Cosmological constraints on TeV-scale dark matter subcomponents decaying between recombination and reionisation

This paper demonstrates that future global 21-cm signal observations could provide more sensitive constraints than current Cosmic Microwave Background data on TeV-scale dark matter subcomponents decaying between recombination and reionisation, particularly for lifetimes exceeding $10^{15}$ seconds and decays into neutrinos.

The Gist

Imagine the universe as a giant, dark ocean. For billions of years after the Big Bang, this ocean was pitch black. There were no stars, no galaxies, just a cold, silent fog of gas. Astronomers call this era the "Dark Ages," followed by the "Cosmic Dawn" when the first stars finally flickered on.

For a long time, we've been trying to figure out what the "water" in this ocean is made of. We know most of it is Dark Matter, an invisible substance that holds galaxies together but doesn't shine. The standard theory says Dark Matter is boring: it just sits there, never changing, never talking to anything else.

But what if Dark Matter isn't boring? What if a tiny, tiny fraction of it is actually "leaking" energy, like a slow-dripping faucet?

This paper is a detective story about that leak. The authors are asking: If Dark Matter particles are slowly decaying (breaking apart) into energy between the time the universe was a baby and the time the first stars were born, could we see it?

Here is the breakdown of their investigation using simple analogies:

1. The Two Detective Tools

The scientists have two main ways to look for this "leaking" Dark Matter:

• Tool A: The Cosmic Microwave Background (CMB)
  Think of the CMB as an old, faded photograph of the universe when it was just a baby (380,000 years old). If Dark Matter started leaking energy back then, it would have left a smudge or a blur on the photo. We have very high-resolution cameras (satellites like Planck) that have already taken this picture. They tell us that if there was a leak, it must have been very small, or the photo would look too blurry.

  • The Limit: The CMB is great at seeing big, early leaks, but it's a bit "blurry" when it comes to the specific type of energy leaking out.

• Tool B: The 21-cm Radio Signal
  Imagine the universe as a giant radio station. The hydrogen gas in the Dark Ages emits a very faint, specific radio hum (the 21-cm signal). If Dark Matter leaks energy, it acts like a heater, warming up the gas. This changes the pitch and volume of the radio hum.

  • The Advantage: Future radio telescopes are going to be incredibly sensitive to this "hum." The authors argue that this new tool might be more sensitive than the old photo (CMB) for certain types of leaks, especially those happening later in the timeline (between the baby phase and the first stars).

2. The Three Types of "Leaks"

The team tested three different ways Dark Matter could decay:

1. Into Light (Photons): Like a lightbulb turning on.
2. Into Electrons: Like throwing hot rocks into the water.
3. Into Neutrinos: This is the tricky one. Neutrinos are "ghost particles" that usually pass right through everything without interacting. It's like throwing a ghost into the room; you wouldn't expect it to warm up the furniture.

The Big Surprise:
Usually, scientists think that if Dark Matter decays into ghosts (neutrinos), it doesn't matter because the ghosts just float away. But the authors found something fascinating: For very heavy Dark Matter particles, these "ghosts" don't stay ghosts.

When a heavy Dark Matter particle breaks into neutrinos, the neutrinos are so energetic that they crash into other things and create a shower of light and electrons later on. It's like throwing a ghost into a room, and the ghost accidentally knocks over a lamp, which then breaks a window, letting in the sun.

3. The "Spectral" Difference (The Flavor of the Leak)

Here is the core discovery of the paper:

• The CMB (The Baby Photo) only cares about the total amount of energy leaked. It doesn't care if the energy came as light, electrons, or ghosts. It just sees the total heat.
• The 21-cm Signal (The Radio Hum) is much more picky. It cares about when and how the energy is delivered.

The authors found that for neutrino decays, the energy is delivered in a way that is perfect for heating up the gas during the "Cosmic Dawn" (the time of the first stars). Because the energy arrives in a specific "flavor" (lower energy electrons created later), it heats the gas more efficiently at the exact moment the radio telescopes are listening.

The Analogy:
Imagine you are trying to warm up a cold room.

• CMB is like checking the thermostat from yesterday. It tells you how much total heat was added.
• 21-cm is like feeling the air right now.
• If you drop a hot brick (photons) into the room, it heats up immediately.
• If you drop a "ghost" (neutrinos) that slowly turns into a hot brick later, the CMB might miss the timing, but the 21-cm radio signal will feel that specific, delayed warmth perfectly.

4. The Verdict

The paper concludes that:

1. Future radio telescopes (like the ones being built to listen to the Cosmic Dawn) could be more powerful than our current best satellites at finding this specific type of Dark Matter decay.
2. This is especially true if the Dark Matter particles are heavy and decay into neutrinos.
3. If the Dark Matter is extremely heavy (like 10 times heavier than a proton), the difference between the decay types disappears, and the old CMB rules apply again.

Why Does This Matter?

If we can detect this signal, we won't just know that Dark Matter exists; we will know what it is made of and how it behaves. We could prove that Dark Matter isn't just a boring, invisible rock, but a dynamic particle that interacts with the universe in subtle, complex ways.

In short: The universe is whispering a secret about its invisible ingredients. The old photos (CMB) gave us a hint, but the new radio microphones (21-cm) might finally let us hear the whisper clearly, especially if the secret ingredient is a "ghostly" neutrino.

Technical Summary

1. Problem Statement

The paper addresses the potential existence of a subcomponent of Dark Matter (DM) that decays between the epoch of recombination ($z \sim 1100$) and reionization ($z \sim 6-10$). While standard cosmological models assume DM is a stable, cold, and collisionless fluid, many particle physics models predict DM instability.

• The Gap: Previous studies have largely focused on DM masses below the TeV scale or decays into photons/electrons. There is a need to understand the constraints on TeV-scale DM (specifically $0.5 - 10$ TeV) and decays into neutrinos, a channel often overlooked because neutrinos do not directly interact with the intergalactic medium (IGM).
• The Challenge: Decaying DM injects energy into the IGM, altering the ionization fraction ($x_e$) and gas temperature ($T_k$). These changes affect two key observables:
  1. Cosmic Microwave Background (CMB): via increased scattering of CMB photons.
  2. Global 21-cm Signal: via modifications to the spin temperature of neutral hydrogen during the "Cosmic Dawn" ($z \sim 10-20$).
• The Specific Question: Can future 21-cm radio telescopes provide tighter constraints on TeV-scale decaying DM (especially into neutrinos) than current CMB data, and how does the decay channel (photons vs. electrons vs. neutrinos) influence these constraints?

2. Methodology

The authors employ a multi-stage computational approach combining cosmological parameter estimation with astrophysical simulations.

A. Model Setup

• Subcomponent: A fraction $f_{\text{decay}}$ of the total DM density decays with a lifetime $\tau_\chi$.
• Decay Channels: The study considers decays into:
  • Photon pairs ($\gamma\gamma$)
  • Electron-positron pairs ($e^+e^-$)
  • Neutrino pairs ($\nu\nu$)
• Electromagnetic Efficiency ($\zeta_{\text{em}}$): For neutrino decays, the primary energy goes to neutrinos. However, for TeV-scale masses, electroweak gauge boson radiation (final state radiation) produces a fraction of electromagnetic energy. The authors use the PPPC4DMID spectra (via the code DarkHistory) to calculate $\zeta_{\text{em}}(M_\chi)$, which ranges from $<1\%$ at low masses to $\sim 10\%$ at 10 TeV.

B. CMB Constraints (Section 3)

• Code: CLASS (Cosmic Linear Anisotropy Solving System) coupled with MontePython for Markov Chain Monte Carlo (MCMC) analysis.
• Approximation: Uses the "on-the-spot" approximation, assuming energy deposition is instantaneous. An effective efficiency factor $f_{\text{eff}}$ is calibrated to match the free electron fraction ($x_e$) at $z=300$ calculated by DarkHistory.
• Data: Utilizes a comprehensive dataset including Planck 2018, ACT DR6, and SPT-3G.
• Goal: Derive 95% confidence upper limits on the decaying fraction $f_{\text{decay}}$.

C. 21-cm Signal Analysis (Section 4)

• Code: DM21cm, which interfaces DarkHistory (for energy injection history) with 21cmFAST (for non-linear evolution of the IGM, radiation fields, and 21-cm brightness temperature).
• Physics: The code tracks the evolution of the spin temperature ($T_S$), kinetic temperature ($T_k$), and ionization fraction ($x_e$).
  • DM decay heats the gas, reducing the depth of the 21-cm absorption trough (which occurs when $T_S < T_{\text{CMB}}$).
• Sensitivity Projections: Instead of a full Fisher analysis (which requires varying astrophysical parameters), the authors define three hypothetical detection thresholds for the deviation in global 21-cm temperature ($\Delta T_{21}$) at $z \sim 16$:
  • Optimistic: 30 mK
  • Intermediate: 50 mK
  • Pessimistic: 80 mK

3. Key Contributions

1. Extension to TeV Scale and Neutrinos: The paper extends previous constraints to DM masses up to 10 TeV and explicitly analyzes decays into neutrinos, a channel previously assumed to be negligible for sub-TeV masses but significant for TeV masses due to electroweak radiation.
2. Refutation of Simple Scaling: The authors demonstrate that the common approximation of simply rescaling constraints by the electromagnetic fraction ($\zeta_{\text{em}}$) is insufficient for 21-cm forecasts.
   • Reason: CMB constraints depend on total energy deposition at high redshift ($z \sim 300$), where the spectral distribution matters less.
   • Contrast: 21-cm constraints depend on energy deposition at lower redshifts ($z \sim 10-20$). The spectral distribution of injected energy (e.g., lower-energy electrons from neutrino decays vs. high-energy electrons from direct electron decays) significantly affects the efficiency of heating and ionization at these epochs.
3. New Simulation Framework: The integration of DarkHistory with DM21cm to handle the depletion of decaying DM subcomponents with lifetimes shorter than the age of the universe.

4. Results

A. CMB Constraints

• CMB limits are primarily sensitive to the total injected electromagnetic energy ($f_{\text{decay}} \times f_{\text{eff}} \times \zeta_{\text{em}}$).
• The constraints are relatively insensitive to the specific decay channel or DM mass (within the TeV range) once the total electromagnetic energy is accounted for.
• The derived limits are consistent with previous studies (e.g., Ref. [10]) but use a more sophisticated energy deposition treatment.

B. 21-cm Sensitivity vs. CMB

• Neutrino Decays ($\nu\nu$): This is the most significant finding. For DM masses around 1 TeV and lifetimes $\tau \gtrsim 10^{15}$ s, future 21-cm observations are more sensitive than current CMB data, even under pessimistic assumptions.
  • Mechanism: Decays into neutrinos produce a softer spectrum of electromagnetic energy (more low-energy electrons/positrons) compared to direct electron decays. These lower-energy particles deposit their energy more efficiently in the IGM at $z \sim 15$, leading to a stronger heating effect on the 21-cm signal.
• Electron/Photon Decays:
  • For $e^+e^-$ and $\gamma\gamma$ decays, 21-cm constraints generally surpass CMB limits only in the optimistic scenario (30 mK threshold).
  • The dependence on DM mass is stronger for electrons (lower mass = better sensitivity) due to the energy loss mechanisms (inverse Compton scattering).
• High Mass Regime ($M_\chi \sim 10$ TeV):
  • As mass increases, the spectral differences between decay channels diminish (due to the development of electromagnetic cascades).
  • For $M_\chi = 10$ TeV, the 21-cm sensitivity for neutrino decays converges toward that of photon/electron decays. In this regime, CMB constraints generally remain stronger than 21-cm projections unless the lifetime is very long ($\tau \sim 10^{16}$ s).

C. Parameter Space Coverage

• The study identifies a "sweet spot" for 21-cm detection: $\tau \sim 10^{15} - 10^{16}$ s and $M_\chi \sim 1$ TeV for neutrino decays. In this region, the 21-cm signal can probe decaying fractions ($f_{\text{decay}}$) roughly an order of magnitude lower than current CMB bounds.

5. Significance and Conclusion

• Complementarity: The paper establishes that global 21-cm observations are a powerful, complementary probe to the CMB for decaying DM, specifically for the "Dark Ages" and "Cosmic Dawn" epochs.
• Neutrino Channel: It highlights that decays into neutrinos, often ignored in sub-TeV studies, become a critical target for TeV-scale DM. The unique spectral signature of these decays makes them uniquely detectable via 21-cm heating, offering a path to constrain DM properties that CMB data alone cannot.
• Future Outlook: The authors note that while current 21-cm experiments (like EDGES or SARAS) have disputed signals, future telescopes (e.g., SKA, HERA) could achieve the necessary sensitivity. The study provides a roadmap for interpreting future data, emphasizing that simple scaling laws are insufficient and that detailed spectral modeling is required.
• Limitations: The analysis is currently limited to $M_\chi < 10$ TeV due to tabulation limits in DarkHistory, and relies on simplified astrophysical assumptions (though it uses non-linear 21-cmFAST simulations). Future work should include Fisher matrix analyses to account for astrophysical uncertainties in star formation.

In summary, this work demonstrates that future 21-cm radio telescopes have the potential to significantly improve constraints on TeV-scale dark matter decaying into neutrinos, probing lifetimes and fractions that are currently unconstrained by CMB observations.