Cosmological Evolution, Analytical Parametrization, and Dynamical Stability of a Bouncing Universe in Non-Minimal Kinetic Coupling Gravity
In this paper, the bouncing cosmology is studied in the framework of the non-minimal kinetic coupling theory between the scalar field and the Einstein tensor. After deriving the modified Friedmann equations and the field equation, by applying the Bounce condition, the system of equations is solved numerically without assuming any analytical form for the scale factor. Thus, the time evolution of the scale factor, the scalar field, and other cosmological quantities are obtained directly from the model dynamics. Then, in order to provide an explicit form for the cosmic evolution, an analytical parameterization for the scale factor is introduced, which is fitted to the numerical solution with high accuracy and its validity is confirmed by comparing the Hubble parameter obtained from the parameterization with the numerical solution. Using this framework, the behavior of cosmological parameters including the Hubble parameter, the comoving Hubble horizon, the energy density, the pressure, and the equation of state (EoS) parameter during the evolution of the universe is investigated, and a smooth transition from the contraction phase to the expansion phase without the occurrence of a singularity is shown. Next, the stability of the model is studied using an autonomous dynamical system and critical point analysis in phase space. The results show that the presented model, in addition to describing a non-singular bouncing scenario, has stable dynamic behavior and the introduced analytical parameterization can be used as a suitable tool for future analytical studies.