⚛️ phenomenology

Gravitational ultra-relativistic freeze-out during general reheating

This paper generalizes the ultrarelativistic freeze-out (UFO) mechanism for dark matter to arbitrary reheating temperature profiles, demonstrating that gravitational particle production at the onset of reheating significantly alters the parameter space and relic abundance, a phenomenon termed gravitational UFO (GUFO).

Original authors: Mathieu Gross, Stephen E. Henrich, Fotis Koutroulis

Published 2026-06-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mathieu Gross, Stephen E. Henrich, Fotis Koutroulis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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: Finding the Missing Piece of the Universe

Imagine the universe is a giant, expanding balloon. Scientists know that most of the matter in this balloon is "Dark Matter"—an invisible substance that holds galaxies together but doesn't shine or interact with light.

For decades, scientists have tried to figure out how this Dark Matter was made. The two main theories were:

The "WIMP" Theory: Dark Matter particles were like busy bees in a crowded hive, constantly bumping into each other until they reached a perfect balance (thermal equilibrium) and then stopped interacting as the universe cooled.
The "FIMP" Theory: Dark Matter particles were like shy ghosts. They were so weakly interacting that they never really met each other. They just slowly trickled into existence over time, accumulating until we have the amount we see today.

This paper introduces a third, more complex scenario called UFO (Ultra-relativistic Freeze-out). It suggests that Dark Matter particles were once so hot and fast (ultra-relativistic) that they did mix with the rest of the universe, but then they "froze out" (stopped interacting) while still moving at near-light speed.

The Setting: The "Reheating" Phase

To understand this paper, you have to imagine the very beginning of the universe, right after the Big Bang.

Inflation: The universe expanded incredibly fast, like a balloon being blown up by a super-powered pump.
The Crash: When inflation stopped, the energy of that expansion had to go somewhere. It dumped into particles, creating a hot soup of radiation. This process is called Reheating.

Think of Reheating as a pot of water on a stove. The "inflaton" (the field driving inflation) is the heat source. As it cools down, it transfers its energy to the water (the universe), making it boil.

The Problem: The "Gravitational Leak"

The authors realized that previous studies of UFO had a flaw. They assumed the "pot" was heated only by the main stove (the inflaton decaying into particles).

However, the paper points out that even before the main stove turns on, there is a tiny, unavoidable leak of heat coming from gravity itself. In the language of physics, gravity can spontaneously create a small amount of radiation just by the nature of space-time expanding.

The Analogy: Imagine you are filling a bathtub (the universe) with a hose (the inflaton). Previous models assumed the tub was empty until the hose started. This paper says, "Wait, there's a tiny drip from the faucet (gravity) that starts filling the tub before the hose even turns on."

The Discovery: GUFO (Gravitational UFO)

The authors call their new discovery GUFO (Gravitational Ultra-relativistic Freeze-out). Here is what happens in their scenario:

The Early Drip: Before the main reheating process begins, the "gravity drip" creates a small, hot bath of radiation.
The Freeze-Out: The Dark Matter particles interact with this early drip. Because the universe is expanding and cooling rapidly, the Dark Matter particles stop interacting (freeze out) while they are still moving incredibly fast.
The Twist: In the old models, if the main "hose" (reheating) turned on later, it would wash away the Dark Matter or change the rules. But in this new model, the Dark Matter has already "locked in" its abundance based on that early gravitational drip.

Why This Matters: Opening New Doors

The paper claims this changes the rules of the game in two major ways:

1. It allows for "Heavier" Dark Matter
In standard models, if you try to make Dark Matter too heavy, the math says it should have been produced in huge quantities, making the universe look very different than it does.

The Paper's Claim: Because of the gravitational drip, the "freezing" happens differently. This allows for Dark Matter particles to be much heavier (up to 10 million times the mass of a proton) without breaking the universe's balance.

2. It saves "Bosonic" Channels
There are different ways the universe can be reheated. Some involve particles called fermions (like electrons), and some involve bosons (like photons).

The Problem: In standard models, the "bosonic" way of reheating was considered a dead end for creating Dark Matter because the temperature dropped too slowly, preventing the particles from freezing out correctly.
The Paper's Claim: The gravitational drip changes the temperature curve just enough to make the "bosonic" channel work! It opens up a whole new set of possibilities that were previously thought impossible.

The "Freeze-In" Aftermath

One of the most interesting parts of the paper is what happens after the Dark Matter freezes out.

Standard WIMP: Once they freeze out, they are done.
Standard FIMP: They never freeze out; they just slowly accumulate.
UFO/GUFO: The Dark Matter freezes out, but because the universe is still "reheating" (the temperature is changing in a weird way), the Dark Matter might start interacting again later, but this time in a "freeze-in" mode. It's like the particles took a break, then came back to work a little bit more before the universe cooled down completely.

The Bottom Line

The authors are saying: "We looked at how Dark Matter was made during the universe's 'reheating' phase. We realized we forgot about a tiny, unavoidable contribution from gravity. When we add this 'gravity drip' into our calculations, it completely changes the rules. It allows for heavier Dark Matter, it makes previously impossible scenarios possible, and it suggests that many models we thought were 'Freeze-in' might actually be 'Freeze-out' in disguise."

They conclude that to truly understand Dark Matter, we can't just look at the main events of the early universe; we have to account for the subtle, background hum of gravity that was there from the very start.

Technical Summary: Gravitational Ultra-Relativistic Freeze-out During General Reheating

Problem Statement
The standard Weakly Interacting Massive Particle (WIMP) paradigm and the Feebly Interacting Massive Particle (FIMP) freeze-in mechanism have been extensively studied, yet experimental evidence remains elusive. This motivates the exploration of alternative production scenarios, particularly those involving non-standard cosmological histories like the reheating era. A specific mechanism, Ultra-Relativistic Freeze-out (UFO), was previously identified where dark matter (DM) enters thermal equilibrium during reheating and decouples while ultra-relativistic. However, previous analyses of UFO were restricted to specific reheating channels (specifically $\phi \to f\bar{f}$ ) and assumed a simplified temperature evolution. Furthermore, the impact of unavoidable gravitational particle production of radiation at the onset of reheating had not been integrated into the UFO framework. The authors investigate how a generic temperature profile and the inclusion of gravitationally produced radiation modify the UFO parameter space, potentially altering the relic abundance and the nature of the production (UV vs. IR dominated).

Methodology
The authors generalize the UFO mechanism to arbitrary reheating scenarios characterized by a monomial inflaton potential $V(\phi) \sim \phi^k$ and a generic temperature scaling $T \sim a^{-\xi}$ .

Thermal Evolution: They model the reheating epoch using coupled continuity equations for the inflaton and radiation energy densities. They consider three specific reheating channels: fermionic decay ( $\phi \to f\bar{f}$ ), bosonic decay ( $\phi \to bb$ ), and bosonic scattering ( $\phi\phi \to bb$ ).
Gravitational Radiation (GUFO): They incorporate the minimal, unavoidable production of radiation via gravitational interactions (graviton portal) immediately following inflation. This creates an early radiation bath with a temperature scaling $T \sim a^{-1}$ before the standard reheating channel dominates.
Kinetic Analysis: Using the Boltzmann equation, they derive the conditions for DM to enter and exit thermal equilibrium. They analyze the thermally averaged cross-section $\langle \sigma v \rangle \sim T^n/\Lambda^{n+2}$ to determine the decoupling temperature ( $T_{FO}$ ) and the transition between UV-dominated and IR-dominated production regimes.
Relic Abundance Calculation: They compute the final DM yield ( $Y_\chi$ ) by integrating the source term across different epochs: the gravitational bath phase, the transition phase, and the standard reheating phase. They distinguish between cases where freeze-out occurs in the gravitational bath (GUFO) versus the standard reheating bath (UFO).

Key Contributions

Generalization of UFO: The paper extends the UFO framework to generic temperature profiles $T \sim a^{-\xi}$ , explicitly mapping the conditions required for relativistic decoupling across different inflaton potentials ( $k=2, 4, 6$ ) and reheating channels.
Introduction of GUFO: The authors identify a new regime, Gravitational Ultra-Relativistic Freeze-out (GUFO), where DM decouples from the gravitationally produced radiation bath. This occurs when the reheating temperature is sufficiently low such that the gravitational bath dominates the energy density at the time of freeze-out.
UV/IR Regime Shift: They demonstrate that the inclusion of the gravitational bath can shift the nature of the production from IR-dominated to UV-dominated, or vice versa, depending on the crossing temperature ( $T_\times$ ) where the gravitational bath is overtaken by the standard reheating bath.
Thermalization Constraints: The study refines the thermalization conditions, showing that GUFO allows for thermalization at higher BSM scales ( $\Lambda$ ) than standard UFO in certain channels, effectively relaxing constraints on the interaction strength.

Results

Parameter Space Expansion: For the specific case of a quadratic potential ( $k=2$ ) and $n=2$ (e.g., 4-Fermi interactions), GUFO allows for DM masses up to $10^7$ GeV for $\Lambda \lesssim 10^9$ GeV. This is achieved because the thermalization constraint is softened; the freeze-out temperature becomes independent of the reheating temperature ( $T_{RH}$ ) in the gravitational regime.
Accessibility of Bosonic Channels: Standard UFO is often forbidden or highly constrained for bosonic decay channels ( $\phi \to bb$ ) due to the shallow temperature scaling ( $T \sim a^{-3/4}$ for $k=4$ ). The authors show that GUFO makes this channel accessible, with a parameter space comparable to the fermionic decay channel.
Mass Bounds: In the case of a quartic potential ( $k=4$ ), the authors find that for UV GUFO, the DM mass is fixed to $m_\chi \sim 10^3$ GeV, independent of the reheating temperature and the interaction index $n$ . This arises because the duration of the gravitational domination era is independent of $T_{RH}$ for $k=4$ .
Relic Abundance Formulas: The paper provides analytic expressions for the relic abundance in both UV and IR GUFO regimes. Notably, in the UV GUFO regime, the abundance is independent of $\Lambda$ and depends primarily on the reheating temperature and the DM mass.
Compatibility with Cosmology: The authors verify that UV GUFO scenarios naturally satisfy constraints from Big Bang Nucleosynthesis (BBN) and Lyman- $\alpha$ forest observations (structure formation), provided the DM mass is sufficiently large ( $m_\chi \sim 10^3$ GeV).

Significance and Claims
The authors claim that their work necessitates a re-evaluation of DM production mechanisms in non-instantaneous reheating scenarios.

Reclassification of Freeze-in: They argue that many existing studies classifying DM production as "freeze-in" during low- $T_{RH}$ reheating may be misclassified. If the DM thermalizes at temperatures $T > T_{RH}$ due to the non-instantaneous nature of reheating and the presence of gravitational radiation, these scenarios should be re-classified as UFO or GUFO.
Resolution of Overproduction: GUFO offers a solution to the overproduction problem faced by freeze-in models in high-scale inflation. The initial thermalization (freeze-out) followed by dilution during the reheating phase prevents the excessive accumulation of DM that typically plagues freeze-in scenarios with minimal gravitational production.
Robustness of Bosonic Channels: The finding that GUFO renders the bosonic decay channel ( $\phi \to bb$ ) viable is significant, as this channel is less susceptible to fragmentation effects compared to fermionic decays, potentially offering a more robust production mechanism.
Model Independence: The results highlight that the intrinsic properties of UFO require a coherent treatment with the full thermal evolution of the early universe, including unavoidable gravitational effects, rather than relying on simplified, instantaneous reheating approximations.

The paper concludes that while UFO was previously considered a niche scenario, the inclusion of gravitational radiation (GUFO) significantly broadens its phenomenological viability, making it a competitive and testable alternative to WIMP and FIMP paradigms.