Cosmological Evolution and Stability of a Bouncing Universe with Non-Minimal Kinetic Coupling Gravity

TL;DR

The paper addresses the singularity problem in standard cosmology by constructing a bouncing scenario within non-minimal kinetic coupling gravity. It derives modified FRW equations and energy-momentum expressions, reconstructs a bouncing evolution with a scalar potential $V(\phi)=v_0/\cosh(\lambda\phi)$ and a quadratic coupling $F(\phi)=1+c\phi^2$, and fits the scale factor with an explicit ASF form to obtain a corresponding $H(t)$ that crosses zero at the bounce ($H_b=0$, $dotH_b>0$). Stability is examined via a dynamical-system analysis in phase space, revealing fixed points that include a stable inflationary attractor with $\omega \approx -1$ under suitable parameter choices. The results demonstrate a viable, non-singular pre- to post-bounce evolution with an inflationary phase, highlighting the potential of non-minimal kinetic coupling gravity to model early-universe dynamics in a controlled, stable framework.

Abstract

In this paper, we model the bounce phase, stability, and the reconstruction of the universe by non-minimal kinetic coupling. In the process, we obtained importance information about the energy density and the matter pressure of the universe in relation to the previous universe through the bounce quantum phase. The novelty of the work is that the scale factor is obtained directly from the model and is fitted with an exponential function, with this view we explore the process of the early universe even the bounce phase. After that, we plot the cosmological parameters in terms of time evolution. In what follows, we investigate the stability of the model by dynamical system analysis in a phase plane. Finally, we examine the stability of the universe, especially in the inflationary period, by using the phase-space trajectories.

Figures (10)

• Figure 1: Graph of the scale factor in terms of cosmic time.
• Figure 2: Graph of the Hubble parameter in terms of cosmic time.
• Figure 3: Graph of $\frac{1}{aH}$ in terms of cosmic time.
• Figure 4: Graph of the scale factor in terms of cosmic time in the form of the numerical solution and the adopted scale factor.
• Figure 5: Graph of the Hubble parameter in terms of cosmic time in the form of the numerical solution and the calculated Hubble parameter.