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In the framework of spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time, we investigate a two-fluid cosmological model where a tachyon scalar field with self-interacting potential and a modified chaplygin gas with non-linear equation of state are taken as the background fluids. We perform phase space analysis of the autonomous system obtained from the cosmological governing equations by a suitable transformation of variables. Linear stability theory is employed to characterise the stability criteria for hyperbolic critical points. Numerical investigation is carried out for non-hyperbolic points. Our study reveals that modified chaplygin fluid dominated solutions cannot provide the late-time evolution. Late-time accelerated evolution is obtained only when the solution is dominated by tachyon fluid. This study also yields a late-time scaling attractor providing similar order of energy densities in its evolution. The adiabatic sound speed is evaluated for both the fluids and test the stability of the models independently. Further, we perform cosmographic analysis in the model independent way by evaluating all the cosmographic parameters and then $Om$ diagnostic is also found to compare our model with $\Lambda$CDM model., Comment: 19 pages, 10 captioned figures

An interacting Holographic dark energy (HDE) with different infra-red (IR) cutoffs (Hubble horizon and future event horizon) is investigated in the background dynamics of flat Friedmann Lemaitre Robertson Walker (FLRW) universe where gravitational particle creation effects via different form of particle creation rates (1) $\Gamma=3\beta H$ and (2) $\Gamma=3\alpha H_{0}+3\beta H$ are considered. The created particles are considered to be pressureless Dark Matter (DM) which interacts with the HDE through a phenomenological choice of interaction term $Q=3\gamma H \rho_{m}$. We obtain an analytic solution of the cosmological dynamics with Hubble horizon as IR cutoff when the creation rate is taken as $\Gamma=3 \beta H$. We find that the interacting HDE from the Hubble horizon as the IR cutoff can give the late-time acceleration and non-interacting cannot give. On the other hand, employing the Hubble horizon and the future event as IR cutoffs for the model of HDE does not provide the analytic solution when the creation rate is taken as $\Gamma=3\alpha H_{0}+3\beta H$. We then analyze the model separately using the dynamical systems theory. From the analysis, the model (with Hubble horizon as IR cutoff) provides two sets of critical points. One can give a late-time accelerated universe evolving in quintessence, the cosmological constant, or the phantom era. But, it does not show any matter-dominated era. On the other hand, by applying the future event as an IR cutoff, the model provides the complete evolution of the universe. It also exhibits the late-time scaling attractor gives the possible solution of the coincidence problem. Global dynamics of the model are investigated by defining the appropriate Lyapunov function. Finally, the adiabatic sound speeds of all the models have been calculated and plotted numerically to find the stability of the models., Comment: 27 pages, 10 captioned figures

This paper presents an investigation of cosmological dynamics of tachyon fluid coupled to varyingmass dark matter particles in the background of spatially flat FLRW universe. The mechanism of varying mass particles scenario assumes the mass of the dark matter depends on time t through the scalar field ${\phi}$ in the sense that the decaying of dark matter reproduces the scalar field. First, we analyze the model from dynamical systems perspective by converting the cosmological evolution equations into an autonomous system of ordinary differential equations with a suitable transformation of variables. We choose the mass of dark matter as exponential function of scalar field and the exponential potential of the tachyon field is undertaken in such a way that the autonomous system is reduced in three dimensional form. The critical points obtained from the system are non-hyperbolic in nature. The center manifold theory is employed to discuss the nature of the critical points. Numerical investigation also carried out for some critical points. From this analysis, we obtain dust dominated decelerated transient phase of the universe followed by dark energy dominated scaling attractor alleviating the coincidence problem. Next, we perform the statefinder diagnostic approach to compare our model to ${\Lambda}$CDM and finally we study the evolution of the Hubble parameter and the distance modulus and compare this with observational data., Comment: 17 pages, 8 Caption figures, 21 figures

The present work aims to investigate an interacting Umami Chaplygin gas in the background dynamics of a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe when adiabatic particle creation is allowed. Here, the universe is taken to be an open thermodynamical model where the particle is created irreversibly and consequently, the creation pressure comes into the energy-momentum tensor of the material content. The rate at which the particle created is assumed to have a linear relation with the Hubble parameter and the created particle is dark matter (pressureless). The Umami Chaplygin gas is considered dark energy, pressureless dust is taken as dark matter and a phenomenological interaction term is taken for mathematical simplicity. Dynamical analysis is performed to obtain an overall evolution of the model we consider. The autonomous system is obtained by considering dimensionless variables in terms of cosmological variables. The local stability of the critical points and the classical stability of the model are also performed at each critical point. This study explores some cosmologically viable scenarios when we constrain the model parameters. Some critical points exhibit the accelerated de Sitter expansion of the universe at both the early phase as well as the late phase of evolution which is characterized by completely Umami Chaplygin fluid equation of state. Scaling solutions are also described by some other critical points showing late-time accelerated attractors in phase space satisfying present observational data, and solving the coincidence problem. A unified cosmic evolution is also achieved within this model describing the evolution of the universe starting from inflation to late time acceleration connecting through a matter-dominated intermediate phase. Finally, the non-singular bouncing behavior of the universe is also investigated for this model numerically., Comment: 29 pages, 12 captioned figures

In this work, a two-fluid interacting model in a flat FLRW universe has been studied considering particle creation mechanism with a particular form of particle creation rate $\Gamma=\Gamma_0 H+\frac{\Gamma_1}{H}$ from different aspects. Statistical analysis with a combined data set of SNe Ia (Supernovae Type Ia) and Hubble data is performed to achieve the best-fit values of the model parameters, and the model is compatible with current observational data. We also perform a dynamical analysis of this model to get an overall qualitative description of the cosmological evolution by converting the governing equations into a system of ordinary differential equations considering a proper transformation of variables. We find some non-isolated sets of critical points, among which some usually are normally hyperbolic sets of points that describe the present acceleration of the universe dominated by dark energy mimicking cosmological constant or phantom fluid. Scaling solutions are also obtained from this analysis, and they can alleviate the coincidence problem successfully. Statefinder diagnosis is also carried out for this model to compare it with the $\Lambda$CDM, and any other dark energy models by finding various statefinder parameters. Finally, the thermodynamic analysis shows that the generalized second law of thermodynamics is valid in an irreversible thermodynamic context., Comment: 27 pages, 14 captioned figures. The title is changed and thoroughly modified. The version is accepted for publication in the journal Monthly Notices of the Royal Astronomical Society

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as dark energy and pressureless dust as dark matter are the main matter content of the universe. We perform dynamical system analysis to characterize the cosmological evolution of the model with and without interaction in the dark sector separately. First, we convert the evolution equation into an autonomous system of ordinary differential equations by using a suitable choice of dimensionless variables, which are normalized over the Hubble scale. We choose scalar field coupling and potential in such a way that the autonomous system converted to a 2D system. Linear stability theory is employed to the extracted critical points to find the nature. From the analysis, we find some interesting cosmological scenarios, such as late-time scalar-field dominated solutions, which evolve in the quintessence era, cannot solve the coincidence problem. Accelerated scaling attractors are also obtained that correspond to the late phase evolution in agreement with present observational data, and these solutions also provide possible mechanisms to alleviate the coincidence problem. A complete cosmic evolution is obtained from early inflation to a late-time dark energy-dominated phase, connecting through a matter-dominated transient phase of the universe. Furthermore, we find that for different values of the interaction parameter $\alpha$, the evolutionary trajectories of the Hubble parameter, and the distance modulus forecasted by the model are in quite well agreement with observational datasets., Comment: 35 pages, six captioned figures

We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical system tools to obtain a complete qualitative idea of the evolution of such a universe. It is interesting to note that we ought to consider an approximation for the pressure of the logotropic dark fluid in the form of an infinite series so as to be able to construct the autonomous system required for a dynamical system study. This series form provides us with a power law in the rest-mass energy density of the logotropic dark fluid. We compute the critical points of the autonomous system and analyze these critical points by applying linear stability theory. Our analysis reveal a scenario of late-time accelerated universe dominated by the logotropic fluid which behaves as cosmological constant, preceded by an intermediate phase of the Universe dominated by logotropic fluid which behaves as dark matter in the form of perfect fluid. Moreover, it also crosses the phantom divide line., Comment: 13 pages, 4 captioned figures. Version accepted for publication in Physics of the Dark Universe

In the background dynamics of a spatially flat FLRW model of the universe, we investigate an interacting dark energy model in the context of Lyra's geometry. Pressure-less dust is considered as dark matter, mass of which varies with time via scalar field in the sense that decaying of dark matter particles reproduces the scalar field. Here, quintessence scalar field is adopted as dark energy candidate which evolves in exponential potential. Mass of the dark matter particles is also considered to be evolved in exponential function of the scalar field. Cosmological evolution equations are studied in the framework of dynamical systems analysis. Dimension-less variables are chosen properly so that the cosmological evolution equations are converted into an autonomous system of ordinary differential equations. Linear stability is performed to find the nature of critical points by perturbing the system around the critical points in the phase space. Classical stability is also executed by finding out the speed of sound. Dynamical systems explore several viable results which are physically interested in some parameter regions. Late-time scalar field dominated attractors are found by critical points, corresponding to the accelerating universe. Scalar field-displacement vector field scaling solutions are realized that represent late time decelerated universe. Dark energy -dark matter scaling solutions are also exhibited by critical points which correspond to accelerated attractors possessing similar order of energy densities of dark energy and dark matter, that provides the possible solutions of coincidence problem., Comment: 20 pages, 4 captioned figures. Title is changed, some subsections are added and the paper is thoroughly modified. The version is ready for publication in International Journal of Modern Physics D

In this work, considering the background dynamics of flat Friedmann-Lemaitre-Robertson-Walker(FLRW) model of the universe, we investigate a scalar field model as dark energy candidate which interacting with the pressure-less dust as dark matter from dynamical systems perspective. From phenomenological vantage point two interaction terms are chosen: one depends on Hubble parameter $H$ and other is local, independent of Hubble parameter. In interaction model 1, the scalar field potential as well as the coupling are considered to be in the form of inverse square and accordingly a two-dimensional autonomous system is obtained. On the other hand, Interaction model 2 comprises with the potential as well as coupling of scalar field which are considered in form of exponential function of scalar field ($\phi$) and as a result of which a four-dimensional autonomous system is achieved. We study two systems separately and come by several critical points in 2D system as well as in 4D system. We have derived sound speed and the classical stability conditions. Furthermore, for 2D autonomous system we analyzed the stability of some critical points at infinity. From this autonomous system, we obtain scalar field dominated solutions representing late time accelerated evolution of the universe that does not elucidate the coincidence problem. Late time scaling solutions are also realized by the accelerated expansion of the universe which evolves in quintessence era that alleviates the coincidence problem successfully. From the analysis of 4D system, we obtain non-hyperbolic sets of critical points which are analyzed by the center manifold theory. In this model, the de Sitter like solutions represent the transient evolution of the universe., Comment: 29 pages, 10 captioned figures. Title changed. The paper is revised thoroughly. The version is published in The Physics of the Dark Universe

In this work interacting Umami Chaplygin gas has been studied in flat FRW model of universe in context of it's thermodynamic and dynamical behaviour. In particular, considering Umami fluid as dark energy interacting with dark matter, irreversible thermodynamics has been studied both for apparent and event horizon as bounding horizon in two separate cases. Also the model has been investigated in purview of dynamical systems analysis by converting the cosmological evolution equations to an autonomous system of ordinary differential equations. With some restrictions on model parameter $\omega$ and coupling parameter $\lambda$, some cosmologically interesting critical points describing late time accelerated evolution of the universe attracted by cosmological constant and accelerated scaling attractor in quintessence era have been found to alleviate coincidence problem., Comment: Accept 16 pages, 8 figures

The present work is a second in the series of investigation of the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here, dark matter is chosen in the form of perfect fluid with barotropic equation of state while a real scalar field with self interacting potential is chosen as dark energy. The scalar field potential is chosen as exponential or hyperbolic in nature and three different choices for the interaction between the dark species are considered. In the background of spatially flat, homogeneous and isotropic Friedmann-Robertson-Walker (FRW) brane model, the evolution equations are reduced to an autonomous system by suitable transformation of variables and a series of critical points are obtained for different interactions. By analyzing the critical points, we have found cosmologically viable model describing an early inflationary scenario to dark energy dominated era connecting through a matter dominated phase., Comment: 26 pages, 11 captioned figures. Version is accepted for publication in IJGMMP

In this work we present the cosmological dynamics of interacting dark energy models in the framework of particle creation mechanism. The particle creation mechanism presented here describes the true non equilibrium thermodynamics of the universe. In spatially flat Friedmann-Lema{\^\i}tre-Robertson-Walker universe considered here, the dissipative bulk viscous pressure is due to the non conservation of particle number. For simplicity, we assume that the creation of perfect fluid particles to be isentropic (adiabatic) and consequently the viscous pressure obeys a linear relationship with particle creation rate. Due to complicated nature of the Einstein's field equations, dynamical systems analysis has been performed to understand deeply about the cosmological dynamics. We have found some interesting cosmological scenarios like late-time evolution of universe dominated by dark energy which could mimic quintessence, cosmological constant or phantom field through a dark matter dominated era. We also obtained a possibility of crossing the phantom divide line which is favored by observations., Comment: 19 pages, 10 figures; version accepted for publication in Physical Review D

The present work deals with an interacting dark energy model in the framework of f(T) cosmology. A cosmologically viable form of f(T) is chosen (T is the torsion scalar in teleparallelism) in the background of flat homogeneous and isotropic Friedmann-Robertson-Walker (FRW) space-time model of the universe. The matter content of the universe is chosen as dust interacting with minimally coupled scalar field. The evolution equations are reduced to an autonomous system of ordinary differential equations by suitable transformation of variables. The nature of critical points are analyzed by evaluating the eigenvalues of the linearized Jacobi matrix and stable attractors are examined from the point of view of cosmology. Finally, both classical and quantum stability of the model have been discussed., Comment: 21 pages, 9 figures, Accepted for publication in Int. J. Mod. Phys. D. arXiv admin note: text overlap with arXiv:1202.4926, arXiv:1207.2735 by other authors

In this paper, we investigate the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here we consider an homogeneous and isotropic Friedmann-Robertson-Walker (FRW) brane model and the evolution equations are reduced to an autonomous system by suitable transformation of variables. The nature of critical points are analyzed by evaluating the eigenvalues of linearized Jacobi matrix. Finally, the classical stability of the model is also studied., Comment: 22 pages, 7 figures