Pandora's Box I: The Derivation of the Cosmological Constant

Project Title: Box of Pandora I: The Derivation of the Cosmological Constant

Author: André Eduardo Pereira da Silva

Contact: andre.eduardocgart@gmail.com

DOI (Digital Object Identifier): [10.5281/zenodo.15785815]

Abstract: This project presents the first part of a new line of research, titled "Box of Pandora," which proposes a solution to the cosmological constant problem (Λ). The theory postulates that the physical vacuum is not empty, but a continuous and vibrational scalar medium. This work mathematically demonstrates that the observed dark energy density (ρΛ) emerges as a rescaled projection of the intrinsic energy density of this "scalar mesh." The connection between the two scales is made by a dimensionless zoom factor, Z, which, in turn, is determined by the internal geometry of the mesh itself, without the need for free parameters or fine-tuning.

Scientific Context: Modern physics faces a discrepancy of approximately 120 orders of magnitude between the theoretically predicted value for the vacuum energy from Quantum Field Theory and the value measured by cosmological observations. This project directly addresses this "worst adjustment in the history of physics," proposing that the error lies not in the calculation, but in the premise of an empty vacuum.

The Scalar Mesh Hypothesis: The theory models the vacuum as a real, three-dimensional scalar field, whose stable and localized excitations (oscillons) form the building blocks of reality. In this paradigm:

• The observable universe is a rescaled projection of this mesh's structure.

• The relationship between the cosmological density and the mesh's density is ρΛ=Z4⋅ρmesh.

• The rescaling factor Z is not a free parameter but emerges from the minimal action (Sosc) of an oscillon, via Z=αTE⋅Sosc.

Key Results of This Work (Article I):

• Internal Consistency: Demonstration of the "dual emergence" of the factor Z≈0.0487, which satisfies both the density relationship and the action relationship with an emergent coupling constant, αTE≈1.2.

• Derivation of Λ: The model derives the value ΛTE=1.433×10−52 m−2 from its own principles.

• Falsifiable Prediction: The predicted value is confronted with the latest cosmological data (2025), which points to Λobs≈1.127×10−52 m−2. The tension of ≈27% establishes a clear and testable prediction for future observations.

• Robustness: The stability of the constant αTE is numerically validated under variations in simulation parameters.

Significance and Next Steps: This article establishes the Scalar Mesh as a viable and predictive hypothesis. It serves as the foundation for the next articles in the "Box of Pandora" series, which will explore:

• The theoretical derivation of the constant αTE from first principles.

• The emergence of a tensor gravity compatible with General Relativity.

• The reconstruction of particles and forces of the Standard Model from the topology of the mesh.

Repository Content:

1. Article: Box_of_Pandora_I.pdf - The complete scientific paper detailing the theory and results.

2. Scripts: /Dados_Pandora_Box_1/ folder containing the Python code used for simulations, analysis, and figure generation, ensuring the full reproducibility of the work.

3. README.md: This description file.

4. LICENSE: License for the use of the code (e.g., MIT License).