The Dynamics of Cosmic Evolution: Insights from Bouncing Cosmology

The primary aim of this work is to explore feasible bouncing cosmological solutions in the framework of $f(\mathcal{Q}, \mathcal{C})$ gravity, where $\mathcal{Q}$ denotes non-metricity and $\mathcal{C}$ indicates the boundary term. To achieve this, we analyze the dynamics of a Bianchi type-I spacetime with perfect fluid distribution. We consider various functional forms of $f(\mathcal{Q,C})$ theory to assess how this modified gravity framework influences cosmic evolution. Additionally, we examine the dynamics of different cosmological parameters to explore non-singular bounce solutions. We also use linear perturbation to study the stability analysis. Our findings reveal the breach of the null energy conditions, which is required for the existence of viable bounce solutions. The equation of state parameter demonstrates either a quintessence phase or a phantom regime of the universe, demonstrating that the cosmos is undergoing accelerating expansion. This gravitational framework presents a promising alternative to the standard cosmological model, presenting an innovative viewpoint on gravitational interactions and the dynamics of the early universe.