Dynamics of Bouncing Cosmology in Brans-Dicke Gravity with Kaniadakis Holographic Dark Energy

Abstract

We examine bouncing cosmology in the anisotropic Bianchi type-III framework within Brans-Dicke gravity, incorporating Kaniadakis holographic dark energy with Hubble and Granda-Oliveros radii as infrared cutoff. We reconstruct bouncing model through correspondence scheme utilizing power-law form of the scalar field in terms of average scale factor. The natural anisotropy in Bianchi type-III model modifies expansion dynamics, offering a broader perspective on early-universe evolution beyond standard isotropic models. We analyze key cosmological parameters, including deceleration, jerk, equation of state ω_de , energy conditions, squared sound speed \({\upsilon }_{s}^{2}\) and \({{\omega }_{de}-\omega }_{de}{\prime}\) plane. Models are exhibiting oscillatory transitions across the phantom divide and evolves smoothly toward ω_de at late times. The stability analysis based on the squared sound speed \({\upsilon }_{s}^{2}\) reveals that models remain dynamically stable over most of the cosmic history and admit instabilities near the bounce. A dynamical phase-space study in the \({{\omega }_{de}-\omega }_{de}{\prime}\) plane shows that both models evolve predominantly in the thawing region, implying an asymptotic approach to a cosmological constant. The energy condition analysis further confirms that the violation of the null and strong energy conditions is a necessary feature for the realization of the bounce.