Three-Body Recombination Model

This repository contains the Python code used for calculations and plotting graphs presented in the paper on three-body recombination of y-charged particles in the early Universe. The code models the evolution of the relative density of these particles as a function of the temperature of photons from the cosmic microwave background (CMB).

Overview

The code performs the following tasks:

1. Computation of Relative Density: It calculates the evolution of the relative density of y-charged particles for different recombination mechanisms (three-body, radiative, and classical recombination).

2. Limitations of Three-Body Recombination: The code also evaluates the applicability of the three-body recombination formula within certain model parameters and presents a restriction graph showing the boundaries of its validity.

3. Visualization: The script generates multiple plots that compare different recombination mechanisms and highlight the constraints on the use of the three-body recombination formula.

Main Features

• Temperature-Dependent Calculations: The code computes the relative density of y-charged particles as a function of the temperature of photons.
• Multiple Recombination Models: It includes calculations for three types of recombination:
  • Three-body recombination.
  • Radiative recombination.
  • Classical recombination.
• Validity Range Calculation: The code calculates the limits of applicability for the three-body recombination formula and plots these regions on the graphs.
• Graphical Output: The resulting graphs are saved and can be used for further analysis or directly in publications.

Requirements

To run the code, you need the following dependencies:

• Python 3.x
• numpy for numerical calculations.
• matplotlib for plotting.
• scipy for scientific computing functions.

To install the required dependencies, you can run:

pip install numpy matplotlib scipy

Usage

1. Run the Script: Simply execute the Python script rec.py to perform all calculations and generate the graphs.

   python rec.py

2. Adjust Parameters: You can modify the model parameters (e.g., particle masses, temperature range) directly in the script by changing the respective variables at the top of the file.

3. Output: The script will output the following plots:

   • Relative density of y-charged particles vs. Temperature for various recombination mechanisms.
   • Limitations of three-body recombination with shaded regions indicating the valid parameter space.

   The graphs will be saved as .png files in the working directory.

Key Sections of the Code

• Computation of Relative Density: This section solves the equations that describe the change in relative density ($r/r_0$) based on the recombination mechanism.
• Limitations of Applicability: This part of the code calculates the boundaries where the three-body recombination formula is valid.
• Plotting Functions: The final part of the code generates the graphs, formatting the curves and adding labels and legends.

Graphs

• The script produces the following graphs:
  • Three-Body Recombination vs. Other Mechanisms: A comparison of different recombination processes.
  • Applicability of the Three-Body Formula: Displays the region where the formula is valid, with an overlay on the recombination curves.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

The code and models are based on the methods and formulas presented in the research paper: IN PROCESS.

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