The scalar field can behave like a fluid with equation of state $p_ϕ=wρ_ϕ$, where $w \in [-1,1]$. In this Letter we derive a class of the scalar field potentials for which $w=$ const. Scalar field with such a potential can mimic ordinary matter, radiation, cosmic strings, etc. We perform our calculations in the framework of the loop cosmology with holonomy corrections. We solve the model analytically for the whole parameter space. Subsequently, we perform similar consideration for the model with a phantom field ($w<-1$). We show that scalar field is monotonic function in both cases. This indicates that it can be treated as a well-defined internal time for these models. Moreover we perform preliminary studies of the scalar field perturbations with this potential. We indicate that non-Gaussian features are present admitting for the possible observational constraints of the model.
Fluid cosmologies are consistent with the generally accepted observational evidence during intermediate and late times, and they need not have singular behavior in primordial times. A general form for fluid cosmology consistent with Einstein's equation is demonstrated, and a dynamic metric that incorporates fluid scale is developed. The large scale causal structure of a multi-fluid cosmology exemplary of standard cosmology is then examined. This is done through developing coupled rate equations for radiation, dust, and dark components. The beginning of the dissolution of the primordial fluid i…
Specific dark energy models with linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that the choice of such 4d inhomogeneous fluid models may lead to a brane FRW cosmology without any explicit account of higher dimensions at all. Effectively, we thus obtain a brane dark energy universe without introducing the brane concept explicitly. Several examples of brane Rip cosmology arising from 4d inhomogeneous dark fluid models are given.
The conditions for the appearance of the Little Rip, Pseudo Rip and Quasi Rip universes in the terms of the parameters in the equation of state of some dark fluid are investigated. Several examples of the Rip cosmologies are investigated.
The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known solutions are singled out from those obtained. The existence of the wormholes is proved.
The dynamics of a spinning fluid in a flat cosmological model is investigated. The space-time is itself generated by the spinning fluid which is characterized by an energy-momentum tensor consisting a sum of the usual perfect-fluid energy-momentum tensor and some Belinfante-Rosenfeld tensors. It is shown that the equations of motion admit a solution for which the fluid four-velocity and four-momentum are not co-linear in general. The momentum and spin densities of the fluid are expressed in terms of the scale factor.
D-dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing both shear and bulk viscosity in n Ricci-flat spaces is investigated. The second equations of state are chosen in some special form of metric dependence of the shear and bulk viscosity coefficients. The equations of motion are integrated and the dynamical properties of the exact solutions are studied. It is shown the possibility to resolve the cosmic coincidence problem when the x-fluid plays role of quintessence and the viscous fluid is used as cold dark matter.
We investigate the bounce cosmology induced by inhomogeneous viscous fluids in FRW space-time (non necessarly flat), taking into account the early-time acceleration after the bounce. Different forms for the scale factor and several examples of fluids will be considered. We also analyze the relation between bounce and finite-time singularities and between the corresponding fluids realizing this scenarios. In the last part of the work, the study is extended to the framework of $f(R)$-modified gravity, where the modification of gravity may also be considered as an effective (viscous) fluid produc…
We review the Eulerian description of hidrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials. With this we can obtain the evolution equations of the fluid and its Hamiltonian. In the scenario of quantum cosmology the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models.
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the fluid and that it yields regular curvature invariants.
Specific dark energy models with a linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that such 4d inhomogeneous fluid models may lead to a turbulence FRW cosmology. Both one-component and two-component models from 4d inhomogeneous dark fluid models are considered. In the one-component model the universe may develop from a viscous era with, for instance, a constant bulk viscosity, into a turbulent era. In the two-component model the fluid can be decomposed into two components, one non…
In this paper, we investigate $f(T)$ cosmology and find an exact solution for $f$ which gives a Little Rip cosmology. Also, considering accelerating cosmology with dark matter, the time-dependent solution is found. For these cases, by using solutions obtained from $f(T)$ gravity we find expressions for $ω$ and $Λ$ defined as time functions via equivalent description in terms of inhomogeneous fluid. This puts the question: which theoretical model describes the observational cosmology?
We investigate $(n+1)$-dimensional string-dilaton cosmology with effective dilaton potential in presence of perfect-fluid matter.We get exact solutions parametrized by the constant $\gam$ of the state equation $p=(\gam-1)ρ$, the spatial dimension number $n$, the bulk of matter, and the spatial curvature constant $k$. Several interesting cosmological behaviours are selected. Finally we discuss the recovering of ordinary Einstein gravity starting from string dominated regime and a sort of asymptotic freedom due to string effective coupling.
In this work we present an analysis of the phantom zone in a causal viscous cosmology from a thermodynamic point of view. In this description we consider a chemical potential and the approach of irreversible processes. We assume a flat universe filled with a single dissipative fluid described by a barotropic equation of state, $p = ωρ$. This model allows to construct a negative chemical potential for the phantom regime but also this construction allows us to have positive definite temperature and entropy.
Present paper deals with flat Friedmann - Robertson - Walker (FRW) model with two - fluid source in fractal cosmology. In this model one fluid represents matter content of the universe and another fluid is radiation field modeling the cosmic microwave background. To get the deterministic model, we have used the relation between pressure and density for matter through the gamma law equation of state $p_{m} = (γ-1)\, ρ_{m}, \,\, 1\leq γ\leq2$ . The solutions of fractal field equations are obtained in terms of Kummer's confluent hypergeometric function of the first kind. Some physical parameters …
We investigate the background dynamics when dark energy is coupled to dark matter in the universe described by Einstein cosmology and Loop Quantum Cosmology. We introduce a new general form of dark sector coupling, which presents us a more complicated dynamical phase space. Differences in the phase space in obtaining the accelerated scaling attractor in Einstein cosmology and Loop Quantum Cosmology are disclosed.
The dynamical behaviors of interacting dark energy in loop quantum cosmology are discussed in this paper. Based on defining three dimensionless variables, we simplify the equations of the fixed points. The fixed points for interacting dark energy can be determined by the Friedmann equation coupled with the dynamical equations {in Einstein cosmology}. But in loop quantum cosmology, besides the Friedmann equation, the conversation equation also give a constrain on the fixed points. The difference of stability properties for the fixed points in loop quantum cosmology and the ones in Einstein cosm…
We studied the expectation value of the scale factor in radiation and dust quantum perfect fluid cosmology. We used Schutz variational formalism to describe perfect fluid and selected the conjugate coordinate of perfect fluid be dynamical variable. After quantization and solving the Wheeler-DeWitt equation can obtain the exact solution. By superposition of the exact solution, we obtained one wave packets and used it to compute the expectation value of the scale factor. We found that if one select different dynamical variable be the time variable in each of these two systems, the expectation va…
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.
The coupling of a stringlike fluid with ordinary matter and gravity may lead to a closed Universe with the dynamic of an open one. This can provide an alternative solution for the age and horizon problems. A study of density perturbations of the stringlike fluid indicates the existence of instabilities in the small wavelength limit when it is employed a hydrodynamic approach. Here, we extend this study to gravitational waves, where the hydrodynamical approach plays a less important role, and we argue that traces of the existence of this fluid must be present in the anisotropies of the cosmic b…
This article examines the foundation of the recently developed relativistic variational formalism[1]. Our work is heavily based on [2, 27] which extends this approach to the multi-fluid theory and examines its utility in astrophysics and cosmology. Unlike the extension to the formalism mentioned above, that looks at the general interaction between different types of matter, we use the formalism to examine the interaction involving, ordinary matter, dark matter (DM) and dark energy (DE). We focus on entrainment phenomena involving the dark-sector constituents.
The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and f…
In this work we investigate the effects of torsion in the framework of Einstein-Cartan theory in early cosmology. We study solutions for a homogeneous and isotropic relativistic Weyssenhoff spin fluid with dynamical timelike axial current, also homogeneous and isotropic. The general solutions can mostly be described by means of three particular solutions. The properties of these solutions (such as singularity avoidance and primordial or late accelerated expansion) are analysed and depend on the relations between the source parameters.
In this paper we construct the Hamiltonian constraint operator of loop quantum cosmology using holonomies defined for arbitrary irreducible SU(2) representations labeled by spin J. We show that modifications to the effective semi-classical equations of motion arise both in the gravitational part of the constraint as well as matter terms. The modifications are important for phenomenological investigations of the cosmological imprints of loop quantum cosmology. We discuss the implications for the early universe evolution.
In this letter, we demonstrate that Loop Quantum Cosmology equations, with a near vanishing late time cosmological constant, can be induced on a brane in a Randall-Sundrum II scenario, corresponding to the holographic dual of a strongly coupled string regime in the bulk. Such results can establish a possible connection between Loop Quantum Gravity and string theory.
In this paper a possibility of the accelerated expansion of the large scale universe with a varying polytropic fluid of a certain type is presented. About a special role of non-gravitational interactions between dark energy and dark matter, in particular, about a possibility of improvement and solution of problems arising in modern cosmology, has been discussed for a long time. This motivates us to consider new models, where non-gravitational interactions between varying polytropic fluid and cold dark matter are allowed. Mainly non-linear interactions of a specific type is considered, found in…
Here we shall find the green's function of the difference equation of loop quantum cosmology. To illustrate how to use it, we shall obtain an iterative solution for closed model and evaluate its corresponding Bohmian trajectory.
As a first step to generalize the structure of loop quantum cosmology to the theories with the spacetime dimension other than four, the isotropic model of loop quantum cosmology in 2+1 dimension is studied in this paper. We find that the classical big bang singularity is again replaced by a quantum bounce in the model. The similarities and differences between the 2+1 dimensional model and the 3+1 dimensional one are also discussed.
We study oscillatory universes within the context of Loop Quantum Cosmology. We make a comparative study of flat and positively curved universes sourced by scalar fields with either positive or negative potentials. We investigate how oscillating universes can set the initial conditions for successful slow-roll inflation, while ensuring that the semi-classical bounds are satisfied. We observe rich oscillatory dynamics with negative potentials, although it is difficult to respect the semi-classical bounds in models of this type.
An action functional for the loop quantum cosmology difference equation is presented. It is shown that by guessing the general form of the solution and optimizing the action functional with respect to the parameters in the guessed solution one can obtain approximate solutions which are reasonably good.
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.
We study the problem of gauge-invariance and gauge-dependence in one-loop quantum cosmology. We formulate some requirements which should be satisfied by boundary conditions in order to give gauge-independent path integral. The case of QED is studied in some detail. We outline difficulties in gauge-invariant quantization of gravitational field in a bounded region.
For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained from loop quantum gravity, has shed new light on this question. In this case, boundary conditions are not chosen by hand with some particular physical intuition in mind, but they are part of the dynamical law. It is then natural to ask if there are any relations between these boundary conditions and the ones provided before. After discussing the technical foundation of loop quantum cosmology which l…
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.
A temporally discrete Schroedinger time evolution equation is proposed for isotropic quantum cosmology coupled to a massless scalar source. The approach employs dynamically determined intrinsic time and produces the correct semiclassical limit.
We consider the inflation produced by two coupled fluids in the flat Friedmann-Robertson-Walker universe. Different cosmological models for describing inflation by use of an inhomogeneous equation of state for the fluid are investigated. The gravitational equations for energy and matter are solved, and analytic representations for the Hubble parameter and the energy density are obtained. Corrections in the energy density for matter inducing the inflation and the coupling with energy are discussed. We analyze the description of inflation induced by non-constant equation-of-state parameters from…
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and exciting views of the gravitational phenomena that took place in the early universe, or that occur in spacetime regions where Einstein's theory predicts singularities. We provide a brief introduction to the bases of Loop Quantum Cosmology and summarize the most important results obtained in homogeneous scenarios. These results include a mechanism to avoid the…
Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classi…
We investigate dynamics of (4+1) and (5+1) dimensional flat anisotropic Universe filled by a perfect fluid in the Gauss-Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter $w=1/3$ have been found. For other values of $w$ structure of cosmological singularity have been studied numerically. We found that for $w > 1/3$ the singularity is isotropic. Several important differences between (4+1) and (5+1) dimensional cases are discussed.
This article is devoted to the application of the holographic principle to describe Rip brane cosmological models in the presence of a bulk viscosity. We make use of the generalized infrared-cutoff holographic dark energy, introduced by Nojiri and Odintsov We consider various examples: Rip brane cosmology corresponding to the Little Rip case, asymptotic de Sitter theory, and the so-called Big Freeze theory leading to a singularity. Analytical expressions for infrared cutoffs, as well as the particle and the future horizons at the brane, are obtained. The equations for energy conservation on th…
This paper is devoted to investigate the thermodynamic stability of a generic cosmological fluid known as Van der Waals fluid in the context of flat FRW universe. It is treated as a perfect fluid that obeys the equation of state $P=\frac{γρ}{1-βρ}-αρ^{2}, 0\leqγ<1$, where $ρ$ stands for energy density and $P$ stands for pressure of the fluid. In this regard, we discuss the behavior of physical parameters to analyze the evolution of the universe. We investigate whether the cosmological scenario fulfills the third law of thermodynamics using specific heat formalism. Next we discuss the thermal e…
We shall show that it is possible to make a causal interpretation of loop quantum cosmology using the momentum as the dynamical variable. We shall show that one can derive Bohmian trajectories. For a sample cosmological solution with cosmological constant, the trajectory is plotted.
Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. And the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but are actually also found to be the thermodynamic quantities.…
The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter γin controlling space-time discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit γ\to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the volume eigenvalues, and the simultaneous limit is technically the same as the classical limit \hbar \to 0, l \to \infty of angular momentum in quantum mechanics. Possible lessons for semiclassical states at the dynamical level in th…
The purpose of this short review is to describe cosmological models with a linear inhomogeneous time-dependent equation of state (EoS) for the dark energy, when the dark fluid is coupled with dark matter. This may lead to a bounce cosmology. We consider equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double-exponential law for the scale factor $a$. Stability issues are discussed by considering small perturbations around the critical points for the bounce, in the early as well as in the late, universe. The latter part of the paper is concerned with d…
Open FRW model in Loop Quantum Cosmology is under consideration. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of $k=-1$ it is possible to construct a suitable loop which provides us with quantum scalar constraint originally introduced by Vandersloot. The quantum scalar constraint operator with negative cosmological constant is proved to be essentially self-adjoint.
We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmology. With regards to the inflationary cosmologies, we study the intermediate inflation scenario, the $R^2$ inflation scenario and two constant-roll inflation scenarios and with regards to the bouncing cosmologies we study the matter bounce scenario, the singular bounce and the super bounce scenario. Within the context of the classical cosmology, we calculate the spectral index of the power spectrum of …
The article gives an account of several aspects of the space known as the Bohr compactification of the line, featuring as the quantum configuration space in loop quantum cosmology, as well as of the corresponding configuration space realization of the so-called polymer representation. Analogies with loop quantum gravity are explored, providing an introduction to (part of) the mathematical structure of loop quantum gravity, in a technically simpler context.
We study Weyssenhoff spin fluids in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity; the resulting field equations are derived and discussed in both Jordan and Einstein frames, clarifying the role played by the spin and the non-linearity of the gravitational Lagrangian f(R) in generating the torsional dynamical contributions. The general conservation laws holding for f(R)-gravity with torsion are employed to provide the conditions needed to ensure the preservation of the Hamiltonian constraint and the consequent correct formulation of the associated initial v…
The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studie…
A cosmological model describing the evolution of $n$ Einstein spaces $(n>1)$ with $m$-component perfect-fluid matter is considered. When all spaces are Ricci-flat and for any $α$-th component the pressures in all spaces are proportional to the density: $p_{i}^{(α)} = (1- h_{i}^{(α)}) ρ^{(α)}$, $h_{i}^{(α)}$ = const, the Einstein and Wheeler-DeWitt equations are integrated in the cases: i) $m=1$, for all $h_{i}^{(α)}$; ii) $m > 1$, for some special sets of $h_{i}^{(α)}$. For $m=1$ the quantum wormhole solutions are also obtained. \\
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.
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full th…
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.
