Anisotropic cosmology in <italic>q</italic>-deformed entropic gravity

In this work, we examine the implications of q-deformed theory on anisotropic Bianchi type-I cosmological model within the framework of Verlinde's entropic gravity. The q-deformed theory, rooted in quantum group structures, provides a natural generalization of classical particle dynamics and offers a useful framework for exploring deviations in standard cosmological models. By incorporating the principles of entropic gravity, which conceptualize gravity as an emergent entropic force, we derive the dynamical equations governing the Bianchi type-I anisotropic model influenced by q-deformation. Finally, we analyze the axisymmetric solution of Bianchi type-I model and these findings highlight the potential impact of q-deformation on the dynamics of the early universe and its subsequent evolution.