Narrow Results

This paper deals with a nonminimally coupled scalar field in the background of homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) flat spacetime. As Einstein field equations are coupled second-order nonlinear differential equations, it is very hard to find exact solutions. By suitable choice of variables, we transform Einstein field equations to an autonomous system and critical points are determined. We use center manifold theory to characterize nonhyperbolic critical points and are found to be saddle in nature. We discuss possible bifurcation scenarios, which indicate the existence of the cosmological bouncing model.

This work is an example of the application of the dynamical system analysis in the context of cosmology. Here cosmic evolution is considered in the background of homogeneous and isotropic flat FLRW spacetime with interacting dark energy and varying mass dark matter as the matter content. The DE is chosen as phantom scalar field with self-interacting potential while the DM is in the form of dust. The potential of the scalar field and the mass function of dark matter are chosen as exponential or power-law form or in their product form. Using suitable dimensionless variables, the Einstein field equations and the conservation equations constitute an autonomous system. The stability of the nonhyperbolic critical points is analyzed by using center manifold theory. Finally, cosmological phase transitions have been detected through bifurcation analysis which has been done by Poincaré index theory.