Gravitational Baryogenesis Constrains Zero-Point Length to Approximately 10−35 Meters

The very fabric of spacetime may possess a fundamental limit to how small distances can become, a concept known as zero-point length, predicted by theories attempting to unify gravity with quantum mechanics. Ava Shahbazi Sooraki and Ahmad Sheykhi, both from Shiraz University, investigate the consequences of this minimal length scale for the early Universe and the origin of matter. Their work demonstrates how zero-point length affects the process of gravitational baryogenesis, a mechanism that could explain the observed imbalance between matter and antimatter in the cosmos. By analysing the amount of matter created during this process, the researchers establish a constraint on the possible size of this fundamental length, finding it to be approximately one millionth the Planck length, and reveal that a universe with a zero-point length expands more slowly at high energies, maintaining higher temperatures for longer periods than previously thought. This research establishes a testable connection between gravity, fundamental length scales, and observable features of the early Universe, offering new insights into the cosmos’ thermal history.

In this paper, we investigate the implications of zero-point length l0-corrected gravity for gravitational baryogenesis and early universe thermodynamics, deriving constraints on l0 from observational baryon asymmetry data. We observe that under the condition of non-equilibrium thermodynamics, l0 generates ̇R ≠ 0 during the radiation epoch, where R is the Ricci scalar. This yields a baryon asymmetry parameter η ∝ l20T9D/MPl. The observed baryon asymmetry η ∼ 9. 9 × 10−11 constrains l0 ≲ 7. 1 × 10−33m, approximately 440times 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.

Zero-Point Length Impacts Baryogenesis and Gravity

This research explores the consequences of a fundamental zero-point length, a minimal scale predicted by some approaches to quantum gravity, for our understanding of cosmology, gravity, and the origin of matter. The team investigates how incorporating this zero-point length affects the expansion of the universe and the imbalance between matter and antimatter. The core idea is that spacetime itself may have a granular structure at extremely small distances, rather than being perfectly continuous. This granularity, if it exists, would modify the standard equations governing the universe’s evolution.

The authors examine how this zero-point length influences the Friedmann equations, which describe the expansion of the universe, and baryogenesis, the process that created the observed matter-antimatter asymmetry. They focus on gravitational baryogenesis, a mechanism where gravity itself plays a role in generating this asymmetry, requiring deviations from thermal equilibrium in the early universe. The research also considers the connection between gravity and entropy, exploring the possibility that gravity is not a fundamental force, but an emergent phenomenon related to disorder. The team’s calculations demonstrate that incorporating a zero-point length modifies the Friedmann equations and leads to a non-zero time derivative of the Ricci scalar, a measure of spacetime curvature.

This is crucial for enabling gravitational baryogenesis. By comparing the predicted baryon asymmetry to observed values, the researchers establish a stringent upper limit on the zero-point length: l0 ≤ 7. 1x 10-33 meters, approximately 440times the Planck length. Furthermore, the analysis reveals that the zero-point length alters the early universe’s cooling rate, causing it to retain higher temperatures for a given time. This leads to a new time-temperature relation for the universe with a zero-point length.

This work provides a potential observational constraint on theories of quantum gravity and offers a testable prediction for other early universe phenomena, such as primordial nucleosynthesis and the cosmic microwave background. It also presents an alternative mechanism for baryogenesis that doesn’t rely on new particles or interactions beyond the Standard Model of particle physics. The connection to entropic gravity suggests that gravity might not be a fundamental force, but rather an emergent phenomenon related to entropy.

Minimal Length Slows Early Universe Expansion

This research establishes a modified cosmological framework incorporating a fundamental zero-point length, a minimal scale predicted by theoretical physics, and explores its implications for the early universe. By applying thermodynamics to cosmological horizons, the team derived modified Friedmann equations, which govern the expansion of the universe, demonstrating how this zero-point length alters the relationship between entropy and spacetime geometry. The analysis reveals that incorporating this minimal length effectively slows the expansion rate in the early universe, leading to a modified time-temperature relationship where the universe remained hotter for a longer duration than predicted by standard cosmology. Furthermore, the team investigated gravitational baryogenesis, a process that could explain the observed asymmetry between matter and antimatter in the universe, within this modified framework. Calculations show that the zero-point length influences the generation of baryon asymmetry during the radiation epoch, and observational constraints on the amount of baryon asymmetry present today place limits on the magnitude of this fundamental length, constraining it to be approximately 440times the Planck length. The findings establish zero-point length cosmology as a viable framework for connecting gravity to observable cosmological properties and provide a testable link between fundamental length scales and the thermal history of the early universe.