Constraining Zero-Point Length from Gravitational Baryogenesis

TL;DR

This work links quantum-gravity-inspired minimal length ($l_0$) to early-universe cosmology by deriving $l_0$-corrected horizon entropy and the resulting modified Friedmann equations. The authors show that $l_0$ induces a nonzero $\dot{\mathcal{R}}$ during radiation, enabling gravitational baryogenesis and producing an baryon asymmetry $\eta$ that scales as $\eta \propto \frac{l_0^2 T_D^9}{M_{\rm Pl}^7}$. Using the observed $\eta_{\rm obs} \sim 9.9 \times 10^{-11}$ and a high decoupling temperature $T_D$, they constrain $l_0 \lesssim 7.1 \times 10^{-33}$ m (about $440$ times the Planck length). Additionally, the modified expansion alters the time–temperature relation, yielding a hotter early universe for a given $t$, thus (i) connecting quantum gravity to cosmological data and (ii) offering a testable framework for zero-point length cosmology.

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 $η\propto l_0^2 T_D^9/M_{\rm Pl}^7$. The observed baryon asymmetry $η\sim 9.9 \times 10^{-11}$ 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.

Figures (2)

• Figure 1: The predicted baryon asymmetry $\eta$ as a function of the zero-point length $l_0$. The horizontal dashed line marks the observational upper limit. The viable parameter space, consistent with measurements, is the area beneath this line ($\eta<9.9\times 10^{-11}$).
• Figure 2: The behavior of the temperature vs time in the radiation dominated era of zero-point length cosmology for different values of the zero-point length parameter $\tilde{l}_0=[ 0.5\times 10^{-10}, 7\times 10^{-10}, 10^{-9}]$.