Constraining Zero-Point Length from Gravitational Baryogenesis

TL;DR

This paper explores how a fundamental zero-point length affects early universe cosmology and baryogenesis, deriving constraints on its size from observational data and showing its impact on cosmic expansion and thermodynamics.

Contribution

It introduces a zero-point length correction to gravity affecting baryogenesis and cosmology, providing observational constraints and analyzing its effects on early universe dynamics.

Findings

Zero-point length $l_0$ constrained to be less than $7.1 imes 10^{-33}$ m.

Zero-point length modifies the Friedmann equations, slowing early universe expansion.

Baryon asymmetry parameter $ o l_0^2 T_D^9/M_{Pl}^7$.

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.