WIMP/FIMP dark matter and primordial black holes with memory burden effect

This paper proposes a unified dark matter scenario where the total relic abundance arises from the sum of thermally produced WIMPs, PBHs stabilized by the memory burden effect, and non-thermal WIMPs or FIMPs emitted from those PBHs, provided specific conditions prevent the emitted particles from thermalizing and ensure PBHs do not dominate the universe's energy density.

The Gist

Imagine the universe as a giant, bustling city. For decades, scientists have been trying to figure out what the "invisible citizens" of this city are. We call them Dark Matter. We know they are there because they hold the city together with their gravity, but we can't see them, touch them, or hear them.

This paper proposes a new, slightly chaotic, and very interesting theory about who these invisible citizens might be. It suggests that Dark Matter isn't just one type of person; it's a mix of three different groups living in the same neighborhood.

Here is the breakdown of the paper's ideas using simple analogies:

1. The Three Groups of Invisible Citizens

The authors suggest that our Dark Matter is a "composite" population made of:

• The "Regulars" (WIMPs/FIMPs): These are the standard suspects. Think of them as people who either hang out at the local bar (thermal equilibrium) or are so shy they never talk to anyone (feeble interactions). They were born from the heat of the early universe.
• The "Spillover" (PBH-Evaporated Particles): These are particles that were "spit out" by tiny black holes. Imagine a popcorn machine (the black hole) popping kernels (particles) into the air. Some of these kernels become Dark Matter.
• The "Survivors" (Primordial Black Holes): These are the tiny black holes themselves that didn't disappear. Usually, tiny black holes are supposed to evaporate and vanish quickly. But this paper argues that some of them are "stuck" and survived until today, acting as Dark Matter themselves.

2. The "Memory Burden" Effect: The Heavy Backpack

This is the paper's main twist.

In standard physics, a tiny black hole is like a melting ice cube. It gets smaller and smaller until it vanishes completely. The paper introduces a concept called the "Memory Burden Effect."

The Analogy: Imagine a black hole is a person carrying a heavy backpack full of memories (information about everything it has ever eaten or absorbed).

• Without the burden: The person walks lightly and evaporates quickly.
• With the burden: The backpack is so heavy that it slows the person down. They can't move as fast, and they can't "evaporate" (disappear) as quickly.

Because of this "heavy backpack," tiny black holes that should have vanished billions of years ago are actually slowed down. They are still walking around the universe today, acting as Dark Matter.

3. The Big Challenge: Not Getting Too Hot

The authors had to solve a tricky problem. If these black holes are popping out particles (like the popcorn machine), wouldn't those particles mix with the rest of the universe's "soup" and change the recipe?

If the particles from the black holes mix too well with the hot plasma of the early universe, they would ruin the standard calculation of how much Dark Matter we should have.

The Solution: The authors found a "safe zone." They showed that if the black holes are rare enough and the particles they spit out interact very weakly, the "popcorn" lands in the soup but doesn't dissolve. It stays distinct. This allows the three groups (Regulars, Spillover, and Survivors) to coexist without messing up the math.

4. The Rules of the City (Constraints)

The paper checks this theory against the "laws of the city" (observational data):

• The Big Bang Nucleosynthesis (BBN) Rule: The black holes must have finished their "melting phase" before the universe started cooking the first atoms (like hydrogen and helium). If they were still melting then, they would have ruined the recipe for the elements we see today.
• The Cosmic Microwave Background (CMB) Rule: The black holes can't be too heavy or too light, or they would leave a fingerprint on the "afterglow" of the Big Bang that we don't see.
• The "Warm" Rule: The particles from the black holes can't be moving too fast. If they are too fast (like a hot gas), they would wash away the small clusters of galaxies we see today. The "Memory Burden" actually helps here by slowing down the evaporation, keeping the particles "cooler" and more clumpy.

5. The Conclusion

The paper concludes that this "Three-Part Mix" is a very plausible explanation for Dark Matter.

• We have the standard particles.
• We have the particles spit out by black holes.
• We have the black holes themselves, saved from destruction by their "heavy backpacks" (the memory burden).

Why does this matter?
It opens the door to a universe where Dark Matter is more complex and interesting than we thought. It suggests that if we look closely enough, we might find evidence of these tiny, ancient black holes that refused to die, carrying the weight of the early universe's memories with them.

In short: Dark Matter might be a team effort between shy particles, black hole "spit," and the black holes themselves, all kept alive by a cosmic backpack.

Technical Summary

1. Problem Statement

The nature of Dark Matter (DM) remains a central mystery in cosmology. Traditional models focus on Weakly Interacting Massive Particles (WIMPs) produced via thermal freeze-out (FO) or Feebly Interacting Massive Particles (FIMPs) produced via freeze-in (FI). Simultaneously, Primordial Black Holes (PBHs) formed in the early universe are viable DM candidates, provided they survive Hawking evaporation.

Standard Hawking radiation predicts that PBHs with initial masses $M_{in} \lesssim 10^{15}$ g would have evaporated by the present day. However, recent theoretical developments suggest the memory burden effect (a quantum back-reaction effect) can significantly extend the lifetime of PBHs, allowing lighter PBHs to survive to the present day.

The Core Problem: Previous studies often treated PBHs as the sole DM source or neglected the interplay between thermally produced particles (WIMPs/FIMPs) and PBHs. This paper addresses the complex scenario where DM is a composite of three components:

1. Thermally produced WIMPs/FIMPs.
2. WIMPs/FIMPs produced via Hawking radiation from PBHs.
3. Surviving PBHs (extended by the memory burden effect).

The authors aim to determine the conditions under which these components coexist without the PBH-produced particles disrupting the standard thermal history (i.e., without thermalizing with the bath) and to quantify the resulting relic abundance.

2. Methodology

The authors employ a semi-analytical approach combining cosmological evolution equations with particle physics production mechanisms.

• PBH Evolution with Memory Burden:

  • They modify the standard Hawking evaporation rate ($dM/dt \propto -M^{-2}$) by introducing a suppression factor $[S(M_{BH})]^{-k}$, where $S$ is the black hole entropy and $k$ characterizes the back-reaction efficiency.
  • The evolution is divided into two phases:
    • Phase I (Semiclassical): Standard evaporation until the mass reaches $q M_{in}$ (where $0 < q < 1$).
    • Phase II (Quantum/Back-reaction): Evaporation slows significantly due to the memory burden effect, allowing survival to the present day.
  • They derive expressions for the PBH lifetime, evaporation temperature, and the number of particles emitted in both phases.

• Cosmological Constraints:

  • BBN (Big Bang Nucleosynthesis): Ensures PBHs do not dominate the energy density or inject excessive entropy before $t \approx 1$ s.
  • CMB (Cosmic Microwave Background): Constrains the initial PBH mass ($M_{in} \gtrsim 0.1$ g) based on inflationary generation limits.
  • Gravitational Waves (GWs): Analyzed under the assumption that PBHs never dominate the universe ($\beta < \beta_c$), implying negligible induced GWs compared to the early-matter-dominated scenario.
  • Warm Dark Matter (WDM): Constrains the mass of DM particles produced by PBHs to prevent the erasure of small-scale structures (Lyman-$\alpha$ forest constraints).

• Thermalization Analysis:

  • The authors derive a sufficient condition ($\Gamma_{ev} \ll H$) to ensure that DM particles injected by PBH evaporation do not thermalize with the Standard Model plasma. This allows the standard FO (for WIMPs) or FI (for FIMPs) mechanisms to remain the dominant production channel.
  • They define a threshold initial PBH density, $\beta_{nt}$, below which non-thermalization is guaranteed.

• Relic Abundance Calculation:

  • The total DM relic density ($\Omega_{DM}h^2$) is calculated as the sum of three terms:
    $$\Omega_{DM}h^2 = \Omega_{FO/FI}h^2 + \Omega_{PBH}h^2 + \Omega_{ev}h^2$$
  • They specifically focus on the regime where $\Omega_{FO/FI} \gg \Omega_{ev}$, meaning thermal production dominates, and PBH contributions are sub-dominant corrections.

3. Key Contributions

1. Unified Framework: The paper provides the first comprehensive framework simultaneously considering thermally produced WIMPs/FIMPs, Hawking-radiation-induced WIMPs/FIMPs, and surviving PBHs, all within the context of the memory burden effect.
2. Non-Thermalization Condition: They derived a rigorous analytical condition (Eq. 57/63) ensuring that PBH-produced particles do not disturb the thermal equilibrium of the early universe. This justifies treating the three DM components as additive rather than requiring complex coupled Boltzmann equations.
3. Memory Burden Impact on Constraints: They demonstrated how the memory burden effect (parameterized by $q$ and $k$) alters the constraints on PBH initial mass and density. Specifically, a stronger memory burden (higher $q$) allows for a higher initial PBH density ($\beta$) while maintaining the non-thermalization condition, as evaporation is suppressed.
4. Gravitational Freeze-in Sub-dominance: The authors explicitly calculated the contribution of gravitational freeze-in (via graviton exchange) and proved it remains sub-dominant compared to the standard FIMP production mechanism in their considered parameter space.

4. Results

• Survival of Light PBHs: Due to the memory burden effect, PBHs with initial masses as low as $M_{in} \sim 10^7$ g (for $k=1, q=0.5$) can survive to the present day, making them viable DM candidates.
• Relic Abundance Sensitivity: The total relic abundance is highly sensitive to the memory burden parameter $q$.
  • For WIMPs: With a benchmark $m_\chi = 700$ GeV and $\Omega_{FO}h^2 = 0.08$, the surviving PBHs ($\Omega_{PBH}$) and evaporated WIMPs ($\Omega_{ev}$) fill the gap to the observed $\Omega_{DM}h^2 \approx 0.12$. The allowed initial PBH density $\beta$ increases with $q$.
  • For FIMPs: Similar results hold, but the constraints on the FIMP mass $m_\chi$ are driven by WDM limits rather than the $\beta < \beta_c$ condition (which dominates in the WIMP case).
• Parameter Space:
  • Non-thermalization: For typical WIMP couplings ($\alpha_{WIMP} \sim 0.01 - 0.5$) and initial PBH densities $\beta \ll 10^{-9}$, the condition for non-thermalization is easily satisfied.
  • Mass Limits: The WDM constraint imposes a lower bound on the mass of PBH-produced DM particles, which becomes stronger (higher mass required) as the memory burden effect increases (delaying evaporation and increasing the kinetic energy of emitted particles at matter-radiation equality).
• Gravitational Production: The contribution from graviton-mediated freeze-in is shown to be negligible ($\Omega_{grav} \ll \Omega_{FI}$) for the reheating temperatures and coupling strengths considered.

5. Significance

This work significantly advances the phenomenology of Primordial Black Holes by integrating the memory burden effect into a multi-component Dark Matter scenario.

• Theoretical Robustness: It validates the "additive" approach to DM relic abundance, showing that in a wide parameter range, PBHs can coexist with thermal WIMPs/FIMPs without disrupting the successful predictions of the standard thermal history.
• Observational Implications: By extending the lifetime of light PBHs, the paper opens up new parameter spaces for PBHs to constitute a fraction of Dark Matter, potentially detectable via microlensing or gravitational wave signatures (though GWs are suppressed in the non-dominant regime).
• Future Directions: The study establishes a baseline for future numerical investigations, particularly regarding scenarios closer to the thermalization boundary and systematic scans over the back-reaction parameter $k$.

In conclusion, the paper demonstrates that the memory burden effect is a crucial mechanism that allows light PBHs to survive and contribute to the Dark Matter budget alongside standard particle candidates, provided the initial PBH density remains below a specific threshold to avoid thermalization.