Strongly interacting singlet scalar dark matter during reheating

This paper demonstrates that a singlet scalar dark matter model operating in the strongly interacting massive particle (SIMP) regime, which is typically ruled out in standard radiation-dominated cosmology due to constraints on mass and couplings, becomes viable during non-standard cosmological eras by allowing for perturbative couplings and satisfying astrophysical bounds.

The Gist

Here is an explanation of the paper using simple language and creative analogies.

The Big Mystery: What is Dark Matter?

Imagine the universe is a giant, invisible ocean. We can see the islands (stars and galaxies), but the water itself (Dark Matter) is invisible. We know it's there because the islands move as if they are being pulled by something heavy, but we can't see what it is.

Scientists have a favorite theory: Dark Matter is made of tiny particles that were created in the Big Bang. Usually, they think these particles were like "WIMPs" (Weakly Interacting Massive Particles)—heavy, slow-moving ghosts that occasionally bump into each other and disappear, leaving behind just the right amount of "ghosts" to explain the universe today.

The Problem with the "SIMP" Idea

There is another idea called SIMP (Strongly Interacting Massive Particles). Imagine these aren't ghosts, but more like a crowded dance floor. The particles are constantly bumping into each other, swapping partners, and changing the number of dancers on the floor (e.g., four dancers merge into two).

In the standard story of the universe (the "Standard Model"), this SIMP idea hits a wall. To get the right amount of Dark Matter today, the particles would have to be incredibly light (like a feather) and bump into each other too hard. If they bumped that hard, they would have smashed apart galaxy clusters (like the famous "Bullet Cluster") in ways we don't see. It's like trying to build a house out of Jell-O; it's too squishy to hold its shape.

The Twist: A Different History for the Universe

The authors of this paper asked a simple question: "What if the universe didn't expand the way we think it did?"

Imagine the universe's expansion as a car driving down a highway.

• Standard View: The car drives at a steady, predictable speed (Radiation Domination).
• New View: What if, for a while, the car was stuck in a traffic jam or driving through mud (an "Early Matter-Dominated Era")?

If the universe expanded slower or differently in its early days (before it settled into its current rhythm), the rules of the game change.

The Solution: Changing the Rules of the Dance

The authors showed that if the universe had this "traffic jam" phase (a non-standard history) before it settled down, the SIMP idea suddenly works perfectly.

Here is the analogy:

• The Standard Scenario: Imagine a dance party where the music is loud and fast. The dancers (Dark Matter particles) are so energetic that they fly apart too quickly. To get the right number of dancers left over, they have to be tiny and move so frantically that they break the furniture (violating astrophysical rules).
• The New Scenario: Now, imagine the music slows down, or the room gets bigger before the party really starts. The dancers have more time to interact. They can be heavier (like a person instead of a feather) and they can bump into each other gently (without breaking the furniture).

Because the universe expanded differently, the "freeze-out" (the moment the particles stop interacting and get stuck in their final numbers) happens at a different time. This allows the particles to be heavy enough to be stable, but interact strongly enough to create the right amount of Dark Matter, all without breaking the laws of physics we observe today.

What Did They Actually Do?

1. The Model: They used a simple model where Dark Matter is a single, invisible scalar particle (a "singlet") that talks to the visible world only through the Higgs boson (the particle that gives things mass).
2. The Math: They did complex calculations to show that if the universe had an "Early Matter-Dominated Era," the math works out. The particles can have masses ranging from very light to incredibly heavy (from the weight of a virus to the weight of a mountain).
3. The Checks: They checked if this idea survives real-world tests:
   • Direct Detection: Can we catch these particles in underground labs? (Some parts of the theory are already being tested; others are waiting for future super-sensors like DARWIN).
   • Colliders: Can we create them at the Large Hadron Collider (LHC)? (The Higgs boson might be decaying into them invisibly).
   • Galaxy Clusters: Do they smash into each other too hard? (No, the new math says they interact just right).

The Takeaway

This paper is like finding a new key to a locked door. For years, scientists thought the "SIMP" door was locked because the standard rules of the universe didn't allow it. This paper says, "Wait, what if the rules were different in the beginning?"

By changing the history of the universe's expansion, they unlocked a whole new world of possibilities. Dark Matter could be a "Strongly Interacting" particle that is heavy, stable, and consistent with everything we see in the sky today. It reminds us that to understand the present, we sometimes have to rewrite the history books of the past.

Technical Summary

Here is a detailed technical summary of the paper "Strongly interacting singlet scalar dark matter during reheating" by Bélanger, Bernal, and Pukhov.

1. Problem Statement

The paper addresses the viability of the Strongly Interacting Massive Particle (SIMP) mechanism within the context of the Singlet Scalar Dark Matter (DM) model.

• The Standard Scenario: In standard radiation-dominated cosmology, the SIMP mechanism (where DM relic abundance is set by $4 \to 2$ self-annihilations while maintaining kinetic equilibrium with the Standard Model bath) is generally considered non-viable for singlet scalar models.
• The Conflict: To achieve the correct relic density via $4 \to 2$ processes in the standard scenario, the model requires:
  • Very light DM masses ($m \sim \text{keV}$).
  • Large quartic self-couplings ($\lambda_S \sim \mathcal{O}(1)$).
  • Tension: These requirements lead to DM self-interaction cross-sections ($\sigma_{SS}/m$) that violate astrophysical constraints, particularly those derived from the Bullet Cluster and galaxy cluster collisions, which limit $\sigma_{SS}/m \lesssim 0.47 \text{ cm}^2/\text{g}$.

The authors investigate whether this conclusion changes if the freeze-out occurs during a non-standard cosmological history prior to Big Bang Nucleosynthesis (BBN), specifically during a reheating phase or an early matter-dominated era.

2. Methodology

The authors employ a combination of analytical derivations and numerical validation to study the dynamics of DM freeze-out in modified cosmological backgrounds.

• Cosmological Framework:
  • They parameterize the pre-radiation-dominated era using an equation-of-state parameter $w$ and a temperature scaling exponent $\alpha$.
  • The Hubble expansion rate $H(a)$ and SM temperature $T(a)$ evolve differently than in the standard case ($w=1/3, \alpha=1$).
  • Specific scenarios analyzed include an early matter-dominated era ($w=0, \alpha=3/8$) and radiation-dominated eras with non-standard entropy injection ($\alpha \neq 1$).
• Particle Physics Model:
  • Singlet Scalar DM: A real scalar field $S$ (odd under $Z_2$) coupled to the SM Higgs doublet $\Phi$ via a portal coupling $\lambda_{\Phi S}$.
  • Potential: $V = \mu^2_\Phi |\Phi|^2 + \lambda_\Phi |\Phi|^4 + \mu^2_S S^2 + \lambda_S S^4 + \lambda_{\Phi S} |\Phi|^2 S^2$.
  • Dominant Process: The study focuses on the regime where $4 \to 2$self-annihilations dominate the number-changing processes, while$2 \to 2$ annihilations into SM particles are suppressed (to avoid WIMP dominance) but sufficient to maintain kinetic equilibrium between the dark and visible sectors.
• Analytical & Numerical Tools:
  • Derivation of analytical expressions for the freeze-out temperature ($T_{fo}$) and the asymptotic DM yield ($Y_0$) in both standard and non-standard cosmologies.
  • Use of the Lambert W function to solve for the freeze-out condition $H(T_{fo}) \approx \langle \sigma v^3 \rangle_{4\to2} n_{eq}^3$.
  • Numerical cross-checking using a modified version of micrOMEGAs (incorporating new routines for non-standard cosmology).
  • Calculation of interaction rates (Appendix A) to derive the thermally averaged cross-section $\langle \sigma v^3 \rangle_{4\to2}$.

3. Key Contributions

1. Revival of the SIMP Mechanism: The paper demonstrates that the Singlet Scalar SIMP scenario, previously ruled out in standard cosmology, becomes fully viable if freeze-out occurs during a non-standard era (specifically an early matter-dominated phase).
2. Relaxation of Constraints: The altered Hubble expansion rate in non-standard cosmologies causes an earlier decoupling of the DM number density. This allows the observed relic density to be achieved with:
   • Perturbative couplings: $\lambda_S$ can be in the range $5 \times 10^{-3} \lesssim \lambda_S \lesssim 10$.
   • Broad Mass Range: DM masses can range from sub-GeV ($10^{-1}$GeV) to ultra-heavy scales ($10^{12}$ GeV), avoiding the sub-MeV regime that conflicts with self-interaction bounds.
3. Kinetic Equilibrium Conditions: The authors derive the minimal Higgs-portal coupling ($\lambda_{\Phi S}$) required to maintain kinetic equilibrium between the DM and SM sectors during freeze-out. They show that for $m \gg m_W$, equilibrium is maintained via scattering with $W$ bosons, while for $m < m_W$, scattering with light fermions requires larger portal couplings to compensate for Yukawa suppression.
4. Parameter Space Mapping: They delineate the regions where SIMP production dominates over the standard WIMP mechanism and where it is excluded by direct detection, collider bounds, and BBN constraints.

4. Results

• Viable Parameter Space:
  • Mass: $10^{-1} \text{ GeV} \lesssim m \lesssim 10^{12} \text{ GeV}$.
  • Self-Coupling: $5 \times 10^{-3} \lesssim \lambda_S \lesssim 10$.
  • Portal Coupling: $10^{-5} \lesssim \lambda_{\Phi S} \lesssim 10$ (dependent on mass).
  • These regions are consistent with the Bullet Cluster bounds ($\sigma_{SS}/m < 0.47 \text{ cm}^2/\text{g}$) and perturbativity ($\lambda_S \lesssim 10$).
• Impact of Cosmology:
  • In the standard scenario (black lines in Fig. 2/3), the viable SIMP region is excluded by self-interaction bounds.
  • In the early matter-dominated scenario ($w=0, \alpha=3/8$), the viable region (white areas in Fig. 3) opens up significantly, allowing for heavy DM masses and perturbative couplings.
• Experimental Constraints:
  • Direct Detection: Current limits from LZ and projected sensitivity of DARWIN/XLZD constrain the lower mass end of the parameter space.
  • Collider Physics:
    • For $m < m_h/2$, the invisible Higgs width ($Br_{h \to inv}$) constrains $\lambda_{\Phi S}$. Current LHC limits ($<10.7\%$) and future HL-LHC ($<2\%$) and FCC-ee ($<0.05\%$) sensitivities are mapped.
    • The Higgs resonance region ($m \approx 62$ GeV) creates a specific dip in the allowed portal coupling due to resonant WIMP production.
• WIMP vs. SIMP: The paper identifies the upper bound on $\lambda_{\Phi S}$ above which the standard WIMP mechanism ($2 \to 2$) dominates, rendering the SIMP mechanism irrelevant for the final relic density.

5. Significance

• Paradigm Shift: The work challenges the assumption that specific DM production mechanisms (like SIMP) are intrinsically ruled out for certain particle models (like Singlet Scalar). It highlights that cosmological history is as critical as particle physics in determining model viability.
• Theoretical Consistency: It resolves the tension between the need for large self-couplings (for SIMP) and astrophysical bounds by shifting the freeze-out epoch, allowing for a consistent, perturbative, and observationally viable model.
• Future Prospects: The identified parameter space is testable. Future experiments like DARWIN/XLZD (direct detection), HL-LHC, and FCC-ee (Higgs precision measurements) will probe significant portions of the viable region, potentially confirming or ruling out this specific realization of SIMP dark matter.
• Generalizability: The analytical framework developed can be applied to other DM models and non-standard cosmological scenarios (e.g., different $w$ and $\alpha$ values), providing a robust tool for exploring the early Universe's thermal history.

In conclusion, the paper establishes that Singlet Scalar Dark Matter can successfully function as a SIMP if the Universe underwent an early matter-dominated phase, thereby reconciling the model with both the observed relic density and stringent astrophysical self-interaction limits.