Project Overview
The EREBUS-ALP framework provides a high-precision numerical solution for non-equilibrium Axion-Like Particle (ALP) cosmology. This advanced tool implements exact momentum-dependent Boltzmann equations for interactions between lepton and photon couplings, calibrated against leading datasets such as Planck, ACT, and DESI DR2.

Key Features

• ** NEURAL-KINETIC Framework**: A sophisticated numerical solver that enhances traditional fluid approximations by accurately addressing non-thermal phase-space distributions. This capability enables the detailed analysis of spectral distortions in the Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN) observables.

• Exact Phase-Space Mapping: Solves collision integrals without the assumption of thermal spectra, allowing for improved modeling of astrophysical phenomena.

• Prior Sensitivity Optimization: The framework is optimized for Markov Chain Monte Carlo (MCMC) analysis, sampling over the effective number of neutrino species (9;9; 9;N_{eff}9;9;) instead of the axion decay constant (9;9;f_a9;9;), thus enhancing constraints derived from observational data.

• UV-Dominated Production: Includes specialized solvers for Primakoff production processes occurring at high initial temperatures (T_{in} 8;gt; 10^3 GeV).

• Multi-Channel Coupling: Offers dedicated modules for the interactions of electron (e), muon (45;48;) and tau (C4) decay and scattering channels.

Mathematical Framework
The EREBUS-ALP framework utilizes the generalized 2 e; 2 collision integral defined in high-energy kinetic theory, formalized as:

C[f_1, f_2, f_3] = \frac{1}{2E_k} \int d\Pi_1 d\Pi_2 d\Pi_3 (2\pi)^4 \delta^{(4)}(P_1 + P_2 - P_3 - K) |M|^2 f_1 f_2 (1 \mp f_3)  

Where |M|^2 represents the channel-specific matrix element, which is systematically integrated into cosmological observables using vectorized momentum grids.

Cosmological Constraints and Forecasts
The framework is calibrated against cutting-edge cosmological data, yielding 95% confidence level limits on ALP-lepton interactions and ALP-photon couplings:

• ALP-Lepton Constraints:
  f_a > 1.63 x 10^6 GeV (electron), 9.41 x 10^6 GeV (muon), 8.06 x 10^4 GeV (tau).
• ALP-Photon Coupling:
  g_{aB3} < 1.98 x 10^{-8} GeV^{-1}.
• Next-Generation Sensitivity: Pre-configured for experiments such as LiteBIRD, Simons Observatory, and CMB-HD, targeting a sensitivity range of 9;9; 9;N_{eff}9;9; of approximately 0.01 - 0.03.

Implementation Details

• Programming Language: Python 3.10+
• Dependencies: Utilizes libraries including NumPy, SciPy (Quadrature & ODE solvers), and Matplotlib.
• Core Logic: Employs a Sovereign Non-thermal Offset (SNO) algorithm, ensuring high-momentum convergence for computational precision.

This framework provides robust capabilities for analyzing ALP cosmology, ensuring controlled theoretical uncertainties and supporting high-precision measurements in cosmology.