The Role of MOND Theory in Cosmological Paradigms Under q-Statistics

Abstract

This study is about the consequences of fermionic q-deformation on Friedmann equations and its effects on cosmology within the framework of Verlinde's entropic gravity proposal. We begin by examining the thermodynamic properties of q-deformed fermion gas model in two-dimensional space. We then extend our research to derive modified Friedmann equations using the Friedmann-Robertson-Walker (FRW) metric to study cosmological dynamics using q-deformed MOND theory. The study describes the effective energy density, pressure, and equation of state of dark energy within this modified framework. Finally, by providing an analytical expression for the effective density parameter of dark energy, we provide valuable insights into the interaction between quantum deformation and cosmological events.