Core Concepts

The paper proposes an alternative scenario for the emergence of baryon asymmetry in the Universe, realized in a lattice gravity model associated with the Dirac field. At ultra-high temperatures, the system is in a PT-symmetric phase, but as the temperature decreases, a phase transition occurs where the wave function splits into two states, |+⟩ and |−⟩, with different tetrad field signs. During the initial Planck time, fermion transitions between these states are possible, leading to a small but persistent imbalance in the fermion charge between the states, which is the source of baryon asymmetry.

Abstract

The paper presents an alternative scenario for the emergence of baryon asymmetry in the early Universe, based on a lattice theory of gravity coupled to Dirac fields.

At ultra-high temperatures (around the Grand Unification scale of 10^18 GeV), the system is in a PT-symmetric phase, where the Dirac and conjugate Dirac fields are interchangeable. However, as the temperature decreases, a phase transition occurs, and the wave function of the system splits into a superposition of two states, |+⟩ and |−⟩, with different signs of the tetrad field (the field that defines the Minkowski metric).

During the initial Planck time (about 10^-43 seconds) after the phase transition, there is a non-zero matrix element for fermion transitions between the |+⟩ and |−⟩ states. These transitions are not correlated across different regions of space, leading to a small but persistent imbalance in the fermion charge between the two states.

After the Planck time, the interaction between the |+⟩ and |−⟩ states ceases, and the accumulated fermion charge imbalance is preserved, providing a source for the observed baryon asymmetry in the Universe.

The author argues that this scenario satisfies Sakharov's conditions for baryogenesis, with the violation of C and CP symmetry occurring due to the non-equivalence of the |+⟩ and |−⟩ states, and the absence of thermal equilibrium being ensured by the rapid phase transition and the cessation of interactions between the states after the Planck time.

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Stats

The paper provides the following key figures and metrics:
The phase transition temperature is estimated to be around Tc ∼ 10^18 GeV or Tc ∼ 10^31 K.
The duration of the initial Planck time when fermion transitions between the |+⟩ and |−⟩ states are possible is about τ ∼ tP ≈ 10^-43 seconds.
The estimated density of the fermion asymmetry is δn+ ∼ ν(L0/lP)^-3/2 ∼ ν · 10^6 cm^-3, where ν ∼ 10^-10 is a small parameter related to the amplitude of fermion transitions between the states.
The observed experimental value of the baryon asymmetry is δn+(exp) ∼ 10^-5 cm^-3.

Quotes

"At ultra-high temperatures of the Grand Unification order Tc ∼1018 GeV and higher, the system is in a PT-symmetric phase. But when the temperature decreases, a phase transition to an asymmetric phase occurs, in which a non-zero tetrad appears, that is, space-time with the Minkowski metric, and the system's wave function splits into two: |⟩= |+⟩+ |−⟩."
"During this small Planck time τ ∼tP ≈ 10^-43 sec. matrix element ⟨+|HΨ|−⟩̸= 0. Since the Hamiltonian preserves the total number of fermions, the indicated inequality contains the amplitudes of fermion transitions from |−⟩to |+⟩, and vice versa."
"For times t > τ we have ⟨+| ˆO|−⟩= 0 for all local operators ˆO. Therefore, the imbalance of fermions between the states |+⟩and |−⟩accumulated over time τ is preserved, which is the source of baryon asymmetry."

Key Insights Distilled From

by S.N. Vergele... at **arxiv.org** 10-01-2024

Deeper Inquiries

Several mechanisms have been proposed to explain the observed baryon asymmetry in the Universe, each with its own theoretical framework and implications. Some of the most notable include:
Electroweak Baryogenesis: This mechanism relies on the electroweak phase transition, where the Higgs field acquires a vacuum expectation value, leading to the violation of baryon number conservation. The Kobayashi-Maskawa mechanism, which involves CP violation in the quark sector, is often invoked to explain how baryon asymmetry can arise during this transition. Compared to the lattice gravity model presented in the paper, electroweak baryogenesis is more established within the Standard Model framework but faces challenges in producing sufficient baryon asymmetry without additional sources of CP violation.
Sphaleron Processes: Proposed by Kuzmin, Rubakov, and Shaposhnikov, sphaleron baryogenesis involves non-perturbative processes in the electroweak sector that can convert lepton asymmetry into baryon asymmetry. This model requires a departure from thermal equilibrium and is sensitive to the details of the phase transition. The lattice gravity model offers a different approach by focusing on the dynamics of fermion states in a PT-symmetric framework, potentially providing a new avenue for understanding baryon asymmetry without relying on sphaleron processes.
Affleck-Dine Mechanism: This model suggests that a scalar field can develop a non-zero expectation value during inflation, leading to a baryon asymmetry through its decay. The Affleck-Dine mechanism operates at high energy scales and can generate a significant asymmetry. In contrast, the lattice gravity model emphasizes the role of fermionic states and their transitions, which may provide a complementary perspective on baryon asymmetry generation.
Gravity-Induced Baryogenesis: Some models propose that gravitational effects during inflation can lead to baryon asymmetry. This approach aligns more closely with the lattice gravity model, as both consider the role of gravity in the early Universe. However, the lattice model specifically incorporates a discrete symmetry breaking mechanism that distinguishes it from other gravity-induced scenarios.
In summary, while various mechanisms exist to explain baryon asymmetry, the lattice gravity model presented in the paper offers a unique perspective by focusing on the interplay between fermionic states and PT symmetry breaking, potentially addressing some of the limitations faced by traditional models.

To enhance the predictive power of the proposed lattice gravity model regarding baryon asymmetry, several avenues for development and refinement can be pursued:
Numerical Simulations: Implementing numerical simulations of the lattice gravity model could provide insights into the dynamics of fermionic states during the phase transition. By simulating the evolution of the system at various temperatures and observing the behavior of the wave functions, researchers could quantify the degree of baryon asymmetry generated and its dependence on initial conditions.
Analytical Calculations: Further analytical work could be done to derive explicit expressions for the baryon asymmetry in terms of model parameters. This could involve perturbative expansions around the phase transition point and exploring the role of different coupling constants in the fermionic transitions.
Incorporation of CP Violation: The model could be refined by explicitly incorporating sources of CP violation, which are crucial for generating baryon asymmetry. By examining how different forms of CP violation affect the transitions between states |+⟩ and |−⟩, the model could yield more accurate predictions.
Connection to Observational Data: Establishing a direct connection between the model's predictions and observable quantities, such as the baryon-to-photon ratio or the cosmic microwave background (CMB) anisotropies, would strengthen its validity. This could involve calculating the expected signatures of baryon asymmetry in the CMB and comparing them with observational data.
Exploration of Phase Transition Dynamics: Investigating the nature of the phase transition (first-order vs. second-order) and its implications for baryon asymmetry generation could provide deeper insights. Understanding how the dynamics of the transition influence the fermionic states and their interactions would be crucial for making quantitative predictions.
By pursuing these avenues, the lattice gravity model could evolve into a more robust framework for understanding baryon asymmetry, ultimately leading to testable predictions that could be compared with experimental and observational results.

Validating or falsifying the proposed mechanism for baryon asymmetry generation in the early Universe requires innovative experimental and observational approaches, particularly given the high energy scales involved. Some potential tests include:
High-Energy Particle Colliders: Experiments at facilities like the Large Hadron Collider (LHC) could search for signatures of new physics associated with the high-energy phase transitions predicted by the lattice gravity model. Specifically, looking for processes that exhibit CP violation or baryon number violation could provide indirect evidence supporting the model.
Cosmic Microwave Background (CMB) Observations: The CMB provides a snapshot of the early Universe and contains imprints of baryon asymmetry. Analyzing the CMB for anomalies or patterns that could be attributed to the dynamics of baryon asymmetry generation, as predicted by the lattice model, could offer crucial insights. For instance, deviations in the temperature fluctuations or polarization patterns could hint at the underlying mechanisms.
Gravitational Wave Detection: The early Universe's dynamics, particularly during phase transitions, may produce gravitational waves. Observatories like LIGO and future space-based detectors (e.g., LISA) could potentially detect these waves, providing evidence for the phase transitions and the associated baryon asymmetry generation mechanisms.
Neutrino Observations: The generation of baryon asymmetry may be linked to processes involving neutrinos, particularly in scenarios where lepton asymmetry is converted into baryon asymmetry. Observing neutrino fluxes from astrophysical sources or during supernova events could provide indirect evidence for the mechanisms proposed in the lattice gravity model.
Astrophysical Baryon Asymmetry Measurements: Observations of the baryon-to-photon ratio in the Universe, particularly through the study of primordial nucleosynthesis and the distribution of baryonic matter in galaxies, could be compared with the predictions of the lattice gravity model. Discrepancies between observed and predicted values could challenge the model's validity.
Cosmological Simulations: Conducting cosmological simulations that incorporate the dynamics of the lattice gravity model could help predict the large-scale structure of the Universe and the distribution of baryonic matter. Comparing these simulations with observational data from galaxy surveys could provide a means to validate or falsify the model.
By employing these experimental and observational strategies, researchers can rigorously test the key aspects of the proposed mechanism for baryon asymmetry generation, contributing to our understanding of the early Universe and the fundamental processes that shaped it.

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