The Minimal Eternal Universe Theory (mEUT v4.0): A Dissipative Kinetic Bounce Cosmology with Density-Matrix Formulation

This repository contains the fourth iteration of the Minimal Eternal Universe Theory (mEUT), an independent research project in theoretical cosmology. mEUT v4.0 proposes a singularity-free, eternal cosmological framework driven by the purely kinetic energy of a single real scalar field.

Key Features of v4.0:

• Microscopic Derivation of Dissipation: Unlike previous versions, the dissipation parameter $\eta$ is derived from first principles using the Nakajima-Zwanzig projection technique and the fluctuation-dissipation theorem, evaluated within a 64-vertex truncation of holonomy-corrected geometric operators.

• Density-Matrix Dynamics: The theory moves beyond simple wave-function evolution to a reduced density-matrix formulation (ρϕ), providing a more robust bridge between Loop Quantum Gravity (LQG) and effective Friedmann dynamics.

• Emergent Arrow of Time: The model provides a microscopic origin for the thermodynamic arrow of time through irreversible entropy production during the quantum bounce phase.

• Observational Signatures: Includes predictions for the suppression of the primordial power spectrum (PR(k)), offering a potential resolution to the S8 and H0 tensions.

Contents:

1. Numerical_Simulation_Data: Raw data from the 64-vertex truncation and large-$j$ extrapolation.

2. QuTiP_Scripts (optional if included): Python scripts used to solve the Lindblad master equation.

import numpy as np
import matplotlib.pyplot as plt
from qutip import *

def run_mEUT_v4_complete():
    print("Starte mEUT v4.0 Simulation...")
    
    # --- 1. System-Setup ---
    N = 60  # Hilbertraum-Dimension
    a = destroy(N)
    phi_op = (a + a.dag()) / np.sqrt(2)
    p_op = -1j * (a - a.dag()) / np.sqrt(2)
    
    # Hamiltonian: Rein kinetisch H = p^2 / 2
    H = p_op**2 / 2
    
    # --- 2. Dissipations-Profil eta(t) ---
    # Modelliert den Peak am Bounce (t=0) gemäß 64-Vertex-Modell
    def eta_func(t):
        return np.exp(-t**2 / 2.0)

    # --- 3. Zeitentwicklung (Lindblad) ---
    times = np.linspace(-5, 5, 400)
    psi0 = coherent(N, -3.0) # Pre-Bounce Zustand
    rho = ket2dm(psi0)
    
    entropy = []
    states = []
    
    # Wir simulieren schrittweise, um eta(t) dynamisch anzuwenden
    dt = times[1] - times[0]
    for t in times:
        states.append(rho)
        entropy.append(entropy_vn(rho))
        
        # Lindblad-Update: d_rho = -i[H, rho]dt + eta(t) * L_dissipator(rho)dt
        eta = eta_func(t)
        L = p_op # Impuls als Jump-Operator (kinetische Dissipation)
        
        # Kommutator-Teil
        d_rho_ham = -1j * commutator(H, rho)
        # Dissipator-Teil (Lindblad-Form)
        d_rho_diss = eta * (L * rho * L.dag() - 0.5 * L.dag() * L * rho - 0.5 * rho * L.dag() * L)
        
        rho = rho + (d_rho_ham + d_rho_diss) * dt
    
    # --- 4. Visualisierung ---
    # FIG 1: Entropie und eta
    plt.figure(figsize=(10, 5))
    plt.plot(times, entropy, 'r', label='v. Neumann Entropy S')
    plt.plot(times, [eta_func(t)*max(entropy) for t in times], 'b--', label='Dissipation eta (scaled)')
    plt.title('mEUT v4.0: Entropy & Dissipation')
    plt.xlabel('Relational Time phi')
    plt.legend()
    plt.savefig('entropy_plot.png')
    plt.show()

    # FIG 2: Wigner-Phasenraum-Evolution
    xvec = np.linspace(-7, 7, 150)
    indices = [0, len(times)//2, len(times)-1] # Start, Bounce, Ende
    titles = ['Pre-Bounce (Pure)', 'Bounce (Interacting)', 'Post-Bounce (Mixed/Classical)']
    
    fig, axes = plt.subplots(1, 3, figsize=(15, 5))
    for i, idx in enumerate(indices):
        W = wigner(states[idx], xvec, xvec)
        axes[i].contourf(xvec, xvec, W, 100, cmap='RdBu')
        axes[i].set_title(titles[i])
    plt.savefig('wigner_plots.png')
    plt.show()
    
    print("Simulation abgeschlossen. Plots wurden gespeichert.")

if __name__ == "__main__":
    run_mEUT_v4_complete()