In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function $Γ$ that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function $Γ$, along with their cosmological interpretations. The second part of our work provides two examples with specific $Γ$ functions. In the first example we provide a $Γ$ function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys.Rev. D {\bf 74}, 023523 (2006) by comparing our approach with their analysis.
The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmologies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode n…
Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature…
The quantization of gravity coupled to barotropic perfect fluid as matter field and cosmological constant is made and the wave function can be determined for any $κ$ in the FRW minisuperspace model. The meaning of the existence of the classical solution is discussed in the WKB semiclassical approximation
Using the known connection between Schroedinger-like equations and Dirac-like equations in the supersymmetric context, we discuss an extension of FRW barotropic cosmologies in which a Dirac mass-like parameter is introduced. New Hubble cosmological parameters H_K(eta) depending on the Dirac-like parameter are plotted and compared with the standard Hubble case H_0(eta). The new H_K(eta) are complex quantities. The imaginary part is a supersymmetric way of introducing dissipation and instabilities in the barotropic FRW hydrodynamics
Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H(η) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type n^2({3/2}γ-1)^2 (γ\neq 2/3) in the sech FRW adiabatic index soliton
Using the superfield approach we construct the $n=2$ supersymmetric lagrangian for the FRW Universe with barotropic perfect fluid as matter field. The obtained supersymmetric algebra allowed us to take the square root of the Wheeler-DeWitt equation and solve the corresponding quantum constraint. This model leads to the relation between the vacuum energy density and the energy density of the dust matter.
Simple linear second-order differential equations have been written down for FRW cosmologies with barotropic fluids by Faraoni. His results have been extended by Rosu, who employed techniques belonging to nonrelativistic supersymmetry to obtain time-dependent adiabatic indices. Further extensions are presented here using the known connection between the linear second-order differential equations and Dirac-like equations in the same supersymmetric context. These extensions are equivalent to adding an imaginary part to the adiabatic index which is proportional to the mass parameter of the Dirac …
The dynamical evolution of the scale factor of FRW cosmological model is presented, when the equation of state of the material content assume the form $\rm p=γρ$, $\rm γ=constant$, including the cosmological term. We use the WKB approximation and the relation with the Einstein-Hamilton-Jacobi equation to obtain the exact solutions.
It is known that barotropic FRW equations written in the conformal time variable can be reduced to simple linear equations for an exponential function involving the conformal Hubble rate. Here, we show that an interesting class of barotropic universes can be obtained in the linear limit of a special type of nonlinear dissipative Ermakov-Pinney equations with the nonlinear dissipation built from Chiellini's integrability condition. These cosmologies, which evolutionary are similar to the standard ones, correspond to barotropic fluids with adiabatic indices rescaled by a particular factor and ha…
Using technique of supersymmetric quantum mechanics we present new cosmological quantum solution, in the regime for FRW cosmological model using a barotropic perfect fluid as matter field.
In the case of barotropic FRW cosmologies, the Hubble parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. We consider these cosmologies in the framework of nonrelativistic supersymmetry that has been effective in the area of supersymmetric quantum mechanics. Recalling that Faraoni [Amer. J. Phys. 67 (1999), 732-734] showed how to reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations, we set the latter equations in the supersymmetric approach and divide their solutions into two classes of 'b…
In this work we perform a dynamical analysis of a broad class of non-minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of o…
In this paper we study the evolution of the dark energy parameter within the scope of a spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy by revisiting the recent results (Amirhashchi et al. in Chin. Phys. Lett. 28:039801, 2011a). To prevail the deterministic solution we select the scale factor $a(t) = \sqrt{t^{n}e^{t}}$ which generates a time-dependent deceleration parameter (DP), representing a model which generates a transition of the universe from the early decelerating phase to the recent accelerating phase. We consider…
In this article, we summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid's energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution para…
We study the evolution of the dark energy parameter within the scope of a spatially flat and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy. To obtain the deterministic solution we choose the scale factor $a(t) = \sqrt{t e^{t}}$ which yields a time dependent deceleration parameter (DP). In doing so we consider the case minimally coupled with dark energy to the perfect fluid as well as direct interaction with it.
The dynamics of a tachyon field plus a barotropic fluid is investigated in spatially curved FRW universe. We perform a phase-plane analysis and obtain scaling solutions accompanying with a discussion on their stability. Furthermore, we construct the form of scalar potential which may give rise to stable solutions for spatially open and closed universe separately.
We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.
Time-independent non-linear Schrödinger-type (NLS) formulation of FRW cosmology with canonical scalar field are considered in case of two barotropic fluids. We derived Friedmann formulation variables in terms of NLS variables. Seven exact solutions found by D'Ambroise \cite{DAmbroise:2010dgl} and one new found solution are explored and tested in cosmology. The result suggests that time-independent NLS formulation of cosmology case should be upgraded to the time-dependent case.
In this work, we study a cosmological model of spatially homogeneous and isotropic accelerating universe which exhibits a transition from deceleration to acceleration. For this, Friedmann Robertson Walker(FRW) metric is taken and Hybrid expansion law $a(t)=t^α \exp(βt )$ is proposed and derived. We consider the universe to be filled with two types of fluids barotropic and dark energy which have variable equations of state. The evolution of dark energy, Hubble, and deceleration parameters etc., have been described in the form of tables and figures. We consider $581$ data's of observed values of…
The barotropic indices and the corresponding FRW scale factors of the so-called Darboux cosmological fluids are presented in the comoving time axis, which is the natural one for the phenomenology related to the cosmological data. Some useful comments on the features of the plots are included
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the literature are based on non-relativistic barotropic irrotational fluids, defined in a flat Newtonian background. The extension, first to special relativistic barotropic fluid flow, and then to general relativistic barotropic fluid flow in an arbitrary background, is less straightforward than it might at first appear. In this article we provide a pedagogical …
We study the closed universe recollapse conjecture for positively curved FRW models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the $R+αR^{2}$ theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted four-dimensional dynamical system with the methods of the center manifold theory and the normal form theory. It is shown that an initially expanding closed FRW universe, starting close to the Minkowski spacetime, cannot avoid recollapse. We discuss the posibility that potentials with a…
We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $\rm[\frac{1}ϕ(8πT^{μν(M)}+T^{μν(ϕ)})]_{;ν}=0$. We take as a first model the flat FRW metric in the Hamilton-Jacobi scheme and we present the Lagrange-Charpit approach in order to find classical solutions. In the quantum scheme, once we determine the characteristic surfaces, the quantum solution is obtained. These two classes of solutions are found for all values of the barotropic parameter $γ$.
The influence of spin on a photon's motion in a Schwarzschild and FRW spacetimes is studied. The first order correction to the geodesic motion is found. It is shown that unlike the world-lines of spinless particles, the photons world-lines do not lie in a plane.
We develop a formalism to calculate the effective action of the strongly coupled conformal field theory (CFT) in curved spacetime. The effective action of the CFT is obtained from AdS/CFT correspondence. The anti de-Sitter (AdS) spacetime has various slicing which give various curved spacetime on its boundary. We show the de Sitter spacetime and the Friedmann-Robertson-Walker (FRW) universe can be embedded in the AdS spacetime and derive the scalar two-point function of the conformal fields in those spacetime. In curved spacetime, the two-point function depends on the vacuum state of the CFT. …
We study the closed universe recollapse conjecture for positively curved Friedmann-Robertson-Walker (FRW) models in the Jordan frame of the second order gravity theory. We analyse the late time evolution of the model with the methods of the dynamical systems. We find that an initially expanding closed FRW universe, starting close to the Minkowski spacetime, may exhibit oscillatory behaviour.
We investigate the cosmic dynamics of Rastall gravity in non-flat Friedmann-Robertson-Walker (FRW) space-time with barotropic fluid. In this context, we are concerned about the class of model satisfying the affine equation of state. We derive the autonomous system for the Rastall model with barotropic fluid. We apply the derived system to investigate the critical points for expanding and bouncing cosmologies and their stable nature and cosmological properties. The expanding cosmology yields de Sitter universe at late times with decelerating past having matter and radiation dominated phases. In…
In this paper, we propose a new phenomenological two parameter parametrization of $q(z)$ to constrain barotropic dark energy models by considering a spatially flat FRW universe, neglecting the radiation component, and reconstructing the effective equation of state (EoS). This two free-parameter EoS reconstruction shows a non-monotonic behavior, pointing to a more general fitting for the scalar field models, like thawing and freezing models. We constrain the $q(z)$ free parameters using the observational data of the Hubble parameter obtained from cosmic chronometers, the joint-light-analysis ty…
It is by now well known that various condensed matter systems may be used to mimic many of the kinematic aspects of general relativity, and in particular of curved-spacetime quantum field theory. In this essay we will take a look at what would be needed to mimic a cosmological spacetime -- to be precise a spatially flat FRW cosmology -- in one of these analogue models. In order to do this one needs to build and control suitable time dependent systems. We discuss here two quite different ways to achieve this goal. One might rely on an explosion, physically mimicking the big bang by an outflow o…
It is well known that for spatially flat FRW cosmologies, the holographic dark energy disfavours the Hubble parameter as a candidate for the IR cutoff. For overcoming this problem, we explore the use of this cutoff in holographic ellipsoidal cosmological models, and derive the general ellipsoidal metric induced by a such holographic energy density. Despite the drawbacks that this cutoff presents in homogeneous and isotropic universes, based on this general metric, we developed a suitable ellipsoidal holographic cosmological model, filled with a dark matter and a dark energy components. At late…
This paper investigates the evolution of collapsing FRW models with a scalar field having the potential which arises in the conformal frame of high order gravity theories, coupled to matter described by a perfect fluid with energy density $ρ$ and pressure $p$, obeying a barotropic equation of state. The solutions are shown to evolve generically to a singular state in a finite time and they are used as sources for radiating objects undergoing complete gravitational collapse. Although these singularities may be naked in some special case, it is shown that generically a black hole forms.
We perform a thorough phase-plane analysis of the flow defined by the equations of motion of a FRW universe filled with a tachyonic fluid plus a barotropic one. The tachyon potential is assumed to be of inverse square form, thus allowing for a two-dimensional autonomous system of equations. The Friedmann constraint, combined with a convenient choice of coordinates, renders the physical state compact. We find the fixed-point solutions, and discuss whether they represent attractors or not. The way the two fluids contribute at late-times to the fractional energy density depends on how fast the ba…
Using tachyon or quintessence fields along with a barotropic fluid on the brane we examine the different cosmological stages in a Friedmann-Robertson-Walker(FRW) universe, from the first radiation scenario to the later era dominated by cosmic string networks. We introduce a new algorithm to generalize previous works on exact solutions and apply it to study tachyon and quintessence fields localized on the brane and study the low and high energy regimes. We show that the tachyon and quintessence fields are driven by an inverse power law potential. Finally, we find several simples exacts solution…
We consider the late-time accelerated universe in the Friedmann-Robertson-Walker (FRW) spacetime with a nonzero curvature, and investigate cosmological models when the cosmic fluid is taken to be inhomogeneous and viscous (bulk viscous), coupled to dark matter. We consider the influence from thermal effects caused by Hawking radiation on the formation of singularities of various classified types, within a finite time. It is shown that under the influence of Hawking radiation the time of formulation of a singularity, and the nature of the singularity itself, can change. It is also shown that by…
A quantum mechanical picture, relating accelerated geodesic deviation to creation of massive particles via quantum tunneling in curved background spacetimes, is presented. The effect is analogous to pair production by an electric field and leads naturally to production of massive particles in de Sitter and superluminal FRW spacetimes. The probability of particle production in de Sitter space per unit volume and time is computed in a leading semiclassical approximation and shown to coincide with the previously obtained expression.
We consider the evolution of electromagnetic fields in curved spacetimes and calculate the exact wave equations of the associated electric and magnetic components. Our analysis is fully covariant, applies to a general spacetime and isolates all the sources that affect the propagation of these waves. Among others, we explicitly show how the different parts of the gravitational field act as driving sources of electromagnetic disturbances. When applied to perturbed FRW cosmologies, our results argue for a superadiabatic-type amplification of large-scale cosmological magnetic fields in Friedmann m…
While a natural ultraviolet cutoff, presumably at the Planck length, is widely assumed to exist in nature, it has proven difficult to implement a minimum length scale covariantly. A key reason is that the presence of a fixed minimum length would seem to contradict the ability of Lorentz transformations to contract lengths. In this paper, we implement a fully covariant Planck scale cutoff by cutting off the spectrum of the d'Alembertian. In this scenario, consistent with Lorentz contractions, wavelengths that are arbitrarily smaller than the Planck length continue to exist. However, the dynamic…
Born-Infeld determinantal gravity formulated in Weitzenbock spacetime is discussed in the context of Friedmann-Robertson-Walker (FRW) cosmologies. It is shown how the standard model big bang singularity is absent in certain spatially flat FRW spacetimes, where the high energy regime is characterized by a de Sitter inflationary stage of geometrical character, i.e., without the presence of the inflaton field. This taming of the initial singularity is also achieved for some spatially curved FRW manifolds where the singularity is replaced by a de Sitter stage or a big bounce of the scale factor de…
The present work deals with a spherically symmetric space-time which is asymptotically (at spatial infinity) FRW space-time and represents wormhole configuration: The matter component is divided into two parts--(a) dissipative but homogeneous and isotropic fluid, and (b) an inhomogeneous and anisotropic barotropic fluid. Evolving wormhole solutions are obtained when isotropic fluid is phantom in nature and there is a big rip singularity at the end. Here the dissipative phenomena is due to the particle creation mechanism in non-equilibrium thermodynamics. Using the process to be adiabatic, the …
In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $ρ_1(t)$ with a stiff equation of state ($p_1=ρ_1$), and an "effective vacuum energy" $ρ_2(t)$ with a cosmological constant equation of state ($p_2=-ρ_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies …
We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids $ρ_1$ and $ρ_2$, with barotropic pressure densities $p_1/ ρ_1=ω_1=const$ and $p_2/ ρ_2=ω_2=const$, where one of the energy densities is given by $ρ_1=C_1 a^α+ C_2 a^β$, with $C_1$, $C_2$, $α$ and $β$ taking constant values. We solve the field equations by using the conservation equation without breaking it into two interacting parts with the help of a coupling interacting term $Q$. Nevertheless, with the found solution may be associated an interacting term $Q$, and then a number of cosmol…
We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius) distribution without boundary is that it is conformal to the ``minimally'' curved (gravitation only manifesting in tidal acceleration and being absent in particle trajectory) spacetime.
In this paper we find new solutions for the so called Einstein-Chern-Simons Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84 (2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in the first case we find some solutions of the five-dimensional ChS-FRW field equations when the $h^a$ field is a perfect fluid that obeys a barotropic equation of state; (ii) in the second case we study the solutions, for the cases $γ=1/2,\ 3/4$, when the $h^a$ field is a five dimensional politropic fluid that obeys the equation $P^{(h)}=ω^{(h)}ρ^{(h)γ}$; (iii) in th…
Motivated by the isotropy of the CMB spectrum, all existing studies of magnetised cosmological perturbations employ FRW backgrounds. However, it is important, to know the limits of this approximation and the effects one loses by neglecting the anisotropy of the background magnetic field. We develop a new treatment, which fully incorporates the anisotropic magnetic effects by allowing for a Bianchi I background universe. The anisotropy of the unperturbed model facilitates the closer study of the coupling between magnetism and geometry. The latter leads to a curvature stress, which accelerates p…
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 …
We investigate the possibility that the late acceleration observed in the rate of expansion of the universe is due to vacuum quantum effects arising in curved spacetime. The theoretical basis of the vacuum cold dark matter (VCDM), or vacuum metamorphosis, cosmological model of Parker and Raval is revisited and improved. We show, by means of a manifestly nonperturbative approach, how the infrared behavior of the propagator (related to the large-time asymptotic form of the heat kernel) of a free scalar field in curved spacetime causes the vacuum expectation value of its energy-momentum tensor to…
We present a detailed and systematic analysis of the nonperturbative, nonequilibrium dynamics of a quantum field in the reheating phase of inflatonary cosmology, including full back reactions of the quantum field on the curved spacetime, as well as the fluctuations on the mean field. We use the O(N) field theory with unbroken symmetry in a spatially flat FRW universe to study the dynamics of the inflaton in the post-inflaton, preheating stage. Oscillations of the inflaton's zero mode induce parametric amplification of quantum fluctuations, resulting in a rapid transfer of energy to the inhomog…
Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three parameter family of perfect fluid solution which is static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates as $R^{-2}, $ for unbounded cosmological model with a barotropic equation of state…
In this paper, the viscous cosmological dynamics are studied in the presence of dark matter Bose-Einstein Condensation (BEC) by curved-FRW background. For this purpose, we use the BEC regime rather than the normal dark matter (the cold dark matter or the barotropic dark matter) with the dark matter Equation of State (EoS) as $p_{dm} \propto ρ_{dm}^2$, which arises from the gravitational form. Therefore, we obtain the corresponding continuity equations with the existence of the universe components by considering an interacting model with modified Chaplygin gas. Afterward, we derive the energy d…
Acoustic perturbations in an expanding hadronic fluid at temperatures below the chiral transition point represent massless pions propagating in curved spacetime geometry. In comoving coordinates the corresponding analog metric tensor describes a hyperbolic FRW spacetime. We study the analog cosmological particle creation of pions below the critical point of the chiral phase transition. We compare the cosmological creation spectrum with the spectrum of analog Hawking radiation at the analog trapping horizon.
We construct a cosmological toy model based on a Finslerian structure of space-time. In particular, we are interested in a specific Finslerian Lorentz violating theory based on a curved version of Cohen and Glashow's Very Special Relativity. The osculation of a Finslerian manifold to a Riemannian leads to the limit of Relativistic Cosmology, for a specified observer. A modified flat FRW cosmology is produced. The analogue of a zero energy particle unfolds some special properties of the dynamics. The kinematical equations of motion are affected by local anisotropies. Seeds of Lorentz Violations…
We investigate dynamics of a flat FRW cosmological model with a barotropic matter and a non-minimally coupled scalar field (both canonical and phantom). In our approach we do not assume any specific form of a potential function for the scalar field and we are looking for generic scenarios of evolution. We show that dynamics of universe can be reduced to a 3-dimensional dynamical system. We have found the set of fixed points and established their character. These critical points represent all important epochs in evolution of the universe : (a) a finite scale factor singularity, (b) an inflation…
In this paper, we apply a method of reducing the dynamics of FRW cosmological models with the barotropic form of the equation of state to the dynamical system of the Newtonian type to detect the finite scale factor singularities and the finite-time singularities. In this approach all information concerning the dynamics of the system is contained in a diagram of the potential function $V(a)$ of the scale factor. Singularities of the finite scale factor manifest by poles of the potential function. In our approach the different types of singularities are represented by critical exponents in the p…
For general number of spatial dimensions we investigate the cosmological dynamics driven by a cosmological constant and by a source with barotropic equation of state. It is assumed that for both those sources the energy density can be either positive or negative. Exact solutions of the cosmological equations are provided for flat models. For models with curved space and with zero cosmological constant the general solutions are expressed in terms of the hypergeometric function. The qualitative evolution is described for all values of the equation of state parameter. We specify the values of tha…
