When direct detection constrains reheating temperature: freeze-in with stronger couplings and inflaton-seeded freeze-in

This paper analyzes how recent direct detection constraints from DAMIC-M and PandaX limit reheating temperatures in freeze-in dark matter models, demonstrating that viable scenarios with stronger couplings or inflaton-seeded initial abundances can still reproduce the correct relic density while evading current experimental bounds.

The Gist

The Big Picture: A New Way to Find "Ghost" Particles

Imagine the universe is a giant, dark ocean. Scientists have been looking for "Dark Matter," which they think is like invisible fish swimming in this ocean. For decades, the main theory was that these fish were "Weakly Interacting Massive Particles" (WIMPs). The idea was that these fish were once swimming around in a warm, crowded pool (the early universe), got too cold to stay together, and froze out into the dark ocean we see today.

However, recent experiments (like DAMIC-M and PandaX) have looked very carefully at this pool and haven't found these fish. In fact, they've ruled out the standard way these fish were supposed to be made for a specific size range (between 3 millionths of a gram and 1 gram).

This paper asks: "What if our theory about how the fish were made is wrong?"

The authors propose two alternative scenarios that could explain why we haven't found the fish yet, or how we might find them soon.

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Scenario 1: The "Cold Start" (Freeze-in at Stronger Coupling)

The Old Idea:
Usually, scientists think Dark Matter interacts so weakly with normal matter that it's like trying to hear a whisper in a hurricane. To get the right amount of Dark Matter today, the "whisper" (the interaction) has to be incredibly faint. Because it's so faint, our detectors can't hear it.

The New Idea (FISC):
The authors suggest the universe didn't start as a hot, roaring hurricane. Instead, imagine the universe started as a very quiet, cold room.

• The Analogy: Imagine you are trying to fill a bucket with water (Dark Matter) using a tiny, leaky cup (the interaction).
  • Standard View: You are in a storm. The water is everywhere, but the cup leaks so much that you can't fill the bucket. You need a super-tiny leak to get the right amount.
  • This Paper's View: You are in a freezing cold room. The water is frozen solid (Boltzmann suppression). Even if your cup has a huge hole (stronger coupling), the water won't flow out easily because it's frozen.
• The Result: Because the universe was so cold (low "reheating temperature"), the "leak" in the cup can actually be much bigger than we thought, and we can still get the right amount of water in the bucket.
• Why it matters: If the "leak" is bigger, our detectors (which are like ears listening for the splash) might actually hear it! The paper shows that if the universe started cold, experiments like DAMIC-M could detect these particles, but only if the universe didn't get too hot later on.

The Catch:
The experiments have already looked and said, "We don't see anything." This means that if this "Cold Start" theory is true, the universe couldn't have been too cold. It sets a new rule: The universe must have been at least as hot as 1 GeV (a specific energy level) to avoid being ruled out by current experiments.

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Scenario 2: The "Seed" from the Big Bang (Inflaton-Seed)

The Problem:
In the first scenario, we assumed the bucket was empty at the start. But what if someone already put some water in the bucket before we started pouring?

The New Idea:
The authors look at the "Inflaton," a field responsible for the rapid expansion of the universe (the Big Bang). They suggest that as the Inflaton field decayed, it might have accidentally "seeded" the universe with a few Dark Matter particles right at the beginning, before the main "pouring" (freeze-in) even started.

• The Analogy: Imagine you are baking a cake (Dark Matter).
  • Standard View: You mix the batter and bake it. The final cake size depends entirely on how much batter you mixed.
  • This Paper's View: Before you even started mixing, someone dropped a few chocolate chips (Dark Matter) into the bowl. Now, even if you don't mix much batter, you still have a decent-sized cake because of those pre-existing chips.
• The Result: If these "chips" were dropped in, it changes the math completely. It means the Dark Matter we see today might not be the result of the "freezing" process alone, but a mix of the "chips" and the "batter."
• Why it matters: This opens up a whole new range of possibilities. Even if the interaction is super weak (or the universe was very cold), the pre-existing "chips" could explain the amount of Dark Matter we see. This allows for scenarios that the standard experiments would otherwise rule out.

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The Conclusion: Detectors as Time Machines

The main takeaway of this paper is a shift in perspective.

Usually, we think of Dark Matter detectors (like DAMIC-M) as tools to measure how "sticky" Dark Matter is to normal matter. But this paper argues that these detectors are actually measuring the history of the universe.

• If we don't find Dark Matter, it doesn't just mean the particles don't exist. It might mean the universe was too cold when it started, or that the Inflaton field didn't drop enough "seeds" at the beginning.
• The authors show that by looking for these particles, we are effectively taking a picture of the very early universe, checking how hot it was and how the "Big Bang" engine worked.

In short: The paper says, "Don't give up on finding Dark Matter just because we haven't seen it yet. The universe might have started colder or had a different 'recipe' than we thought. If we keep looking, we might not just find the particles; we might figure out the secret history of how the universe began."

Technical Summary

Technical Summary: When Direct Detection Constrains Reheating Temperature: Freeze-In with Stronger Couplings and Inflaton-Seeded Freeze-In

Problem Statement
Recent results from the DAMIC-M and PandaX collaborations have placed stringent constraints on the "vanilla" freeze-in production of dark matter (DM) in the mass range $3 \text{ MeV} \lesssim m_\chi \lesssim 1 \text{ GeV}$. These constraints specifically target models featuring an ultra-light $U(1)_X$ gauge boson kinetically mixed with the Standard Model (SM) hypercharge. In the standard freeze-in paradigm, DM never reaches thermal equilibrium, and its relic abundance is determined by extremely feeble couplings. However, the non-observation of DM-electron scattering signals ($\sigma_e$) in this mass range effectively rules out the standard scenario for high reheating temperatures ($T_{RH}$). This work addresses the theoretical uncertainties inherent in the freeze-in framework, specifically investigating how lower reheating temperatures and non-thermal initial conditions (such as inflaton decay) alter the relationship between the DM relic abundance and the direct detection cross-section.

Methodology
The authors analyze a benchmark model extending the SM with an extra $U(1)_X$ gauge symmetry, where the DM candidate $\chi$ is a Dirac fermion coupled to a dark photon $A'$ (or $C_\mu$) with mass $m_{A'} \ll \text{keV}$. The study proceeds through three main analytical and numerical steps:

1. Freeze-In at Stronger Coupling (FISC): The authors investigate the regime where the reheating temperature $T_{RH}$ is significantly below the electroweak scale (down to the Big Bang Nucleosynthesis limit of $\sim 4$ MeV). In this scenario, the Boltzmann suppression factor $\exp(-m_\chi/T_{RH})$ compensates for stronger couplings ($g' \sim \mathcal{O}(1)$ or electroweak scale), allowing the DM to be produced without ever reaching thermal equilibrium. The production rate is calculated using the Boltzmann equation, focusing on the UV-sensitive regime where production occurs primarily at $T \approx T_{RH}$.
2. Direct Detection Constraints: The derived relic abundance is mapped to the DM-electron scattering cross-section $\sigma_e$. The authors compare these theoretical predictions against current exclusion limits from DAMIC-M (2025) and PandaX, as well as projected sensitivities for future runs (DAMIC-M 2028).
3. Inflaton-Seeded Hybrid Freeze-In: To address the "initial condition" problem—where gravitational production or inflaton decays might generate a non-negligible DM abundance before the freeze-in epoch begins—the authors introduce a hybrid scenario. They model the inflaton $\phi$ (with a quadratic potential dominating the end of reheating) decaying into DM pairs with a branching ratio $\text{BR}_{\phi \to \chi\chi}$. The total relic density is computed as the sum of the thermal freeze-in yield and the non-thermal yield from inflaton decay.

Key Contributions and Results

• Constraints on Reheating Temperature ($T_{RH}$): The analysis demonstrates that direct detection experiments effectively constrain the reheating temperature. For a fixed DM mass and relic abundance, the experimental upper limits on $\sigma_e$ translate into a lower bound on $T_{RH}$.

  • The DAMIC-M results exclude a broad band of $T_{RH}$ for DM masses in the range $5 \text{ MeV} \lesssim m_\chi \lesssim 100 \text{ MeV}$.
  • For electroweak-scale DM, the constraints are even more stringent, requiring $T_{RH} \gtrsim \mathcal{O}(10 \text{ GeV})$ to avoid violating current $\sigma_e$ limits. This bound is stronger than the standard BBN constraint ($T_{RH} \gtrsim 4$ MeV).
  • The projected sensitivity of DAMIC-M (assuming a $100\times$ exposure increase) could probe reheating temperatures up to $\sim 50$ GeV for electroweak-scale DM.

• Viability of FISC: The paper identifies viable parameter spaces where the "vanilla" freeze-in is excluded, but the FISC scenario remains consistent with observations. By lowering $T_{RH}$, the required couplings can be increased (making them potentially observable), while the Boltzmann suppression ensures the correct relic density. This transforms direct detection experiments from probes of coupling strength into "cosmic explorers" of the reheating temperature.

• Impact of Inflaton Decay: The inclusion of inflaton decay as a seed mechanism significantly modifies the phenomenology.

  • The total relic density is a sum of the FISC component (exponentially suppressed by $m_\chi/T_{RH}$) and the inflaton decay component (dependent on $\text{BR}_{\phi \to \chi\chi}$ and $m_\phi$).
  • For sufficiently large $m_\chi$, the inflaton decay contribution can dominate, rendering the relic abundance largely independent of the direct detection cross-section $\sigma_e$.
  • The authors derive constraints on the branching ratio $\text{BR}_{\phi \to \chi\chi}$ as a function of $m_\chi$ and $T_{RH}$. They also impose Lyman-$\alpha$ forest constraints, which limit the free-streaming length of DM produced directly from inflaton decay, setting a lower bound on $m_\chi$ relative to $m_\phi$ and $T_{RH}$.

Significance
The paper argues that the absence of signals in current direct detection experiments should not be interpreted solely as a constraint on particle physics couplings. Instead, within the freeze-in framework, these null results provide critical constraints on cosmological parameters, specifically the reheating temperature and the nature of pre-reheating DM production.

The authors conclude that:

1. Reheating Temperature as a Variable: Assuming a high reheating temperature is a significant theoretical bias. Lowering $T_{RH}$ opens a "FISC" regime where stronger couplings are viable, potentially bringing feeble-interaction models within the reach of current and near-future experiments.
2. Hybrid Scenarios: The interplay between thermal freeze-in and non-thermal inflaton decay creates a complex parameter space where direct detection limits constrain both the gauge coupling (via $\sigma_e$) and the inflaton branching ratio.
3. Cosmic Exploration: Direct detection experiments are positioned as tools to probe the thermal history of the early Universe. The non-observation of DM in the MeV–GeV range, when interpreted through FISC and hybrid models, effectively rules out specific ranges of reheating temperatures and inflaton decay properties, thereby guiding the construction of viable dark sector models.

The study emphasizes that interpreting freeze-in DM limits requires a holistic approach that accounts for cosmological uncertainties, including $T_{RH}$ and initial production mechanisms, rather than relying solely on the standard high-temperature, pure-freeze-in assumption.