
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…
In this paper we study the perturbations of a cosmic multi-fluid medium consisting of radiation, dust and a Chaplygin gas. To do so, we follow the 1 + 3 covariant formalism and derive the evolution equations of the fluctuations in the energy density for each species of fluid in the multi-fluid system. The solutions to these coupled systems of equations are then computed in both short-wavelength and long-wavelength modes. Our preliminary results suggest that unlike most dark energy models that discourage large-scale structure formation due to the rapid cosmological expansion (which gives little…
In this work, we study the Friedmann-Robertson-Walker cosmology in which a Chaplygin gas is coupled to a non-linear scalar field in the framework of the Hořava-Lifshitz theory. In writing the action of the matter part, we use the Schutz's formalism so that the only degree of freedom of the Chaplygin gas plays the role of an evolutionary parameter. In a minisuperspace perspective, we construct the Lagrangian for this model and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Hořava theory. In such a set-up and by using of some appr…
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…
The quantum cosmology of the string effective action is considered within the context of the Bianchi class A minisuperspace. An exact unified solution is found for all Bianchi types and interpreted physically as a quantum wormhole. The solution is generalized for types ${\rm VI_0}$ and ${\rm VII_0}$. The Bianchi type IX wavefunction becomes increasingly localized around the isotropic Universe at large three-geometries.
In this paper, we investigate the statefinder, the deceleration and equation of state parameters when universe is composed of generalized holographic dark energy or generalized Ricci dark energy for Bianchi I universe model. These parameters are found for both interacting as well as non-interacting scenarios of generalized holographic or generalized Ricci dark energy with dark matter and generalized Chaplygin gas. We explore these parameters graphically for different situations. It is concluded that these models represent accelerated expansion of the universe.
The Wheeler-DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for Bianchi type I cosmology. Exact solutions are found for two selfinteracting potentials and arbitary coupling function. The WKB wavefunctions are obtained and a family of solutions satisfying the Hawking-Page regularity conditions of wormholes are found.
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those encountered in the analysis of the (anisotropic but spatially flat) Bianchi type I space-times, and of the (spatially curved but isotropic) k=+/-1 models. We address these and show that the big-bang singularity is resolved in the same precise sense as in the recent analysis of the Bianchi I model. Bianchi II space-times are of special interest to quantum cosmo…
In the frame of the scalar field model with non minimal kinetic coupling to gravity, we study the cosmological solutions of the Chaplygin gas model of dark energy. By appropriately restricting the potential, we found the scalar field, the potential and coupling giving rise to the Chaplygin gas solution. Extensions to the generalized and modified Chaplygin gas have been made.
The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present the effective equations which provide modifications to the classical equations of motion due to quantum geometry effects.
Some cosmological solutions of massive strings are obtained in Bianchi I space-time following the techniques used by Letelier and Stachel. A class of solutions corresponds to string cosmology associated with/without a magnetic field and the other class consists of pure massive strings, obeying the Takabayashi equation of state.
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,…
The loop quantum cosmology of the Bianchi type II string cosmological model in the presence of a homogeneous magnetic field is studied. We present the effective equations which provide modifications to the classical equations of motion due to quantum effects. The numerical simulations confirm that the big bang singularity is resolved by quantum gravity effects.
A new class of Bianchi - I cosmological model with magnetic field within the frame work of Lyra geometry has been presented . Exact solutions to the field equations for the model are obtained . The physical and kinematical behaviors of the model have been discussed.
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）
In this article, we study the equations driving the dynamics of a Bianchi-I universe described by holonomy corrected effective loop quantum cosmology. We derive the LQC-modified generalized Friedmann equation, which is used as a guide to find different types of solutions. It turns out that, in this framework, most solutions never reach the classical behavior.
The subject of our interest is an extended Chaplygin gas cosmology. In Literature a variety of cosmological models exist studying the behavior of the universe in the presence of the Chaplygin gas. From its initial form Chaplygin gas evolved and accepted different EoS-s and we will work with one of them. The main purpose of this work is to study behavior of the universe in Lyra Manifold with a varying Effective $Λ$-Term, which gives us modified field equations. We are also interested in the behavior of the universe in the case of an existing coupling between the quintessence DE and extended Cha…
In the current framework of Einstein's equations in general relativity (GR), gravity is described by the spacetime curvature. However, there are other descriptions where the origin of gravity can be understood through torsion and non-metricity $Q$. In this work, we discuss a modified theory of gravity namely $f(Q)$ gravity, which considers a non-linear extension of $Q$. In particular, we study the case where it is non-minimally coupled to matter. Motivated by the recent success of Chaplygin gas models in the explanation of dark energy, we assume a pressureless baryonic matter and a generalized…
We examine the dynamical consequences of homogeneous cosmological magnetic fields in the framework of loop quantum cosmology. We show that a big-bounce occurs in a collapsing magnetized Bianchi I universe, thus extending the known cases of singularity-avoidance. Previous work has shown that perfect fluid Bianchi I universes in loop quantum cosmology avoid the singularity via a bounce. The fluid has zero anisotropic stress, and the shear anisotropy in this case is conserved through the bounce. By contrast, the magnetic field has nonzero anisotropic stress, and shear anisotropy is not conserved …
In this paper, we have studied flat Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state $p_{m}=Aρ-% \frac{B}{ρ^{γ}}$, where $0\leq A\leq 1$, $0\leq γ\leq 1$ and $B$ is any positive constant in }${\footnotesize f(R,T)}${\footnotesize \ gravity with particle creation. We have considered a simple parametrization of the Hubble parameter $H$ in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the…
This brief article sums up results obtained in arXiv:0911.2653, which develops a constrained SU(2) lattice gauge theory in the "dipole" approximation. This is a further step toward the issue of a (inhomogeneous) loop quantum cosmology and its merging into loop quantum gravity.
A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmological string is considered. The first objective of this study is to investigate Einstein equations using a tractable assumption usually accepted in the literature. Quantum effects of the present cosmological model are examined in the framework of loop quantum cosmology. Finally we draw a parallel between the classical and quantum approaches.
The canonical theory of (N=1) supergravity, with a matrix representation for the gravitino covector-spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.
The dynamics of Dvali-Gabadadze-Porrati Cosmology (DGP) braneworld with an anisotropic brane is studied. The Friedmann equations and their solutions are obtained for two branches of anisotropic DGP model. The late time behavior in DGP cosmology is examined in the presence of anisotropy which shows that universe enters a self-accelerating phase much later compared to the isotropic case. The acceleration conditions and slow-roll conditions for inflation are obtained.
In this paper we consider the flat FRW cosmology with a scalar field coupled with the metric along with generalized Chaplygin gas and perfect fluid comprising the matter sector. We use the Schutz's formalism to deal with the generalized Chaplygin gas sector. The full theory is then quantized canonically using the Wheeler-DeWitt Hamiltonian formalism. We then solve the WD equation with appropriate boundary conditions. Then by defining a proper completeness relation for the self-adjointness of the WD equation we arrive at the wave packet for the universe. It is observed that the peak in the prob…
We study the spherical top-hat collapse in Einstein gravity and loop quantum cosmology by taking the non-linear evolution of viscous modified variable chaplygin gas and viscous generalized cosmic chaplygin gas. We calculate the equation of state parameter, square speed of sound, perturbed equation of state parameter, perturbed square speed of sound, density contrast and divergence of peculiar velocity in perturbed region and discussed their behavior. It is observed that both chaplygin gas models support the spherical collapse in Einstein as well as loop quantum cosmology because density contra…
In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid ($γ=1$). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables $\rm q^i$ does not commute, so the simplectic structure was modified.
We investigate Holographic Dark Energy Correspondence of Interacting Generalized Chaplygin Gas model in the framework of compact Kaluza-Klein cosmology. The evolution of the modified holographic dark energy and the equation of state parameter is obtained here.Using the present observational value of density parameter a stable configuration is formed which accommodates Dark Energy. we note a connection between Dark Energy and Phantom field and have shown that Dark Energy might have evolved from a Phantom state in the past.
Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.
The concordance model of cosmology contains several unknown components such as dark matter and dark energy. Many proposals have been made to describe them by choosing an appropriate potential for a scalar field. We study four models in the realm of loop quantum cosmology (LQC): the Chaplygin gas, an inflationary and radiation-like potential, quintessence and an anti-Chaplygin gas. For the latter we show that all trajectories start and end with a type II singularity and, depending on the inital value, may go through a bounce. On the other hand the evolution under the influence of the first thre…
The present study investigates the nature of the field potential via new technique known as reconstruction method for the scalar field potentials. The key point of this technique is the assumption that Hubble parameter is dependent on the scalar field. We consider Bianchi type I universe in the gravitational framework of scalar-tensor gravity and explore the general form of the scalar field potential. In particular, this field potential is investigated for the matter contents like barotropic fluid, the cosmological constant and Chaplygin gas. It is concluded that for a given value of Hubble pa…
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a massless scalar field was recently constructed. In this paper, its effective dynamics with the LQC discreteness corrections is studied and the equations of motion are analytically solved, showing that the big bang singularity is replaced by the big bounces, which take place up to three times, once in each diagonal direction, whenever each of the area scale factors approaches its critical value in the Planck regime measured by the reference of the scalar field momentum.
In this paper, we study the holographic dark energy density and interacting extended Chaplygin gas energy density in the Einstein gravity. We reconstruct the scalar field and the scalar potential describing the extended Chaplygin gas. In the special case, we obtain energy density and investigate some cosmological parameters. Assuming interaction between components we find energy density for some different parametrization of total EoS. We analyze tensor to scalar ratio and use recent observational data of BICEP2 to fix the model parameters.
We consider a new generalized Chaplygin gas model that includes the original Chaplygin gas model as a special case. In such a model the generalized Chaplygin gas evolves as from dust to quiessence or phantom. We show that the background evolution for the model is equivalent to that for a coupled dark energy model with dark matter. The constraints from the current type Ia supernova data favour a phantom-like Chaplygin gas model.
We study numerically the solutions to the effective equations of Bianchi IX spacetimes within Loop Quantum Cosmology. We consider Bianchi IX models with and without inverse triad corrections whose matter content is a scalar field without mass. The solutions are classified using the classical observables. We show that both effective theories --with lapse N=V and N=1-- solve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the spatial compactness, there is an infinity number of bounces and recollapses. We study the limit of large volume and show…
Modified Chaplygin gas as an exotic fluid has been introduced in [34]. Essential features of the modified Chaplygin gas as a cosmological model are discussed. Observational constraints on the parameters of the model have been included. The relationship between the modified Chaplygin gas and a homogeneous minimally coupled scalar field are reevaluated by constructing its self-interacting potential. In addition, we study the role of the tachyonic field in the modified Chaplygin gas cosmological model and the mapping between scalar field and tachyonic field is also considered.
In this letter, we have considered that the universe is filled with normal matter and variable modified Chaplygin gas. Also we have considered the interaction between normal matter and variable modified Chaplygin gas in FRW universe. Then we have considered a correspondence between the holographic dark energy density and interacting variable modified Chaplygin gas energy density. Then we have reconstructed the potential of the scalar field which describes the variable modified Chaplygin cosmology.
A path integral formulation of the Bianchi I models containing a massless scalar field in loop quantum cosmology is constructed. Following the strategy used in the homogenous and isotropic case, the calculation is extended to the simplest non-isotropic models according to the $\barμ$ and $\barμ^{\prime}$ scheme. It is proved from the path integral angle that the quantum dynamic lacks the full invariance with respect to fiducial cell scaling in the $\barμ$ scheme, but it does not in the $\barμ^{\prime}$ scheme. The investigation affirms the equivalence of the canonical approach and the path int…
We study the anisotropic Bianchi I loop quantum cosmology in 2+1 dimensions. Both the $\mubar$ and $\mubar'$ schemes are considered in the present paper and the following expected results are established: (i) the massless scalar field again play the role of emergent time variables and serves as an internal clock; (ii) By imposing the fundamental discreteness of length operator, the total Hamiltonian constraint is obtained and gives rise the evolution as a difference equation; and (iii) the exact solutions of Friedmann equation are constructed rigorously for both classical and effective level. …
We want to study the perturbation growth of an initial seed of an ellipsoidal shape in Top-Hat collapse model of structure formation in the Modified Chaplygin gas cosmology. Considering reasonable values of the constants and the parameters of the model under study, it is shown that a very small deviation from spherical symmetry (ellipsoidal geometry) in the initial seed leads to a final highly non-spherical structure which can be considered as a candidate for justifying already known cosmological structures as cosmic walls and filaments.
Using a conformal version of the Bianchi I metric and a perfect fluid energy-momentum tensor, we show that the resulting Einstein field equations are equivalent to a generalized Ermakov-Milne-Pinney equation. Using a transformation analogous to the known correspondence between the classical EMP and a linear Schrödinger equation, we then construct the linear Schrödinger formulation for this cosmological model. Also, a note is included to show the extra term that arises when the energy-momentum tensor is taken to include a second term in addition to the scalar field.
In this paper we study the exact solutions for a viscous fluid distribution in Bianchi II, VIII, and IX models. The metric is simplified by assuming a relationship between the coefficients and the metric tensor. Solutions are obtained in two special cases: in one, an additional assumption is made where the matter density and the expansion scalar have a definite relation and in the other a barotropic equation of state between the matter density and the thermodynamic pressure is assumed. While the Bianchi II solutions are already found in the literature the other two classes of solutions are app…
We develop the "triangulated" version of loop quantum cosmology, recently introduced in the literature. We focus on the "dipole" cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model…
In this work, we establish a correspondence between the interacting holographic, new agegraphic dark energy and generalized Chaplygin gas model in Bianchi type I universe. In continue, we reconstruct the potential of the scalar field which describes the generalized Chaplygin cosmology. Cosmological solutions are obtained when the kinetic energy of the phantom field is order of the anisotropy and dominates over the potential energy of the field. We investigate observational constraints on the generalized Chaplygin gas, holographic and new agegraphic dark energy models as the unification of dark…
This paper is devoted to investigate the exact solutions of Bianchi type $I$ spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum tensor $T$. For this purpose, we find two exact solutions using the assumption of constant deceleration parameter and variation law of Hubble parameter. The obtained solutions correspond to two different models of the universe. The physical behaviour of these models is also discussed.
We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic $k$=1 model that, classically, is contained within the Bianchi IX mo…
