Thermal Vacuum Cosmology Explains Hubble Tension

This paper proposes that replacing the cosmological constant with the thermal energy of an expanding vacuum, characterized by the Gibbons-Hawking temperature, resolves the Hubble tension within a modified inflationary $\Lambda$CDM framework.

The Gist

Imagine the Universe as a giant, expanding balloon. For decades, scientists have been trying to measure exactly how fast this balloon is inflating. This speed is called the Hubble Constant ($H_0$).

Here is the problem: When we measure the speed using "local" tools (like looking at nearby exploding stars), we get one number (about 74). But when we look at the "baby photos" of the Universe (the Cosmic Microwave Background, or CMB) and use our standard rules of physics to predict how fast it should be expanding today, we get a different, slower number (about 68).

This disagreement is called the "Hubble Tension." It's like two mechanics looking at the same car; one says it's doing 70 mph, and the other says 60 mph. They can't both be right, so something is wrong with either the car or the rules they are using to measure it.

The New Theory: The "Thermal Vacuum"

Robert Alicki, the author of this paper, suggests that our standard rules (the $\Lambda$CDM model) are slightly off. He proposes a new model called the Thermal Vacuum Model (TVM).

To understand this, let's use an analogy:

The Standard Model (The Old Way):
Imagine the Universe is a room with a heater (Dark Energy) that is turned on at a fixed, unchangeable setting. It pushes the walls out at a steady, constant rate. This is the "Cosmological Constant." It's simple, but it doesn't fit the data perfectly.

The Thermal Vacuum Model (The New Way):
Alicki suggests the "heater" isn't a fixed setting. Instead, the empty space itself (the vacuum) acts like a gas of particles that has a temperature.

• As the Universe expands, this "vacuum gas" changes its temperature.
• Think of it like a rubber band. When you stretch a rubber band quickly, it gets hot; when you let it relax, it cools down. In this model, the energy pushing the Universe apart comes from the "heat" of the expanding vacuum itself (specifically, a temperature called the Gibbons-Hawking temperature).
• Crucially, this "heat" changes over time. It's not a fixed constant; it evolves as the Universe grows.

How This Solves the Mystery

The paper argues that the "Hubble Tension" happens because we are using the wrong ruler to measure the past.

1. The Local View (Nearby): When we look at nearby stars (low redshift), the Universe is behaving exactly as the new model predicts. The "running speed" is fast, around 74.
2. The Distant View (Far Away): When we look at the ancient Universe (high redshift), we are using the old rules (the fixed heater model) to interpret the data. Because the old rules assume the "heater" was always the same, they calculate a slower speed, around 68.

The "Running" Speedometer Analogy:
Imagine you are driving a car that is accelerating, but your speedometer is broken and stuck on a "smoothed average" setting.

• If you look at the speed right now, you see the true, fast speed (74).
• If you try to calculate your speed from the past using a broken speedometer that assumes a constant engine, you get a lower, averaged number (68).

Alicki shows that if you use his new "Thermal Vacuum" rules, the speed of the Universe isn't a single fixed number for all time. Instead, it's a "Running Hubble Constant."

• In the distant past (high redshift), the "average" speed calculated by old methods looks like 68.
• In the recent past (low redshift), the speed is actually 74.

The Conclusion

The paper claims that the "Hubble Tension" isn't a mystery or a measurement error. It is simply a translation error.

We have been trying to translate the behavior of the Universe using an old dictionary (the standard model with a fixed constant). Alicki says, "No, the Universe speaks a different language (Thermal Vacuum)." When you translate the data using the new dictionary, the two measurements (74 and 68) stop fighting each other. They are just looking at the same "Running Speed" from different angles.

In short: The Universe isn't expanding at a single, fixed rate. The "push" from empty space changes as the Universe gets bigger and cooler. Once we accept this changing nature, the conflict between local and distant measurements disappears.

Technical Summary

1. The Problem: The Hubble Tension

The paper addresses the "Hubble tension," a significant discrepancy in modern cosmology regarding the value of the Hubble constant ($H_0$), which characterizes the current expansion rate of the Universe.

• The Conflict: Observations of the local (late) Universe (e.g., Type Ia supernovae) yield a value of $H_0 \approx 74$ km s$^{-1}$ Mpc$^{-1}$. In contrast, data from the early Universe (Cosmic Microwave Background, CMB) analyzed under the standard flat $\Lambda$CDM model yield a lower value of $H_0 \approx 68$ km s$^{-1}$ Mpc$^{-1}$.
• Significance: This $\sim 10\%$ discrepancy far exceeds the $\sim 1\%$ precision of modern observational data, suggesting a potential flaw in the standard cosmological model ($\Lambda$CDM) rather than measurement error.

2. Methodology: The Thermal Vacuum Model (TVM)

The author proposes replacing the standard cosmological constant ($\Lambda$) in the Friedmann equations with thermal energy of the expanding vacuum. This approach is based on the Thermal Vacuum Model (TVM).

Core Theoretical Assumptions

• Vacuum as Thermal Equilibrium: The expanding vacuum is treated as a thermal equilibrium state of all degrees of freedom (visible and dark matter).
• Gibbons-Hawking Temperature: The vacuum energy density is characterized by a time-dependent temperature:
  $$T_{dS}(t) = \frac{\hbar H(t)}{2\pi k_B}$$
• Energy Decomposition: The total energy density $\rho$ is decomposed into matter ($\rho_m$) and thermal vacuum "dark energy" ($\rho_{dS}$):
  $$\rho = \rho_m + \rho_{dS}$$
  Unlike the constant $\Lambda$ in $\Lambda$CDM, $\rho_{dS}$ varies with time and depends on the Hubble parameter $H(t)$.
• Late Universe Approximation: For the late Universe, the vacuum is modeled as a cold gas of massive elementary particles. The resulting dark energy density is derived as:
  $$\rho_{dS}(t) = \frac{3c^2}{8\pi G} [H_\infty]^{1/2} [H(t)]^{3/2}$$
  Where $H_\infty$ is an "ultimate Hubble constant" dependent on the mass spectrum of particles.

Mathematical Formulation

The paper derives a redshift-dependent Hubble parameter for the TVM ($H_{TV}(z)$) and compares it to the standard $\Lambda$CDM parameter ($H_\Lambda(z)$):

• TVM Formula:
  $$H_{TV}(z) = H_0 \left[ (1 - \Omega_{TV})(1+z)^{3/4} + \Omega_{TV} \right]^2$$
  (Note the power of $3/4$ for the matter term, differing from the standard $3$).
• $\Lambda$CDM Formula:
  $$H_\Lambda(z) = H_0 \sqrt{(1 - \Omega_\Lambda)(1+z)^3 + \Omega_\Lambda}$$

To facilitate comparison, the author introduces a dimensionless function $f(z) = \frac{H(z)}{H_0(1+z)}$ to analyze the onset of accelerated expansion.

3. Key Contributions and Analysis

The paper's primary contribution is demonstrating that the Hubble tension is an artifact of applying the wrong model ($\Lambda$CDM) to data generated by the true physics (TVM).

• Local Universe Consistency: For low redshifts ($z \ll 1$), both models converge to a linear Hubble law with a quadratic correction. Current observational accuracy cannot distinguish between them locally, yielding $H_0 \approx 74$.
• The "Running" Hubble Constant: The author argues that if the TVM is the correct physical description, but researchers analyze the data assuming the $\Lambda$CDM model, they derive a redshift-dependent "running" Hubble constant, denoted as $\hat{H}_0(z)$.
• Numerical Simulation: By equating the luminosity distance integrals of the TVM (with $H_0=74$ and $\Omega_{TV}=0.42$) against the $\Lambda$CDM integral form, the author calculates $\hat{H}_0(z)$.

4. Results

The numerical analysis yields the following critical findings:

1. Reproduction of Tension: The calculated running Hubble constant $\hat{H}_0(z)$ behaves exactly as observed in the tension:
   • At low redshift ($z \ll 1$): $\hat{H}_0(z) \approx 74$ km s$^{-1}$ Mpc$^{-1}$ (matching local supernova data).
   • At intermediate/high redshift ($0.5 < z < 2.5$): $\hat{H}_0(z)$ drops to $\approx 68$ km s$^{-1}$ Mpc$^{-1}$ (matching CMB-based inferences).
2. Resolution Mechanism: The tension is not a contradiction in data but a consequence of model mismatch. The "true" Hubble constant is $H_0 \approx 74$ (as per TVM). The lower value ($\approx 68$) is an effective average obtained when forcing the $\Lambda$CDM functional form onto data that actually follows the TVM evolution.
3. Acceleration Onset: Both models can be tuned to reproduce the observed redshift of the deceleration-acceleration transition ($z_{ac} \approx 0.7$), but they achieve this via different evolutionary paths for the expansion rate.

5. Significance

• Paradigm Shift: The paper suggests that the cosmological constant $\Lambda$ may not be a fundamental constant but rather a manifestation of the thermal energy of the expanding vacuum (Gibbons-Hawking radiation).
• Elimination of New Physics: It offers a solution to the Hubble tension without invoking exotic new physics (like early dark energy or modified gravity) that typically requires ad-hoc adjustments. Instead, it relies on a thermodynamic interpretation of the vacuum within standard General Relativity.
• Predictive Power: The model predicts that the "Hubble tension" is a systematic bias introduced by the $\Lambda$CDM assumption. If future observations confirm the specific redshift evolution of the Hubble parameter predicted by the TVM (specifically the $(1+z)^{3/4}$ scaling vs $(1+z)^3$), it would validate the Thermal Vacuum Model as the correct description of cosmic evolution.

In conclusion, Alicki argues that the Hubble tension is resolved by recognizing that the Universe's expansion is driven by thermal vacuum energy rather than a static cosmological constant, thereby unifying the local and early Universe measurements under a single, consistent $H_0 \approx 74$.