We investigate the concept of Kaniadakis entropy and its dual formulation, examining their implications for gravitational dynamics within the framework where gravity emerges as an entropic force resulting from changes in the informational content of a physical system. In this context, we derive a modified form of Newton’s law of gravitation that reflects the corrections introduced by both Kaniadakis entropy and its dual state. Furthermore, we apply the emergent gravity scenario at large scales and derive the modified Friedmann equations incorporating corrections from (dual) Kaniadakis entropy. Our results provide deeper insights into the interplay between thermodynamics and gravitational dynamics. In order to constrain the model parameter, we study the big bang nucleosynthesis in the context of (dual) Kaniadakis cosmology. We explore an alternative method to establish limits on the Kaniadakis parameter, denoted as $K$, by examining how (dual) Kaniadakis cosmology influences the primordial abundances of light elements i.e., helium ${}^4\mathrm{He}$, deuterium D, and lithium ${}^7\mathrm{Li}$. Our analysis indicates that the obtained ranges for the dual Kaniadakis parameter (unlike the Kaniadakis parameter) exhibit overlap for the aforementioned light elements, and the allowed values fall within the range $-0.8\times {10}^{-78}\lesssim \widetilde{K^{*}}\lesssim 0.8\times {10}^{-78}$, which shows that the deviations from the conventional Bekenstein-Hawking formula are minimal, as expected. This consistency between the ranges suggests a potential solution to the well-known lithium problem. Furthermore, we discuss the relationship between cosmic time $t$ and temperature $T$ within the framework of (dual) Kaniadakis cosmology. We observe that an increase in the Kaniadakis parameter leads to a rise in the temperature of the early universe. Conversely, when the dual Kaniadakis parameter increases, the temperature of the early universe decreases.

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• Big bang nucleosynthesis
• Cosmology