Constraining Zero-Point Length from Gravitational Baryogenesis

Abstract

The existence of a fundamental zero-point length, $l_0$, a minimal spacetime scale predicted by T-duality in string theory or quantum gravity theories, modifies the entropy associated with the horizon of spacetime. In the cosmological setup, this leads to correction to the Friedmann equations governing the evolution of the Universe. In this paper, we investigate the implications of zero-point length $l_0$-corrected gravity for gravitational baryogenesis and early universe thermodynamics, deriving constraints on $l_0$ from observational baryon asymmetry data. We observe that under the condition of non-equilibrium thermodynamics, $l_0$ generates $\dot{\mathcal{R}}\neq 0$ during radiation epoch, where $\mathcal{R}$ is the Ricci scalar. This yields a baryon asymmetry parameter $\eta \propto l_0^2 T_D^9/M_{\rm Pl}^7$. The observed baryon asymmetry $\eta \sim 9.9 \times 10^{-11}$ constrains $l_0 \lesssim 7.1 \times 10^{-33} m$, approximately $440$ times the Planck length. Furthermore, our analysis reveals that the zero-point length correction in the Friedmann equation, effectively slows the expansion rate at high energies, resulting in a modified time-temperature relationship where the Universe maintains higher temperatures for longer time during early epochs compared to standard cosmology. Our results establish zero-point length cosmology as a testable framework connecting quantum gravity to cosmological observables, with implications for early universe thermal history and fundamental length scales.