Stable Scaling Solution Research Articles

Classifying the behavior of noncanonical quintessence

We derive general conditions for the existence of stable scaling solutions for the evolution of noncanonical quintessence, with a Lagrangian of the form $\mathcal{L}(X,\ensuremath{\phi})={X}^{\ensuremath{\alpha}}\ensuremath{-}V(\ensuremath{\phi})$, for power-law and exponential potentials when the expansion is dominated by a background barotropic fluid. Our results suggest that, in most cases, noncanonical quintessence with such potentials does not yield interesting models for the observed dark energy. When the scaling solution is not an attractor, there is a wide range of model parameters for which the evolution asymptotically resembles a zero-potential solution with equation of state parameter $w=1/(2\ensuremath{\alpha}\ensuremath{-}1)$, and oscillatory solutions are also possible for positive power-law potentials; we derive the conditions on the model parameters which produce both types of behavior. We investigate thawing noncanonical models with a nearly flat potential and derive approximate expressions for the evolution of $w(a)$. These forms for $w(a)$ differ in a characteristic way from the corresponding expressions for canonical quintessence.

Dynamical system analysis of modified chaplygin gas in Einstein-Aether gravity

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by the Einstein-Aether gravity. Dark energy in the form of modified Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of the modified Chaplygin gas in the Einstein-Aether gravity is completely consistent with the notion of an accelerated expansion in the late universe. Finally, it has been shown that the universe follows the power law form of expansion around the critical point.

Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric

In this work, we have considered Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with Variable Modified Chaplygin Gas (VMCG). Here we find normal scalar field ϕ and the self interacting potential V(ϕ) to describe the VMCG Cosmology. We have also graphically analyzed the geometrical parameters named Statefinder Parameters in anisotropic Kaluza-Klein model. Next, we have considered a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter interacts between themselves and for that we also choose the interaction term. We convert that interaction term to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.

Interacting Generalized Cosmic Chaplygin Gas in Loop Quantum Cosmology: A Singularity Free Universe

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by Loop quantum cosmology. Dark energy in the form of Generalized Cosmic Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is taken into account in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy model. Graphs and phase diagrams are drawn to study the variations of these parameters. It is seen that the background dynamics of Generalized Cosmic Chaplygin gas is completely consistent with the notion of an accelerated expansion in the late universe. From the graphs, generalized cosmic Chaplygin gas is identified as a dark fluid with a lesser negative pressure compared to Modified Chaplygin gas, thus supporting a ‘No Big Rip’ cosmology. It has also been shown that in this model the universe follows the power law form of expansion around the critical point, which is consistent with the known results. Future singularities that may be formed in this model as an ultimate fate of the universe has been studied in detail. It was found that the model is completely free from any types of future singularities.

Dynamics of interacting generalized cosmic Chaplygin gas in brane-world scenario

In this work we explore the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by brane cosmology. Here DGP and the RSII brane models have been considered separately. Dark energy in the form of Generalized Cosmic Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of Generalized Cosmic Chaplygin gas is consistent with the late cosmic acceleration, but not without satisfying certain conditions. It has been shown that the universe in both the models follows the power law form of expansion around the critical point, which is consistent with the known results. Future singularities were studied and our models were declared totally free from any types of such singularities. Finally, some cosmographic parameters were also briefly studied. Our investigation led to the fact that although Generalized cosmic Chaplygin gas with a far lesser negative pressure compared to other dark energy models, can overcome the relatively weaker gravity of RS II brane, with the help of the negative brane tension, yet for the DGP brane model with much higher gravitation, the incompetency of Generalized cosmic Chaplygin gas is exposed, and it cannot produce the accelerating scenario until it reaches the phantom era.

Dynamical system analysis of interacting variable modified Chaplygin gas model in FRW universe

In this work, we have considered the interacting dynamical model taking the variable modified Chaplygin gas (VMCG) which plays as dark energy coupled to cold dark matter in the flat FRW universe. For the VMCG equation of state, we have chosen B(a) = B 0 a −n . Since the nature of dark energy and dark matter is still unknown, it is possible to have an interaction between them and phenomenologically we choose the interaction term Q = 3cH ρ, where c is the coupling parameter. We have converted all the equations in the dynamical system of equations by considering the dimensionless parameters and seen the evolution of the corresponding autonomous system. The feasible critical point has been found and for the stability of the dynamical system about the critical point, we linearize the governing equation around the critical point. We found that there exists a stable scaling (attractor) solution at late times of the Universe and found some physical range of n and the interaction parameter c. We have shown that for our calculated physical range of the parameters, the Universe explores upto quintessence stage. The deceleration parameter, statefinder parameters, Hubble parameter and the scale factor have been calculated around the critical point. Finally, some consequences around the critical point, i.e., the distance measurement of the Universe like lookback time, luminosity distance, proper distance, angular diameter distance, comoving volume, distance modulus and probability of intersecting objects have been analyzed before and after the present age of the Universe.

Dynamics of modified Chaplygin gas in brane world scenario: phase plane analysis

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by brane cosmology. Here DGP and the RSII brane models have been considered separately. Dark energy in the form of modified Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of modified Chaplygin gas is completely consistent with the notion of an accelerated expansion in the late universe. Finally, it has been shown that the universe in both the models follows the power law form of expansion around the critical point, which is consistent with the known results.

Interacting modified Chaplygin gas in loop quantum cosmology

We investigate the background dynamics when dark energy is coupled to dark matter in the universe described by loop quantum cosmology. We consider dark energy of the form modified Chaplygin gas. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. It henceforth resolves the famous cosmic coincidence problem in modern cosmology. The statefinder parameters are also calculated to classify this dark energy model.

DYNAMICAL EVOLUTION OF INTERACTING MODIFIED CHAPLYGIN GAS

The cosmological model of the modified Chaplygin gas (MCG) interacting with cold dark matter is studied. Our attention is focused on the final state of the universe in the model. It turns out that there exists a stable scaling solution, which provides the possibility of alleviating the coincidence problem. In addition, we investigate the effect of the coupling constants c1 and c2 on the dynamical evolution of this model from the statefinder viewpoint. It is found that the coupling constants play a significant role during the dynamical evolution of the interacting MCG model. Furthermore, we can distinguish this interacting model from other dark energy models in the s–r plane.

A Single Model of Interacting Dark Energy: Generalized Phantom Energy or Generalized Chaplygin Gas

I present a model in which dark energy interacts with matter. The former is represented by a variable equation of state. It is shown that the phantom crossing takes place at zero redshift, moreover, stable scaling solution of the Friedmann equations is obtained. I show that dark energy is most probably be either generalized phantom energy or the generalized Chaplygin gas.

Interacting New Generalized Chaplygin Gas

We have presented a model in which the new generalized Chaplygin gas interacts with matter. We find that there exists a stable scaling solution at late times in the evolution of the universe. Moreover, the phantom crossing scenario is observed in this model.

Cosmological scaling solutions in generalised Gauss–Bonnet gravity theories

The conditions for the existence and stability of cosmological power-law scaling solutions are established when the Einstein-Hilbert action is modified by the inclusion of a function of the Gauss-Bonnet curvature invariant. The general form of the action that leads to such solutions is determined for the case where the universe is sourced by a barotropic perfect fluid. It is shown by employing an equivalence between the Gauss-Bonnet action and a scalar-tensor theory of gravity that the cosmological field equations can be written as a plane autonomous system. It is found that stable scaling solutions exist when the parameters of the model take appropriate values.

HYBRID CHAPLYGIN GAS

Hybrid Chaplygin gas model is put forward, in which the gases play the role of dark energy. For this model the coincidence problem is greatly alleviated. The effective equation of state of the dark energy may cross the phantom divide w = -1. Furthermore, the crossing behavior is decoupled from any gravity theories. In the present model, w < -1 is only a transient behavior. There is a de Sitter attractor in the future infinity. Hence, the big rip singularity, which often afflicts the models with matter whose effective equation of state less than -1, naturally disappears. There exist stable scaling solutions, both at the early universe and the late universe. We discuss the perturbation growth of this model. We find that the index is consistent with observations.

STATEFINDER DIAGNOSTIC FOR COUPLED TACHYON DARK ENERGY MODEL

In this paper we study the statefinder parameters for the coupled tachyon dark energy model which has two types of stable scaling solutions. It is found that the evolving trajectories of the solutions are different in the statefinder parameters plane. These trajectories lie in the two regions r > 1, s < 0 and r < 1, s > 0, and pass through the LCDM fixed point. So, through the statefinder diagnostic, we not only characterize the properties of the coupled tachyon dark energy model, but also show the difference from other dark energy model.

Scaling cosmologies of gauged supergravity

We construct exact cosmological scaling solutions in gauged supergravity. We restrict to solutions for which the scalar fields trace out geodesic curves on the scalar manifold. Under these restrictions it is shown that the axionic scalars are necessarily constant. The potential is then a sum of exponentials and has a very specific form that allows for scaling solutions. The scaling solutions describe eternal accelerating and decelerating power-law universes, which are unstable. An uplift of the solutions to 11-dimensional supergravity is carried out and the resulting time-dependent geometries are discussed. In the discussion we briefly comment on the fact that gauged supergravity allows accelerating stable scaling solutions.

Gauging CSO groups in Script N = 4 supergravity

We investigate a class of CSO-gaugings of N=4 supergravity coupled to six vector multiplets. Using the CSO-gaugings we do not find a vacuum that is stable against all scalar perturbations at the point where the matter fields are turned off. However, at this point we do find a stable cosmological scaling solution.

General analytic formulas for attractor solutions of scalar-field dark energy models and their multifield generalizations

We study general properties of attractors for scalar-field dark energy scenarios which possess cosmological scaling solutions. In all such models there exists a scalar-field dominant solution with an energy fraction ${\ensuremath{\Omega}}_{\ensuremath{\phi}}=1$ together with a scaling solution. A general analytic formula is given to derive fixed points relevant to dark energy coupled to dark matter. We investigate the stability of fixed points without specifying the models of dark energy in the presence of nonrelativistic dark matter and provide a general proof that a nonphantom scalar-field dominant solution is unstable when a stable scaling solution exists in the region ${\ensuremath{\Omega}}_{\ensuremath{\phi}}<1$. A phantom scalar-field dominant fixed point is found to be classically stable. We also generalize the analysis to the case of multiple scalar fields and show that for a nonphantom scalar-field assisted acceleration always occurs for all scalar-field models which have scaling solutions. For a phantom field the equation of state approaches that of cosmological constant as we add more scalar fields.

Interacting Chaplygin gas

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 $w=\ensuremath{-}1$. 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 Friedamnn-Robertson-Walker (FRW) metric, we also find the deceleration parameter is well consistent with current observations.

Erratum: Scaling of multitension cosmic superstring networks [Phys. Rev. DPRVDAQ0556-282171, 103508 (2005)

Brane inflation in superstring theory ends when branes collide, initiating the hot big bang. Cosmic superstrings are produced during the brane collision. The cosmic superstrings produced in a D3-brane-antibrane inflationary scenario have a spectrum: $(p,q)$ bound states of $p$ fundamental (F) strings and $q$ D-strings, where $p$ and $q$ are coprime. By extending the velocity-dependent one-scale network evolution equations for abelian Higgs cosmic strings to allow a spectrum of string tensions, we construct a coupled (infinite) set of equations for strings that interact through binding and self-interactions. We apply this model to a network of $(p,q)$ superstrings. Our numerical solutions show that $(p,q)$ networks rapidly approach a stable scaling solution. We also extract the relative densities of each string type from our solutions. Typically, only a small number of the lowest tension states are populated substantially once scaling is reached. The model we study also has an interesting new feature: the energy released in $(p,q)$ string binding is by itself adequate to allow the network to reach scaling. This result suggests that the scaling solution is robust. To demonstrate that this result is not trivial, we show that choosing a different form for string interactions can lead to network frustration.

Scaling of multitension cosmic superstring networks

Brane inflation in superstring theory ends when branes collide, initiating the hot big bang. Cosmic superstrings are produced during the brane collision. The cosmic superstrings produced in a $D3$-brane-antibrane inflationary scenario have a spectrum: $(p,q)$ bound states of $p$ fundamental ($F$) strings and $q$ $D$-strings, where $p$ and $q$ are coprime. By extending the velocity-dependent one-scale network evolution equations for Abelian Higgs cosmic strings to allow a spectrum of string tensions, we construct a coupled (infinite) set of equations for strings that interact through binding and self-interactions. We apply this model to a network of $(p,q)$ superstrings. Our numerical solutions show that $(p,q)$ networks rapidly approach a stable scaling solution. We also extract the relative densities of each string type from our solutions. Typically, only a small number of the lowest tension states are populated substantially once scaling is reached. The model we study also has an interesting new feature: the energy released in $(p,q)$ string binding is by itself adequate to allow the network to reach scaling. This result suggests that the scaling solution is robust. To demonstrate that this result is not trivial, we show that choosing a different form for string interactions can lead to network frustration.