From Quantum to Cosmos: Defusing the Hubble Tension with Λ via (ℓₚ·tₚ)/(Rₒᵦₛ·t₀) ⇒ α_σ ≈ 4.60×10⁻¹²³ ⇒ Λ = α_σ/ℓₚ² ≈ 10⁻¹²³

We present a minimal, covariant resolution of the Hubble tension based on the Planck two-measure, σₚ = ℏ G / c⁴. Defining a spacetime fine-structure number αₛ = σₚ / (R·t) --->(Solving the Λ Problem via (ℓₚ·tₚ)/(Rₒᵦₛ·t₀) ⇒ α_σ ≈ 4.60×10⁻¹²³ ⇒ Λ = α_σ/ℓₚ² ≈ 10⁻¹²³). We obtain a late-time H²-running vacuum component ρₛ ∝ ν(a) H²(a) with ν(a) = ν₀ aᵖ, p > 2. This leaves early-universe physics (CMB, BBN, sound horizon) unchanged, while shifting low-redshift distances (SNe Ia, BAO, time-delay lenses) to reconcile CMB+BAO and local H₀ determinations. The framework introduces no new constants beyond {ℏ, c, G, kᴮ} and is fully falsifiable with near-future data. Author: Adrian Zander (Quantum Fruits)Physics: Phase-transition cosmology inspired by der8auer's two-phase cooling""" import numpy as npimport matplotlib.pyplot as pltfrom dataclasses import dataclassfrom enum import Enum # ============================================================================# CONSTANTS & PARAMETERS# ============================================================================ class Phase(Enum): """Universe phase state""" EXPANSION = 1 # Gas phase: High entropy → dV/dt > 0 DEFLATION = -1 # Liquid phase: Cooling → dV/dt < 0 @dataclassclass CosmologicalConstants: """Physical constants in natural units (ℏ=c=k_B=1)""" sigma_P: float = 1.616e-35 # Planck length (m) T_boiling: float = 61.0 # Boiling point of universe (K) - TUNABLE H_0_mean: float = 70.0 # Mean Hubble constant (km/s/Mpc) H_expansion: float = 73.0 # Expansion phase measurement H_deflation: float = 67.0 # Deflation phase measurement # ============================================================================# CORE UNIVERSE CLASS# ============================================================================ class TwoPhaseUniverse: """ Simulates universe evolution with thermal spacetime feedback. Phases: - EXPANSION: High entropy → accelerated expansion (dA/dt > 0) - DEFLATION: Entropy loss → contraction (dA/dt < 0) - Cycle repeats when rethermalization occurs """ def __init__(self, constants: CosmologicalConstants = None): self.const = constants or CosmologicalConstants() # State variables self.time = 0.0 self.scale_factor = 1.0 # a(t), universe size self.temperature = self.const.T_boiling * 0.8 # Start cool self.entropy = 400.0 # bits (initial) self.hubble_parameter = 0.0 # H(t) self.phase = Phase.EXPANSION # History tracking self.history = { 'time': [], 'scale_factor': [], 'temperature': [], 'entropy': [], 'hubble': [], 'phase': [] } def compute_hubble_parameter(self) -> float: """ H(t) = d(ln a)/dt = (1/a) * da/dt Modulated by temperature relative to boiling point. At T=T_boil: expansion maximal At T→0: contraction kicks in """ temp_ratio = self.temperature / self.const.T_boiling # Base oscillation with temperature coupling if self.phase == Phase.EXPANSION: H = self.const.H_expansion * temp_ratio else: # DEFLATION H = -self.const.H_deflation * (1 - temp_ratio) return H def compute_entropy_rate(self) -> float: """ dS/dt = entropy production/dissipation rate - Expansion phase: dS/dt > 0 (entropy grows) - Deflation phase: dS/dt < 0 (entropy decreases) - Hawking radiation provides continuous rethermalization """ if self.phase == Phase.EXPANSION: # Entropy increases during expansion (2nd law) dS_dt = 0.5 * np.sin(self.time / 10.0) + 0.3 else: # Entropy dissipates during deflation dS_dt = -0.2 * np.cos(self.time / 10.0) return dS_dt def phase_transition_check(self) -> None: """ Determine if universe should switch phases. Criteria: - EXPANSION → DEFLATION: T drops below critical, entropy peaks - DEFLATION → EXPANSION: T regenerated by rethermalization """ if self.phase == Phase.EXPANSION: # Switch to deflation if cooling sufficient if self.temperature < self.const.T_boiling * 0.3: self.phase = Phase.DEFLATION print(f"[t={self.time:.2f}] Phase transition: EXPANSION → DEFLATION") else: # Switch back to expansion if rethermalized if self.temperature > self.const.T_boiling * 0.7: self.phase = Phase.EXPANSION print(f"[t={self.time:.2f}] Phase transition: DEFLATION → EXPANSION") def step(self, dt: float = 0.01) -> None: """ Integrate universe state by one timestep. """ # 1. Compute current Hubble parameter self.hubble_parameter = self.compute_hubble_parameter() # 2. Update scale factor: da/dt = H * a da_dt = self.hubble_parameter * self.scale_factor self.scale_factor += da_dt * dt # 3. Temperature evolution: simplified cooling curve if self.phase == Phase.EXPANSION: # Active cooling (radiator in expansion phase) dT_dt = -0.5 * (self.temperature - 20.0) else: # Rethermalization from dark energy/Hawking radiation dT_dt = 0.3 * (self.const.T_boiling - self.temperature) self.temperature += dT_dt * dt self.temperature = np.clip(self.temperature, 10.0, self.const.T_boiling) # 4. Entropy evolution dS_dt = self.compute_entropy_rate() self.entropy += dS_dt * dt # 5. Check for phase transitions self.phase_transition_check() # 6. Update time and record history self.time += dt self._record_state() def _record_state(self) -> None: """Save current state to history for plotting""" self.history['time'].append(self.time) self.history['scale_factor'].append(self.scale_factor) self.history['temperature'].append(self.temperature) self.history['entropy'].append(self.entropy) self.history['hubble'].append(self.hubble_parameter) self.history['phase'].append(self.phase.value) def simulate(self, duration: float = 100.0, dt: float = 0.01) -> None: """Run full simulation for given duration""" steps = int(duration / dt) for _ in range(steps): self.step(dt) def compute_hubble_mean(self) -> float: """Compute ensemble-averaged Hubble constant (resolution to Hubble Tension)""" return np.mean(np.abs(self.history['hubble'])) def plot_results(self) -> None: """Visualize simulation results""" fig, axes = plt.subplots(2, 2, figsize=(14, 10)) fig.suptitle('Two-Phase Universe Evolution (TCP Model)', fontsize=16, fontweight='bold') time = np.array(self.history['time']) # Plot 1: Scale factor (cosmic expansion) ax = axes[0, 0] ax.plot(time, self.history['scale_factor'], 'b-', linewidth=2) ax.set_ylabel('Scale Factor a(t)', fontsize=11) ax.set_title('Expansion-Deflation Cycles', fontweight='bold') ax.grid(True, alpha=0.3) # Plot 2: Temperature (cooling/rethermalization) ax = axes[0, 1] ax.plot(time, self.history['temperature'], 'r-', linewidth=2) ax.axhline(y=self.const.T_boiling, color='orange', linestyle='--', label='Boiling point (61K)') ax.set_ylabel('Temperature (K)', fontsize=11) ax.set_title('Thermal Evolution', fontweight='bold') ax.legend() ax.grid(True, alpha=0.3) # Plot 3: Hubble parameter (expansion rate) ax = axes[1, 0] ax.plot(time, self.history['hubble'], 'g-', linewidth=2, label='H(t)') ax.axhline(y=self.const.H_0_mean, color='purple', linestyle='--', linewidth=2, label=f'⟨H⟩ = {self.const.H_0_mean} km/s/Mpc') ax.axhline(y=self.const.H_expansion, color='red', linestyle=':', alpha=0.7, label=f'Expansion: {self.const.H_expansion}') ax.axhline(y=-self.const.H_deflation, color='blue', linestyle=':', alpha=0.7, label=f'Deflation: {self.const.H_deflation}') ax.set_ylabel('H(t) [km/s/Mpc]', fontsize=11) ax.set_xlabel('Time (a.u.)', fontsize=11) ax.set_title('Hubble Parameter Oscillation\n(Tension = phase difference)', fontweight='bold') ax.legend(fontsize=9) ax.grid(True, alpha=0.3) # Plot 4: Entropy (information content) ax = axes[1, 1] ax.plot(time, self.history['entropy'], 'm-', linewidth=2) ax.set_ylabel('Entropy S (bits)', fontsize=11) ax.set_xlabel('Time (a.u.)', fontsize=11) ax.set_title('Information Content Evolution', fontweight='bold') ax.grid(True, alpha=0.3) plt.tight_layout() plt.show() # ============================================================================# MAIN EXECUTION# ============================================================================ if __name__ == "__main__": print("=" * 70) print("TWO-PHASE COSMOLOGICAL MODEL (TCP)") print("Inspired by: Two-phase PC cooling (der8auer Aqua Exhalare)") print("=" * 70) print() # Initialize universe const = CosmologicalConstants() universe = TwoPhaseUniverse(const) # Run simulation print("[*] Running 100 cosmic cycles...") universe.simulate(duration=100.0, dt=0.05) # Results print() print("[✓] Simulation complete!") print(f" Final scale factor: a(t) = {universe.scale_factor:.4f}") print(f" Final temperature: T = {universe.temperature:.2f} K") print(f" Final entropy: S = {universe.entropy:.1f} bits") print() print(f"[*] Hubble Tension Resolution:") print(f" Mean ⟨H⟩ = {universe.com