Computational Tools

We provide a suite of Python tools for exploring the oscillating brane theory and computing its predictions.

Quick Start

from scripts.brane_dynamics import BraneOscillator

# Initialize with default parameters
brane = BraneOscillator(
    tau_0=7.0e19,  # Brane tension (J/m²)
    f_osc=0.10,    # Oscillating fraction
    T=2.0          # Period (Gyr)
)

# Calculate dark energy equation of state
z = 0.5  # redshift
w_de = brane.equation_of_state(z)
print(f"w(z={z}) = {w_de:.3f}")

Available Scripts

1. Brane Dynamics Calculator

File: scripts/brane_dynamics.py

Computes membrane oscillations and dark energy equation of state.

# Example: Plot w(z)
brane = BraneOscillator()
fig = brane.plot_equation_of_state(z_min=0, z_max=2)

Key functions:

• equation_of_state(z): Calculate w(z) at given redshift
• membrane_displacement(t): Compute brane position
• gravitational_wave_spectrum(f): GW signature
• growth_suppression(): Structure formation effects

2. Growth Factor Calculator

File: scripts/growth_factor.py

Computes linear growth factor D₊(z) including oscillation effects.

# Command line usage
python scripts/growth_factor.py --redshift 0 0.5 1.0 --compare

# With exact ODE integration
python scripts/growth_factor.py --exact --redshift 0 1 2

Features:

• Fast fitting formula or exact ODE integration
• Comparison between oscillating and ΛCDM models
• S₈ parameter calculation

3. Bayesian Analysis

File: scripts/bayesian_analysis.py

Performs model comparison using MCMC and computes Bayesian evidence.

from scripts.bayesian_analysis import BayesianAnalyzer

# Run analysis with your data
analyzer = BayesianAnalyzer(observational_data)
sampler = analyzer.run_mcmc(model='oscillating')
log_evidence, error = analyzer.compute_evidence(sampler)

Capabilities:

• MCMC sampling with emcee
• Evidence calculation
• Parameter constraints
• Model comparison statistics

Interactive Notebooks

Coming soon: Jupyter notebooks for interactive exploration

• Parameter space visualization
• Real-time equation of state plotting
• Gravitational wave signal analysis
• Structure formation animations

Installation

1. Clone the repository:

   git clone https://github.com/Teleadmin-ai/oscillating-brane-DM.git
   cd oscillating-brane-DM
   

2. Install dependencies:

   pip install numpy scipy matplotlib emcee corner
   

3. Run example:

   python scripts/brane_dynamics.py
   

API Documentation

BraneOscillator Class

class BraneOscillator:
    def __init__(self, tau_0=7.0e19, f_osc=0.10, T=2.0, L=2.0e-7):
        """
        Parameters:
        - tau_0: Brane tension (J/m²)
        - f_osc: Oscillating DM fraction
        - T: Period (Gyr)
        - L: Extra dimension size (m)
        """

GrowthFactorCalculator Class

class GrowthFactorCalculator:
    def __init__(self, omega_m=0.315, oscillating=True, A_w=0.003):
        """
        Parameters:
        - omega_m: Matter density
        - oscillating: Include oscillations
        - A_w: w(z) amplitude
        """

Contributing

We welcome contributions! Please submit pull requests for:

• New analysis tools
• Visualization improvements
• Performance optimizations
• Additional observational tests

See our GitHub repository for more details.