In the framework of spatially averaged inhomogeneous cosmologies in classical general relativity, effective Einstein equations govern the dynamics of averaged scalar variables in a scale--dependent way. A particular cosmology may be characterized by a cosmic equation of state, closing the hierarchy of effective equations. In this context a natural candidate is provided by the Chaplygin gas, standing for a unified description of dark energy and dark matter. In this paper, we suppose that the inhomogeneous properties of matter and geometry obey the Chaplygin equation of state. The most extreme interpretation assumes that both dark energy and dark matter are not included as additional sources, but are both manifestations of spatial geometrical properties. This feature is an important conceptual difference in comparison with the standard approach of a Friedmann-Lemaître-Robertson-Walker universe filled with dust and another fundamental field characterized by the Chaplygin equation of state. We finally discuss the consequences of the resulting scenario for effective cosmological parameters in order to establish the framework of a future confrontation with observations, and we note that the standard Chaplygin gas may not be ruled out by them.
The hypothesis that dark matter and dark energy are unified through the Chaplygin gas is reexamined. Using a generalization of the spherical model which incorporates effects of the acoustic horizon we show that an initially perturbative Chaplygin gas evolves into a mixed system containing cold dark matter in the form of gravitational condensate. Furthermore, we demonstrate that the observed CMB angular and baryonic power spectra are reproduced.
We extend the world model of Kamenshchik et al. to large perturbations by formulating a Zeldovich-like approximation. We sketch how this model unifies dark matter with dark energy in a geometric setting reminiscent of M-theory.
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…
A generalized equation of state corresponding to a model that includes a Chaplygin gas and a viscous term is investigated, in the context of the reconstruction program in scalar field cosmology. The corresponding inflationary model parameters can be conveniently adjusted in order to reproduce the most recent PLANCK data. The influence of the Chaplygin gas term contribution, in relation with previous models, is discussed. Exit from inflation is shown to occur quite naturally in the new model.
The Generalized Chaplygin Gas (GCG) model is characterized by the equation of state $P = -A ρ^{-α}$, where $A>0$ and $α< 1$. The model has been extensively studied due to its interesting properties and applicability in several contexts, from late-time acceleration to primordial inflation. Nonetheless we show that the inflationary slow-roll regime cannot be satisfied by most of the parameter space of the GCG model when General Relativity (GR) is considered. In particular, although the model has been applied to inflation with $0 < α< 1$, we show that for $-1 < α\le 1$ there is no expansion of th…
The goal of this paper is to discuss phase space analysis of some interacting Chaplygin gas models in General Relativity. Chaplygin gas is one of the fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. In this paper we have considered various forms of interaction term Q including linear and non linear sign changeable interactions. For each case late time attractors for the field equations are found.
We have examined the possible construction of a stationary, spherically symmetric and spatially inhomogeneous wormhole spacetime supported by the phantom energy. The later is supposed to be represented by the modified Chaplygin gas equation of state. The solutions so obtained satisfy the flare out and the asymptotic flatness conditions. It is also shown that the averaged null energy condition has to be violated for the existence of the wormhole.
We investigate a kind of interacting Chaplygin gas model in which the Chaplygin gas plays the role of dark energy and interacts with cold dark matter particles. We find that there exists a stable scaling solution at late times with the Universe evolving into a phase of steady state. Furthermore, the effective equation of state of Chaplygin gas may cross the so-called phantom divide $w=-1$. The above results are derived from continuity equations, which means that they are independent of any gravity theories. Assuming standard general relativity and a spatially flat FRW metric, we also find the …
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,…
Vacuum energy is a simple model for dark energy driving an accelerated expansion of the universe. If the vacuum energy is inhomogeneous in spacetime then it must be interacting. We present the general equations for a spacetime-dependent vacuum energy in cosmology, including inhomogeneous perturbations. We show how any dark energy cosmology can be described by an interacting vacuum+matter. Different models for the interaction can lead to different behaviour (e.g., sound speed for dark energy perturbations) and hence could be distinguished by cosmological observations. As an example we present t…
The modified Chaplygin gas (MCG) is a strong candidate for the unified model of dark matter and dark energy. The equation of state of this modified model is valid from the radiation era to the $Λ$CDM model. In early epoch (when $ρ$ was large), dark matter had the dominant role while at later stages (when $ρ$ is small), the MCG model behaves as dark energy. In this work, we have found exact solution of static spherically symmetric Einstein equations describing a wormhole for an inhomogeneous distribution of modified Chaplygin gas. For existence of wormhole solution, there are some restrictions …
In this work we study in detail a phenomenological generalization of the Chaplygin cosmological model, which we call as \textit{umami} Chaplygin model. We consider three different cosmological background scenarios in which our fluid can play three different roles: only as a dark energy component; as a dark matter and dark energy component; and as a dark plus baryonic matter and dark energy component. With such analysis we explore the possibility to unify the dark fluids under one single component within the context of General Relativity. We test this hypothesis against the main available data …
In this contribution we summarize two recent applications of a correspondence between backreaction terms in averaged inhomogeneous cosmologies and an effective scalar field (the `morphon'). Backreaction terms that add to the standard sources of Friedmannian kinematical laws and that emerge from geometrical curvature invariants built from inhomogeneities, can be interpreted in terms of a minimally coupled scalar field in the case of a dust matter source. We consider closure conditions of the averaged equations that lead to different evolution scenarii: a) the standard Chaplygin equation of stat…
The Tolman-Bondi-Lemaître type of inhomogeneous spacetime with generalised Chaplygin gas equation of state given by $p = -\frac{A}{ρ^α}$ is investigated where $ α$ is a constant. We get an inhomogeneous spacetime at early stage but at the late stage of universe the inhomogeneity disappear with suitable radial co-ordinate transformation. For the large scale factor our model behaves like $Λ$CDM type which is in accord with the recent WMAP studies. We have calculated $\frac{\partial ρ}{\partial r}$ and it is found to be negative for $α> 0$ which is in agreement with the observational analysis. A …
In a fully inhomogeneous, anisotropic cosmological simulation performed by solving Einstein's equations with numerical relativity, we find a local measurement of the effective Hubble parameter differs by less than 1\% compared to the global value. This variance is consistent with predictions from Newtonian gravity. We analyse the averaged local expansion rate on scales comparable to Type 1a supernova surveys, and find that local variance cannot resolve the tension between the \citet{riess2018b} and \citet{planck2018a} measurements.
We study the late-time evolution of the Universe where dark energy (DE) is parametrized by a modified generalized Chaplygin gas (mGCG) on top of cold dark matter (CDM). We also take into account the radiation content of the Universe. In this context, the late stage of the evolution of the universe refers to the epoch where CDM is already clustered into inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Under these conditions, the mechanical approach is an adequate tool to study the Universe deep inside the cell of uniformity. To be more accurate, we st…
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble …
We model the dark sector of the cosmic substratum by a viscous fluid with an equation of state $p=-ζΘ$, where $Θ$ is the fluid-expansion scalar and $ζ$ is the coefficient of bulk viscosity for which we assume a dependence $ζ\propto ρ^ν$ on the energy density $ρ$. The homogeneous and isotropic background dynamics coincides with that of a generalized Chaplygin gas with equation of state $p = - A/ρ^α$. The perturbation dynamics of the viscous model, however, is intrinsically non-adiabatic and qualitatively different from the Chaplygin-gas case. In particular, it avoids short-scale instabilities a…
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…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. The isovector fields of Einstein's field equation for the models under consideration are derived. A new class of exact solutions of Einstein's field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.
This thesis concentrates on the accelerated expansion of the Universe recently explored by measurements of redshift and luminosity-distance relations of type Ia Supernovae. We have considered a model of the universe filled with modified Chaplygin gas and barotropic fluid. The role of dynamical cosmological constant has been explored with Modified Chaplygin Gas as the background fluid. Various phenomenological models for Λhave been studied in presence of the gravitational constant G to be constant or time dependent. A new form of the well known Chaplygin gas model has been presented by introduc…
We clarify the procedure for expressing the Friedmann equation in terms of directly measurable cosmological scalars constructed out of higher derivatives of the scale factor. We carry out this procedure for pure dust, Chaplygin gas and generalised Chaplygin gas energy-momentum tensors. In each case it leads to a constraint on the scalars thus giving rise to a test of General Relativity. We also discuss a formulation of the Friedmann equation as unparametrised geodesic motion and its connection with the Lagrangian treatment of perfect fluids coupled to gravity.
We provide an explicit calculation of the evolution of the cosmic entanglement entropy in the early universe before the matter dominant era. This is made possible by invoking the generalized Chaplygin gas (GCG) model, which has the advantage of preserving unitarity and providing a smooth transition between the inflation epoch and the radiation dominant era. The dynamics of the universe is described by the quantization in the minisuperspace of the GCG model, following the prescription proposed by Wheeler and DeWitt. Two sources of contribution to the cosmic entanglement entropy are considered: …
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional Euclidean space and deriving the time evolution equations for them. In contrast to the popular Buchert's scheme it allows to coarse-grain tensorial quantities in a coordinate-independent way. The framework can be used to estimate backreaction in inhomogeneous cosmological models.
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions.
A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion ($θ$) in the model is proportional to the eigen value $σ^{1}_{1}$ of the shear tensor $σ^{i}_{j}$. Certain physical and geometric properties of the models are also discussed.
We modify Einstein General Relativity by adding non-dynamical scalar fields to account simultaneously for both dark matter and dark energy. The dark energy in this case can be distributed in-homogeneously even within horizon scales. Its inhomogeneities can contribute to the late time integrated Sachs-Wolfe effect, possibly removing some of the low multipole anomalies in the temperature fluctuations of the CMB spectrum. The presence of the inhomogeneous dark matter also influences structure formation in the universe.
While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, non-linear and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaïtre-Robertston-Walker (FLRW) behavior, however this universe also exhibits loca…
The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for the evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates the landscape with both de Sitter (dS) and AdS vacua. The simulation results show that eventually either the field in different region separates into different vacua, so that the expanding dS or AdS bubbles (the bubble wall is expanding but the spacetime inside AdS bubbles is contracting) come into being with clear bounderies, or overall region is dS expanding with a few smal…
The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those given in the Lagrangian perturbation theory in Newtonian cosmology. Neglecting the cosmological constant and assuming a flat background model we give the solutions of the nonlinear dynamics of cosmological perturbations. We present the complete second-order solutions, which extend and improve earlier works.
Emergent Universe Scenario in the Modified Chaplygin gas : Towards an Exact Solution and Observational Constraints
Netaji Nagar Day College（纳塔吉·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）
For general relativistic spacetimes filled with an irrotational perfect fluid a generalized form of Friedmann's equations governing the expansion factor of spatially averaged portions of inhomogeneous cosmologies is derived. The averaging problem for scalar quantities is condensed into the problem of finding an `effective equation of state' including kinematical as well as dynamical `backreaction' terms that measure the departure from a standard FLRW cosmology. Applications of the averaged models are outlined including radiation-dominated and scalar field cosmologies (inflationary and dilaton/…
For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law go…
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence o…
A Study of Non-Singular Bounce in Myrzakulov-type $f(R,T)$ Gravity with Chaplygin Gas
Amity University Kolkata（加尔各答阿米提大学）；Ahram Canadian University（埃及阿拉姆加拿大大学）；Islamic University of Madinah（麦地那伊斯兰大学）；The Egyptian Center for Theoretical Physics (ECTP)（埃及理论物理中心）
Vacuum energy remains the simplest model of dark energy which could drive the accelerated expansion of the Universe without necessarily introducing any new degrees of freedom. Inhomogeneous vacuum energy is necessarily interacting in general relativity. Although the four-velocity of vacuum energy is undefined, an interacting vacuum has an energy transfer and the vacuum energy defines a particular foliation of spacetime with spatially homogeneous vacuum energy in cosmological solutions. It is possible to give a consistent description of vacuum dynamics and in particular the relativistic equatio…
We analyze the compatibility between the geometrodynamics and thermodynamics of a binary mixture of perfect fluids which describe inhomogeneous cosmological models. We generalize the thermodynamic scheme of general relativity to include the chemical potential of the fluid mixture with non-vanishing entropy production. This formalism is then applied to the case of Szekeres and Stephani families of cosmological models. The compatibility conditions turn out to impose symmetry conditions on the cosmological models in such a way that only the limiting case of the Friedmann-Robertson-Walker model re…
We present cosmological-scale numerical simulations of an evolving universe in full general relativity (GR) and introduce a new numerical tool, {\sc CosmoGRaPH}, which employs the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism on a 3-dimensional grid. Using {\sc CosmoGRaPH}, we calculate the effect of an inhomogeneous matter distribution on the evolution of a spacetime. We also present the results of a set of standard stability tests to demonstrate the robustness of our simulations.
Recently, spatially inhomogeneous cosmological models have been proposed as an alternative to the LCDM model, with the aim of reproducing the late time dynamics of the Universe without introducing a cosmological constant or dark energy. This paper investigates the possibility of distinguishing such models from the standard LCDM using background or large scale structure data. It also illustrates and emphasizes the necessity of testing the Copernican principle in order to confront the tests of general relativity with the large scale structure.
How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedman-Lemaitre-Robertson-Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables …
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods: LeVeque's multi-dimensional high-resolution integration scheme which allows accurate evolution of solutions containing discontinuities or steep gradients, and an adaptive mesh refinement (AMR) algorithm which enables the local resolution of a simulation to vary dynamically in response to the behaviour of the evolved solution. A family of hyperbolic formulations o…
A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant, coordinate-independent manner. The coarse--grained quantities are all quasi-local functionals, depending only on the geometry of the boundary of the considered domain. They can be thought of as relativistic generalizations of simple volume averages of local quantities in a flat space. The procedure is based on the isometric embedding theorem for S^2 surfaces and thus requi…
The applications of numerical relativity to cosmology are on the rise, contributing insight into such cosmological problems as structure formation, primordial phase transitions, gravitational-wave generation, and inflation. In this paper, I present the infrastructure for the computation of inhomogeneous dust cosmologies which was used recently to measure the effect of nonlinear inhomogeneity on the cosmic expansion rate. I illustrate the code's architecture, provide evidence for its correctness in a number of familiar cosmological settings, and evaluate its parallel performance for grids of up…
Motivated by the work [K. Karami, J. Fehri, {\it Phys. Lett. B} {\bf 684}, 61 (2010)] and [A. Sheykhi, {\it Phys. Lett. B} {\bf 681}, 205 (2009)], we generalize their work to the new holographic dark energy model with $ρ_D=\frac{3ϕ^2}{4ω}(μH^2+ν\dot{H})$ in the framework of Brans-Dicke cosmology. Concretely, we study the correspondence between the quintessence, tachyon, K-essence, dilaton scalar field and Chaplygin gas model with the new holographic dark energy model in the non-flat Brans-Dicke universe. Furthermore, we reconstruct the potentials and dynamics for these models. By analysis we c…
We investigate exotic stars composed of dark energy within the context of Einstein's General Relativity, by applying an extended Chaplygin gas equation-of-state. To account for anisotropies, we utilize a formalism based on the complexity factor to obtain numerical solutions. By applying well-established criteria, we demonstrate that the solutions are physically valid and well-behaved. In addition, a comparison with a more conventional approach is also conducted.
We consider the prospects for dark matter/energy unification in k-essence type theories. General mappings are established between the k-essence scalar field, the hydrodynamic and braneworld descriptions. We develop an extension of the general relativistic dust model that incorporates the effects of both pressure and the associated acoustic horizon. Applying this to a tachyon model, we show that this inhomogeneous "variable Chaplygin gas" does evolve into a mixed system containing cold dark matter like gravitational condensate in significant quantities. Our methods can be applied to any dark en…
It is shown that inhomogeneous Szekeres and Stephani universes exist corresponding to non-dissipative binary mixtures of perfect fluids in local thermal equilibrium. This result contradicts a recent statement by Zárate and Quevedo (2004 Class. Quantum Grav. {\bf 21} 197, {\it Preprint} gr-qc/0310087), which affirms that the only Szekeres and Stephani universes compatible with these fluids are the homogeneous Friedmann-Robertson-Walker models. Thus, contrarily to their conclusion, their thermodynamic scheme do not gives new indications of incompatibility between thermodynamics and relativity. T…
This review was given at the 65th birthday meeting of D.W. Sciama, The Renaissance of General Relativity and Cosmology, to be published by Cambridge University Press. It presents progress in the understanding of non-standard relativistic cosmologies during Sciama's career, organized by the areas of application rather than the mathematical types of the models.
The current cosmological model ($Λ$CDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress--energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for m…
A new family of spherically symmetric inhomogeneous solutions of Brans-Dicke gravity is generated using the Fonarev solution of general relativity as a seed and a map from the Einstein to the Jordan conformal frame. The Brans-Dicke scalar field self-interacts with a power-law or inverse power-law potential in the Jordan frame. This 4-parameter family of geometries, which is dynamical and asymptotically Friedmann-Lemaitre-Robertson-Walker, contains as special cases two previously known classes of solutions and solves also the field equations of $f(R)=R^n$ gravity
The dark energy universe equation of state (EOS) with inhomogeneous,Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how crossing of phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for universe with implicit EOS. For instance, the crossing of phantom barrier is …
Bending of light rays by gravitational sources is one of the first evidences of the general relativity. When the gravitational souce is a stationary massive object such as a black hole, the bending angle has an integral representation, from which various series expansions in terms of the parameters of orbit and the background spacetime has been derived. However, it is not clear that it has any analytic expansion. In this paper, we show that such an analytic expansion can be obtained for the case of a Schwarzschild black hole by solving an inhomogeneous Picard-Fuchs equation, which has been app…
We obtain the equations of motions of the $f(T)$ theory considering the Lemaître-Tolman-Bondi's metric for a set of diagonal and non-diagonal tetrads. In the case of diagonal tetrads the equations of motion of the $f(T)$ theory impose a constant torsion or the same equations of the General Relativity, while in the case of non-diagonal set the equations are quite different from that obtained in GR. We show a simple example of an universe dominated by the matter for the two cases. The comparison of the mass in the non-diagonal case shows a sort of increased with respect to the diagonal one. We a…
