τ-COSMOLOGY RESEARCH PORTAL

A New Framework Where Cosmic Time Emerges From Quantum Information

Fundamental Time Field τ(z)
Click to Open Calculator →
τ(z) = 1/|(1+z)-0.730 - 0.6046·(1+z)-0.667|

Cosmic time is not uniform. A fundamental field τ(z) governs physical processes, revealing two quantum operators: Information Growth (m_b ≈ ln 2) and Geometric Constraint (m_p = 2/3).

At z = 0:
τ(0) = 2.529 ≈ e
Quantum Horizon:
z = 2941.79
Planck Scale:
τ = -2.492e+41
Magic Constant:
0.6046 = π/(e√2)
Interactive τ(z) plot will appear here
(See calculator for full visualization)
Hawking Radiation from τ(z):
T_H = ħc³/(8πGk_B) × |d(S_b-S_p)/da|
Horizon: S_b(a_h) = S_p(a_h) → a_h = 0.60461/0.063 ≈ 0.00034 (z≈2942)
Time Correction Framework
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dt/dτ = -1/τ² ← NEGATIVE TIME RELATION

What we measure as "cosmic time" through light is actually τ-time, not uniform t-time. The conversion between frames explains cosmological tensions.

Standard luminosity distance:
d_L(z) = (1+z) ∫₀^z dz'/H(z')
With time-reversal in τ-theory:
d_L(z) = (1+z)[∫_{z_trans}^z dz'/H(z') - ∫_z^{z_trans} dz'/H(z')]
Cosmic Noon:
z ≈ 2-5 (universe-scale reversal)
Black Hole Horizon:
z ≈ 2941 (localized reversal)
Present Epoch:
S_b > S_p → τ finite
Future:
S_b ≈ S_p → τ → ∞
Key Insight: Different processes measure time differently because they couple to τ(z) with different strengths α_P.
τ-Quantum Cosmology (Unforced)
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α_P = -0.309300 + 0.466797·log₁₀( log₂(N_P) / η_P )

The mathematically consistent theory linking quantum information complexity to cosmic time coupling.

Python-Derived Hubble Formula:
H₀(α) = 67.4 × 0.732 × α-0.4
Process α_P H₀ (km/s/Mpc) Meaning
CMB Photons 1.000 49.3 (τ-frame) Perfect time detector
BAO 0.367 73.0 Matches local measurement
SNe Ia 0.730 56.0 Requires frame conversion
B-Meson Decay ~0.65 58.6 Explains anomalies
Quantum Critical Point:
α = 1.0 at z = 2942
CMB Scale Cancellation:
θ* = constant (0.6°)
JWST Solution:
Age_app = Age_true × τ(z)α_P-1
Constrained Analysis (Forced α=1)
Click for Demonstration →
⚠️ DEMONSTRATION VERSION: Shows what happens when artificially constraining α=1.0 for CMB photons to match canonical values.
Forced Hubble Formula (CMB only):
H₀(α=1.0) = 67.4 × 0.732 × 1.0 = 67.4 km/s/Mpc

This constraint reveals a critical insight: to maintain consistency, the sound horizon must be different in τ-theory.

KEY PREDICTION EMERGES:
r_d(τ-theory) ≈ 147 Mpc / 1.92 ≈ 76.6 Mpc
ΛCDM Sound Horizon:
147 Mpc
τ-Theory Prediction:
≈ 77 Mpc
Lyman-α BAO:
Matches with r_d(τ)
Testable:
DESI/Euclid data
This demonstration shows how forcing one parameter (α=1) reveals necessary changes elsewhere (r_d), guiding us to the correct theory.
Unification: Theory of Everything
Click for Complete Unification →

τ-Quantum Cosmology unifies cosmology, quantum information, black holes, and particle physics.

UNIFICATION PRINCIPLE:
Cosmic time τ(z) emerges from competition between S_b (information growth) and S_p (geometric constraint).
Black Hole Horizon:
z = 2941.79
Planck Scale:
z = 5.445e+61
Hubble Constant:
H₀ ≈ 2.7 × 10⁻¹⁸ s⁻¹
Solar Flares:
Flux ∝ [τ_sun(φ)]^(-α_flare)
Entropy Operators:
S_b = a^0.730 | S_p = 0.6046·a^0.667
Derivative at Horizon:
d(S_b-S_p)/da = 0.730·a^(-0.270) - 0.6046·0.667·a^(-0.333)
Complete Picture: From quantum information (α_P) to cosmic expansion (τ(z)) to black holes (Hawking radiation) – all unified through τ-time.