A novel approach to baryogenesis in $f(Q,L_{m})$ gravity and its cosmological implications

We present an examination of the $f(Q,L_{m})$ gravity model, in which the functional form $f(Q,L_{m})=\alpha Q^{n}+\beta L_{m}$ is postulated and discuss its potential impact on cosmological dynamics and the phenomenon of gravitational baryogenesis. Combining observational insights from Hubble, BAO and phantom datasets, we conduct a comprehensive analysis to constrain the model's parameters and determine the baryon-to-entropy ratio $\frac{\eta_{B}}{s}$, providing valuable insights into the model's performance and cosmological implications. In the context of baryogenesis and generalized gravitational baryogenesis, we show that setting $n=\frac{1}{2}$ results in a zero baryon-to-entropy ratio, which is physically implausible. Through a detailed examination of the dependence of $\frac{\eta_{B}}{s}$ on $n$ and $\beta$, we demonstrate that our model predicts a baryon-to-entropy ratio that is both positive and consistent with the observational upper limit of $9.42\times10^{-11}$ for $1.32965<n<1.39252$ and appropriate of $\beta$ and $n$ with $\alpha\simeq-1.95084\times10^{86}$. The excellent agreement between our model's predictions and the phantom dataset demonstrates the model's capacity to accurately describe the physics of baryogenesis and its ability to reproduce the observed features of the cosmological data, showcasing its potential as a reliable tool for understanding the evolution of the Universe.