Cosmological dynamics of the general non-canonical scalar field models

We extend the investigation of cosmological dynamics of the general non-canonical scalar field models by dynamical system techniques for a broad class of potentials and coupling functions. In other words, we do not restrict the analysis to exponential or power-law potentials and coupling functions. This type of investigation helps in understanding the general properties of a class of cosmological models. In order to better understand the phase space of the models, we investigate the various special cases and discuss the stability and viability issues. Performing a detailed stability analysis, we show that it is possible to describe the cosmic history of the universe at the background level namely the early radiation dominated era, intermediate matter dominated era and the late time dark energy domination. Moreover, we find that we can identify a broad class of coupling functions for which it is possible to get an appealing unified description of dark matter and dark energy. The results obtained here, therefore, enlarge the previous analyses wherein only a specific potential and coupling functions describes the unification of dark sectors. Further, we also observe that a specific scenario can also possibly explain the phenomenon of slow-roll inflationary exit.Comment: Revised to match EPJC version; 12 pages, 6 figures; Accepted in EPJ

Global phase space analysis for a class of single scalar field bouncing solutions in general relativity

We carry out a compact phase space analysis of a non-canonical scalar field theory whose generic form of the Lagrangian is $F(X)-V(\phi)$ within general relativity. In particular, we focus on the power law and exponential potentials of the scalar field. A global dynamical system formulation particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. Global dynamical system techniques help us to extract generic conclusions for a wide range of initial conditions. The main aim of this work is to analyze the generic behavior of nonsingular bouncing solutions using global dynamical system tools. We show that for a noncanonical scalar field with exponential potential, nonsingular bouncing cosmologies are a generic feature and stable in past and future directions. However, the same cannot be concluded for power law potential due to the non-existence of global past or future attractors. Our analysis is intended to show how global phase space formulations can be utilized to address questions about the stability of bouncing solutions.Comment: 21 pages, 8 figure

Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models

Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary universe, scaling solutions, convergence to the standard $\Lambda$CDM, etc. While the usual stability analysis helps us determine the evolution of a model geometrically, bifurcation theory allows us to precisely locate the parameters' values describing the global dynamics without a fine-tuning of initial conditions. Using the center manifold theory and bifurcation analysis, we show that the general model undergoes a transcritical bifurcation, which predicts us to tune our models to have certain desired dynamics. We obtained a class of models and a range of parameters capable of describing a cosmic evolution from an early radiation era towards a late time dark energy era over a wide range of initial conditions. There is also a possible scenario of crossing the phantom divide line. We also find a class of models where the late time attractor mechanism is indistinguishable from that of a structurally stable general relativity based model; thus, we can elude the big rip singularity generically. Therefore, bifurcation theory allows us to select models that are viable with cosmological observations.Comment: 17 pages and 18 fig

Scalar-Fluid interacting dark energy: cosmological dynamics beyond the exponential potential

International audienceWe extend the dynamical systems analysis of scalar-fluid interacting dark energy models performed in C. G. Boehmer , Phys. Rev. D 91, 123002 (2015)PRVDAQ1550-799810.1103/PhysRevD.91.123002 by considering scalar field potentials beyond the exponential type. The properties and stability of critical points are examined using a combination of linear analysis, computational methods and advanced mathematical techniques, such as center manifold theory. We show that the interesting results obtained with an exponential potential can generally be recovered also for more complicated scalar field potentials. In particular, employing power law and hyperbolic potentials as examples, we find late time accelerated attractors, transitions from dark matter to dark energy domination with specific distinguishing features, and accelerated scaling solutions capable of solving the cosmic coincidence problem