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Cosmic adiabatic photon creation: Temperature law and blackbody spectrum

This paper demonstrates that gravitationally induced photon production in an expanding universe leads to a consistent extended temperature law and preserves the blackbody spectrum across three independent theoretical frameworks, offering a potential resolution to the Hubble tension and a new test for the standard cosmological model.

Original authors: J. A. S. Lima, S. R. G. Trevisani, R. C. Santos

Published 2026-06-17

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CC0 1.0

Original authors: J. A. S. Lima, S. R. G. Trevisani, R. C. Santos

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Cosmic Thermometer That Might Be Broken

Imagine the universe as a giant, expanding balloon. As the balloon inflates, the air inside gets cooler. In standard physics, we have a very precise rule (a "thermometer") that tells us exactly how much cooler the universe gets as it expands. This rule is called the Temperature-Redshift Relation. It says that if you look at light from the early universe, its temperature is directly tied to how much the universe has stretched since then.

For decades, scientists have trusted this rule completely. It's the foundation of our current understanding of the universe (the $\Lambda$ CDM model). However, there is a problem: measurements of how fast the universe is expanding today (the Hubble constant) don't match up with predictions made using this thermometer. This is known as the "Hubble Tension."

This paper asks a bold question: What if our thermometer is slightly off because we forgot to count new photons being created?

The Core Idea: "Adiabatic" Photon Creation

The authors propose that as the universe expands, gravity might be gently "spawning" new photons (particles of light) out of the fabric of space-time itself.

To understand their specific idea, let's use an analogy:

The Standard View: Imagine a pot of soup cooling down. As it cools, the heat spreads out over a larger volume, but the number of soup molecules stays the same. The temperature drops in a predictable way.
The "Adiabatic" View in this Paper: Imagine the soup is cooling, but at the same time, a magical faucet is dripping more hot soup into the pot.
- Usually, adding more soup would make the pot hotter or mess up the temperature balance.
- However, the authors describe a special, "adiabatic" process where the new soup is added in such a perfect way that the ratio of heat to soup molecules stays exactly the same.
- The total amount of "disorder" (entropy) in the pot increases because there is more soup, but the "disorder per spoonful" stays constant.

In physics terms, this means the universe is creating photons, but it's doing so without ruining the perfect "blackbody" shape of the light spectrum (the specific pattern of colors/energies we see in the Cosmic Microwave Background).

How They Proved It (The Three Paths)

The authors didn't just guess; they used three different mathematical "roads" to reach the same destination, proving their new rule is robust:

The "Heuristic" Road (Common Sense): They started with basic logic. If the universe creates photons, the number of photons grows. They used simple math to show that if the temperature drops in a specific, slightly modified way, everything balances out.
The "Macroscopic" Road (Thermodynamics): They looked at the universe as a giant fluid. They applied the laws of thermodynamics (rules about heat and energy) to a fluid that is gaining new particles. They calculated the "pressure" created by this new matter and found it leads to the same modified temperature rule.
The "Kinetic" Road (Particle Physics): They looked at the individual photons using a complex equation called the Boltzmann equation. They added a new term to the equation representing "gravity creating particles." When they solved it, they found that the light still looks like a perfect blackbody spectrum, provided the temperature follows their new rule.

The Result: A New Rule for the Universe

The paper concludes that if photons are being created by gravity in this specific "adiabatic" way, the temperature of the universe doesn't drop quite as fast as the standard model predicts.

Standard Rule: Temperature drops strictly based on how much the universe stretched ( $T \propto 1+z$ ).
New Rule: Temperature drops based on stretching plus the rate of new photon creation.

This new rule depends on a parameter called $\alpha$ (the creation rate). If $\alpha$ is zero, we get the old standard rule. If $\alpha$ is positive, the temperature evolution changes.

Why This Matters (According to the Paper)

The authors suggest this new rule could help fix the Hubble Tension.

Currently, local measurements say the universe is expanding faster than the Cosmic Microwave Background (CMB) data suggests.
The paper argues that if we use this new "photon-creating" thermometer, the CMB data might actually be consistent with a faster expansion rate, potentially resolving the conflict without needing to invent entirely new physics.

What They Did NOT Claim

It is important to stick to what the paper actually says:

They did not claim that this definitely solves the Hubble Tension; they only suggest it offers a "crucial test" and a "new route" to investigate it.
They did not claim that the blackbody spectrum is destroyed. In fact, they proved the opposite: the spectrum remains perfect even with this creation process.
They did not provide a specific mechanism for how gravity creates the photons (like a specific quantum field theory calculation), but rather showed that if this process happens, the math works out this way.

Summary

Think of the universe as a balloon being blown up. The standard view says the air inside just gets thinner and cooler. This paper suggests that maybe the balloon is also leaking in a little bit of fresh, warm air from the rubber itself. If this is true, the way the air cools down changes slightly. This small change might be the key to fixing a major puzzle in how fast the universe is expanding today.

Problem Statement
The standard cosmological model ( $\Lambda$ CDM) relies heavily on the temperature-redshift relation (TRR), often called the Friedmann law, $T = T_0(1+z)$ . This relation assumes that the Cosmic Microwave Background (CMB) evolves adiabatically with conserved entropy in a comoving volume, preserving a perfect Planckian blackbody spectrum. However, the model currently faces a significant observational challenge: the "Hubble tension," where local measurements of the Hubble constant ( $H_0$ ) using Supernovae Ia (SHOES collaboration) yield values around $74$ km/s/Mpc, while Planck CMB data suggests a lower value near $68$ km/s/Mpc ( $5.4\sigma$ tension). While some attempts to resolve this involve systematic uncertainties in local measurements, this paper investigates a less conservative theoretical avenue: questioning the generality of the standard TRR by considering gravitationally induced photon production. The central problem is whether the blackbody spectrum and the standard temperature law can be preserved if the number of photons in the expanding universe is not conserved.

Methodology
The authors propose a generalized cosmic thermometer by analyzing "adiabatic" photon creation through three independent theoretical frameworks, all yielding the same result:

Heuristic Approach: The authors assume standard equilibrium relations for energy density ( $\rho \propto T^4$ ) and number density ( $n \propto T^3$ ) for a photon creation process. By noting that the average number of photons in a comoving volume ( $N = na^3$ ) is not conserved, they derive a modified relation where $T a N^{-1/3} = \text{const}$ .
Macroscopic Irreversible Thermodynamics: Utilizing a manifestly covariant approach based on Prigogine et al., the authors characterize the radiation fluid with an energy-momentum tensor, particle current, and entropy current. They introduce a "creation pressure" ( $P_c$ ) and define "adiabatic" creation as a process where the specific entropy per photon ( $\sigma = S/N$ ) remains constant ( $\dot{\sigma}=0$ ), even though total entropy and particle number increase. This condition implies the particle production rate equals the entropy production rate ( $\dot{N}/N = \dot{S}/S$ ). Using the Gibbs law and energy conservation, they derive the evolution of temperature and confirm the validity of the equilibrium relations ( $\rho \propto n^{4/3}$ , etc.) under this specific condition.
Kinetic Relativistic Boltzmann Equation: The authors employ a modified Boltzmann equation that includes a non-collisional source term ( $\bar{C}_p$ ) representing gravitationally induced "adiabatic" photon creation. By neglecting standard collisions, they solve the extended Liouville operator. They demonstrate that the equilibrium phase space density (Planckian distribution) remains a valid solution to this equation if and only if the temperature evolution follows the modified law derived in the previous steps.

Key Contributions and Results

Extended Temperature Law: The paper derives a generalized temperature-redshift relation: $T a N^{-1/3} = \text{const}$ , or equivalently $\dot{T}/T = -\dot{a}/a + \Gamma/3$ , where $\Gamma$ is the photon creation rate. This reduces to the standard Friedmann law only if $\Gamma = 0$ .
Preservation of the Blackbody Spectrum: A crucial finding is that "adiabatic" photon creation does not destroy the Planckian blackbody spectrum. The modified kinetic treatment proves that the unperturbed distribution remains a Planck spectrum, provided the creation process satisfies the specific "adiabatic" condition (constant specific entropy).
Handling Distortions: The framework allows for the proper treatment of CMB anisotropies and spectral distortions. The authors show that gravitationally induced creation itself does not cause distortions; distortions arise only when conventional collisional sources (Compton scattering, double Compton, Bremsstrahlung) are added to the modified Boltzmann equation.
Phenomenological Application: Assuming a constant creation rate since recombination, the authors model the temperature evolution $T(z)$ . They find that for non-zero creation rates, the temperature law becomes non-linear and depends on the Hubble constant $H_0$ .
Data Analysis: Using existing CMB temperature measurements (Sunyaev-Zeldovich effect and molecular excitation), the authors constrain the dimensionless creation parameter $\alpha = \Gamma_0 / 3H_0$ . The best fit yields $\alpha \approx 0.0114$ (with $1\sigma$ confidence), corresponding to a creation rate $\Gamma_0 \approx 0.04 H_0$ .

Significance and Claims
The paper claims that the standard TRR is not the only possibility for preserving a blackbody spectrum during cosmic expansion. By introducing "adiabatic" photon creation, the authors offer a new theoretical route to scrutinize the $\Lambda$ CDM model. Specifically, they argue that the new cosmic thermometer, which links the temperature evolution to the Hubble constant in a non-linear way, could potentially alleviate the SN-CMB $H_0$ tension. Furthermore, the results suggest that the pattern of CMB anisotropies (including the Integrated Sachs-Wolfe effect) would be slightly modified compared to the standard approach, opening a new window for testing the thermal sector of the concordance model. The authors note that while the macroscopic and kinetic results are consistent, the underlying physical mechanism (connecting to Quantum Field Theory in curved spacetime) remains a subject for future investigation. They also clarify that if the creation is not "adiabatic" (i.e., specific entropy is not conserved), the blackbody spectrum is likely not preserved.