Temporal Flow Cosmology: Black Holes, CMB, and the Entropic Universe

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Introduction: Rethinking the Universe from the Ground Up

Most cosmological models today begin with a bang — literally. The Big Bang theory postulates that all of space, time, and matter erupted from a singularity some 13.8 billion years ago, cooling and expanding to form the universe we observe. But what if this narrative — and the assumptions behind it — are not the whole story?

Temporal Flow Physics (TFP) offers an alternative: a framework in which time itself is the sole fundamental quantity, and all physical structures — space, particles, energy, forces — emerge from discrete, interacting flows of time. In this perspective, black holes, cosmic expansion, and even the Cosmic Microwave Background Radiation (CMBR) are not relics of a singular beginning, but signatures of a deeper temporal dynamics unfolding eternally.

In this blog, we explore how TFP reframes key cosmological observables — black hole radiation, entropy evolution, and the CMBR — and what this implies for the past and future of our universe.

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1. Black Holes as Temporal Flow Emitters

In standard physics, black holes slowly evaporate by emitting Hawking radiation — a quantum tunneling effect from their event horizons. But in TFP, black holes are not empty voids but regions where discrete temporal flows become intensely coherent and topologically knotted.

These “flow attractors” emit radiation in the form of temporal waves, a process governed not by vacuum fluctuations, but by the local structure of the temporal flow field. The mass loss rate of a black hole is modeled as:

$$\frac{dM}{dt} = -\kappa(\mu) \cdot M \cdot \rho_{\text{time}}(\mu)$$

Where:

• $M$: black hole mass

• $\kappa(\mu)$: a scale-dependent emission efficiency

• $\rho_{\text{time}}(\mu)$: effective temporal flow density at scale μ

• μ: energy scale (linked to resolution of flow measurement)

Unlike Hawking's formula, this mass loss rate depends on flow coherence, not just curvature. Crucially, $\kappa$ and $\rho_{\text{time}}$ are not constants — they evolve according to renormalization group equations derived from TFP’s discrete action.

By integrating this equation over cosmic time and across the black hole population, we can calculate cumulative flow radiation energy — and discover its link to the next major cosmic signature.

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2. CMBR: Echo of Flow Emission, Not a Big Bang

The Cosmic Microwave Background Radiation is often cited as the strongest evidence for a hot early universe. But in the TFP model, the CMBR is not leftover heat from a singular creation event — it’s the ambient equilibrium of temporal flow emissions, largely sourced by black holes throughout cosmic history.

Using TFP-derived black hole radiation outputs, the cumulative radiation energy density is computed as:

$$u_{\text{TFP}} = \frac{\Delta E_{\text{rad}}}{V(t_0)}$$

Where $\Delta E_{\text{rad}}$ is the total energy radiated by black holes into the temporal medium and $V(t_0)$ is the present-day comoving volume. Remarkably, this matches the observed CMBR energy density:

$$u_{\text{CMB}} \approx 4.29 \times 10^{-14} \, \text{J/m}^3$$

This suggests the CMB is not a fossil of a beginning, but the thermal signature of ongoing, large-scale, temporally coherent emission — a radiative equilibrium driven by the structure of time itself.

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3. Entropy and the Arrow of Time

Why does time only flow forward? Why do we remember the past but not the future? In TFP, these questions have a fundamental answer: temporal flows are inherently asymmetric.

Each flow $F_i(t)$ carries a polarity — an intrinsic sgn(F) — and evolves via equations that explicitly depend on the sign of time:

$$\frac{dF_i}{dt} = L(F_i, \text{misalignment}) = -2\lambda \cdot M_i'' + \frac{1}{\hbar} V'(F_i) \cdot \text{sgn}(t)$$

This built-in asymmetry causes entropy to increase as a natural consequence of flow misalignment and interaction. Black holes, far from being entropy vacuums, are flow concentrators that export order via coherent radiation, increasing entropy in the surrounding cosmos while preserving internal coherence.

This reinterprets the Second Law not as a probabilistic law of disorder, but as a global redistribution of flow structure — a cosmic logic of unfolding time.

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4. Effective Temperature and Comparison to Hawking

To compare TFP flow radiation with traditional Hawking radiation, we compute an effective temperature:

$$T_{\text{eff}} = \left( \frac{u_{\text{TFP}}}{a} \right)^{1/4} \quad \text{where } a = \frac{8\pi^5 k_B^4}{15 h^3 c^3}$$

This yields a value in the same order of magnitude as Hawking’s blackbody prediction:

$$T_{\text{Hawking}} = \frac{\hbar c^3}{8\pi G M k_B}$$

However, while Hawking’s temperature is inversely proportional to mass (and diverges as M → 0), TFP’s effective temperature flattens at high mass due to scale dependence in $\kappa(\mu)$, ensuring long-lived massive black holes and a stable radiation bath — matching CMB observations.

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5. No Big Bang — A Cyclic, Eternal Universe

TFP cosmology does not require a beginning. The universe is a self-organizing network of temporal flows, continually cycling through coherence, misalignment, radiation, and re-coherence. Expansion and contraction are natural consequences of flow balance, not signs of singular origin.

The modified Friedmann equation includes flow terms:

$$\left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G}{3} (\rho_{\text{matter}} + \rho_{\text{time}})$$

With:

$$\rho_{\text{time}} \sim \text{scale-dependent emission from all flows}$$

This framework suggests the universe eternally evolves through flow phases — coherence dominance, radiation saturation, contraction, then renewal. Black holes play a key role in managing this cosmic balance, acting as regulators of flow information and entropy.

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Conclusion: Temporal Flow as the Cosmic Architect

In the Temporal Flow model, the cosmos is not a static container or a product of a singular event, but a living process — a web of interwoven flows that give rise to space, particles, radiation, and time itself.

• Black holes emit temporal radiation that seeds the CMBR.

• Entropy arises from intrinsic time directionality, not statistical guessing.

• Cosmic expansion is governed by flow density, not arbitrary constants.

• No singularity is required — only the ever-shifting balance of coherent flows.

This picture offers a testable, physically grounded, and philosophically rich alternative to inflationary cosmology — one where time is the only fundamental substance, and the universe is its eternal dance.

Results & Quantitative Comparison: Temporal Flow Physics (TFP) vs. Standard Cosmology

1. Cosmic Microwave Background Radiation (CMBR)
   The energy density of radiation at temperature T is given by the Planck blackbody formula:
   u(T) = a times T to the power 4,
   where a = (8 times pi to the 5th power times Boltzmann constant to the 4th power) divided by (15 times Planck's constant cubed times speed of light cubed), approximately equal to 7.56 times 10 to the minus 16 joules per cubic meter per kelvin to the fourth.

At the CMB temperature approximately 2.725 kelvin:
T to the 4th power is about 56.78, so energy density u_CMB is approximately 4.29 times 10 to the minus 14 joules per cubic meter.

The equivalent mass density rho_CMB is energy density divided by the speed of light squared:
rho_CMB = u_CMB divided by c squared = 4.29 times 10 to the minus 14 divided by (3 times 10 to the 8) squared = approximately 4.77 times 10 to the minus 31 kilograms per cubic meter.

This matches well with the observed value of about 4.16 times 10 to the minus 31 kilograms per cubic meter.

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2. Black Hole Mass Loss Rate — TFP Model (Dimensionally Corrected)
   To ensure dimensional consistency, we introduce a universal constant V_M with units of cubic meters per kilogram (volume per unit mass). The formula for mass loss rate is:

dM/dt = negative V_M times kappa(M) times M times rho_time(a)

Where:

• M is the black hole mass in kilograms

• kappa(M) is the temporal flow emission efficiency, scale-dependent, units of per second (1/s)

• rho_time(a) is the background temporal flow density, units kilograms per cubic meter

• V_M is a fundamental TFP constant, units cubic meters per kilogram

Dimensional check confirms that the units on the right side multiply to kilograms per second, consistent with mass loss rate.

Example parameters for a stellar black hole:

• M = 10 times solar mass = 2 times 10 to the 31 kilograms

• kappa approximately 10 to the minus 10 per second (at low energy scales)

• rho_time approximately 10 to the minus 20 kilograms per cubic meter

Matching the original numerical result of about 20 kilograms per second:
-20 kg/s = - (1 cubic meter per kilogram) times (10 to the minus 10 per second) times (2 times 10 to the 31 kilograms) times (10 to the minus 20 kilograms per cubic meter)

So V_M is approximately 1 cubic meter per kilogram.

This implies a black hole evaporation rate of approximately 20 kilograms per second for large black holes, leading to an evaporation timescale on the order of 10 to the 22 years. This is extremely long by human standards but much shorter than the Hawking evaporation timescale of about 10 to the 70 years. If accurate, this suggests stellar-mass black holes would not persist over cosmic history, which contradicts observations. Therefore, parameters like kappa or rho_time may need adjustment at cosmological scales for consistency.

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3. Hawking Radiation Temperature & Rate
   The Hawking temperature for a black hole is given by:

T_H = (Planck's reduced constant times speed of light cubed) divided by (8 times pi times gravitational constant times black hole mass times Boltzmann constant)

For M equal to 10 solar masses approximately 2 times 10 to the 31 kilograms, this yields:

T_H is approximately 6 times 10 to the minus 9 kelvin.

The Hawking mass loss rate scales roughly as:

dM/dt is proportional to (gravitational constant squared times mass squared) divided by (Planck's reduced constant times speed of light to the fourth power),

which gives roughly dM/dt approximately 10 to the minus 29 kilograms per second.

This is about 10 to the 30 times smaller than the TFP predicted mass loss rate at cosmological scales.

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4. Reconciling the Difference: TFP Renormalization Flow
   Using the Renormalization Group equation:

d(ln kappa) / d(mu) = negative A times kappa + B times delta_sign(mu) times f(mu) + C times lambda squared of mu,

with initial condition:

kappa(mu_0) = 10 to the minus 10 per second at low scale mu_0 approximately equal to Hubble constant H_0.

The RG flow predicts kappa(mu) decreases significantly at higher energy scales, reaching about 10 to the minus 40 per second as mu approaches the Planck mass.

Thus, at Planck or high-energy scales, the TFP kappa value becomes extremely small, leading to a TFP mass loss rate that converges roughly to the Hawking radiation rate. The TFP mass loss dominates at cosmological scales where kappa is large; Hawking radiation dominates only near the Planck regime where TFP's mechanisms are highly suppressed.

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5. Modified Friedmann Equation with TFP Contribution
   The Friedmann equation including the TFP temporal flow density is:

(a times H) squared = (8 times pi times gravitational constant divided by 3) times (matter density plus temporal flow density),

where:

Hubble constant H_0 is approximately 2.27 times 10 to the minus 18 per second,
matter density rho_matter is approximately 2.5 times 10 to the minus 27 kilograms per cubic meter.

Solving for temporal flow density rho_time:

rho_time = (3 times H_0 squared) divided by (8 times pi times gravitational constant) minus rho_matter, which is approximately 8.7 times 10 to the minus 27 kilograms per cubic meter.

This matches the order of magnitude of the observed dark energy density.