Big-Bang nucleosynthesis constraints on (dual) Kaniadakis cosmology

TL;DR

This work investigates how (dual) Kaniadakis entropy, as a generalization of Bekenstein–Hawking entropy, modifies gravitational dynamics within entropic/ emergent gravity frameworks. It derives corrected Newtonian gravity and Friedmann equations, and demonstrates consistency between two thermodynamic approaches (entropic force and emergent gravity) by introducing a deformation scale $\lambda$ and a correction parameter $\beta$, both tied to the Kaniadakis parameter $K$ and its dual. By confronting these modifications with Big-Bang Nucleosynthesis data, the authors obtain stringent, albeit extremely small, bounds on the deformation parameters, with the dual parameter $\tilde{K}^*$ constrained to roughly $[-0.8\times10^{-78}, 0.8\times10^{-78}]$ in natural units, and a complementary, separate bound for $K$. The study also analyzes the time–temperature relation in the early universe under these corrections, finding that $K$ increases the early-universe temperature while the dual parameter decreases it, and discusses potential implications for the Lithium problem within the dual framework. Overall, the results show that generalized entropic corrections to gravity are tightly constrained by BBN and remain viable without spoiling standard cosmology, while offering a potential pathway to address longstanding discrepancies in primordial lithium.

Abstract

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 $_{}^{4}\textit{He}$, Deuterium $D$ and Lithium $_{}^{7}\textit{Li}$. 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 \tilde {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 \textit{Lithium problem}. Furthermore, we discuss the relationship between cosmic time $t$ and temperature $T$ within the framework of (dual) Kaniadakis cosmology.

Figures (8)

• Figure 1: $Z_{_{}^{4}\textrm{He}}$ vs $\tilde{K}$. The experimental range is reported in (\ref{['zhe']}). We have fixed $\eta_{10}=6$ and the temperature of freeze-out $T_f=1 MeV$.
• Figure 2: $Z_{_{}^{4}\textrm{He}}$ vs $\Tilde{K^*}$. The experimental range is reported in (\ref{['zhe']}). We have fixed $\eta_{10}=6$ and the temperature of freeze-out $T_f=1 MeV$.
• Figure 3: $Z_D$ vs $\tilde{K}$. The experimental range is reported in (\ref{['zobs']}). We have fixed $\eta_{10}=6$ and the temperature of freeze-out $T_f=1 MeV$.
• Figure 4: $Z_D$ vs $\tilde{K^*}$. The experimental range is reported in (\ref{['zobs']}). We have fixed $\eta_{10}=6$ and the temperature of freeze-out $T_f=1 MeV$.
• Figure 5: $Z_{Li}$ vs $\tilde{K}$. The experimental range is reported in (\ref{['lit']}). We have fixed $\eta_{10}=6$ and the temperature of freeze-out $T_f=1 MeV$.