[SKA 2026] Probing Inflationary Footprints: Can 21 cm Cosmology Reveal the Small-Scale Power Spectrum?

Executive Summary

The "Standard Model" of cosmology, $\Lambda$CDM, has been remarkably successful at explaining the large-scale structure of the universe. However, at the smallest scales—those hosting the very first dwarf galaxies and "minihalos"—the power spectrum remains a dark frontier. This paper explores the C25 model, an inflationary scenario where a sudden phase transition causes a $k^6$ surge in primordial fluctuations.

The core insight is that this enhancement doesn't just create more stars; it creates more "shrapnel" in the form of minihalos that suck up ionizing radiation. By simulating the Epoch of Reionization (EoR), the authors show that the Square Kilometre Array (SKA) can detect these small-scale "bumps" not by seeing the halos themselves, but by measuring the fragmented, Swiss-cheese morphology of the ionized universe through the 21 cm signal.

The Problem: The High-z "Excess" and the Missing Small-Scale Data

We have a data gap. The Ly$\alpha$ forest constrains the power spectrum up to $k\sim 10ext{Mpc}^{-1}$, but beyond that, we are blind. Recent JWST observations have hinted at an unexpected abundance of bright galaxies at $z>10$, which some argue contradicts standard $\Lambda$CDM.

If the power spectrum is enhanced at small scales, it could explain this excess. But there's a catch: enhancing small-scale fluctuations also boosts the number of minihalos ($T_{extvir}<10^4$ K). These halos don't form stars efficiently but act as potent "sinks," consuming ionizing photons through recombinations in their dense, self-shielded gas.

Methodology: Simulating a "Booster" Universe

The authors use the C25 model (Cielo et al. 2025) to modify the linear matter power spectrum. This model introduces a "bump" in power at a scale determined by $k_{exttrans}$.

1. The Halo Mass Function (HMF) Shift

As seen in the architecture of the paper's logic, the enhancement in power leads to a massive boost in the HMF for a specific mass range (see Figure 2 in the paper).

Figure 2: HMF for varying $k_{exttrans}$. Note the "bump" where the number of halos exceeds the $\Lambda$CDM fiducial model before hierarchical merging causes a deficit at even smaller scales.

2. Excursion-Set Reionization

The authors extend the standard 21cmFAST approach. Usually, we only care about ionizing sources. Here, the condition for a region to be ionized is: $N_{extion}\ge (1+{\bar{n}}_{extrec})N_{extH}+N_{\xi }$ Where $N_{\xi }$ represents the ionizing photons "sacrificed" to evaporate minihalos.

Results: Morphological Fragmentation

The most striking finding is the change in Bubble Size Distribution (BSD). In a universe with enhanced small-scale power, the ionized "bubbles" are smaller and more fragmented because minihalos act as roadblocks for the ionization fronts.

Figure 4: Comparison of 21 cm signal fields. At $k_{exttrans}=150ext{Mpc}^{-1}$ (top right), the ionized regions are much smaller and more numerous compared to the fiducial model (top left) for the same global neutral fraction.

Detectability with SKA

The 21 cm power spectrum deviations are statistically significant. Even after accounting for the "foreground wedge" (the noise from our own galaxy), the SKA-low AA* array can distinguish these models from $\Lambda$CDM, especially at the late stages of reionization ($z\sim 6$).

Critical Insight & Conclusion

The paper reveals a classic "competition" in astrophysics: Sources vs. Sinks.

• At low $k_{exttrans}$ ($150ext{Mpc}^{-1}$), sources win initially, making reionization start earlier.
• At high $k_{exttrans}$ ($400ext{Mpc}^{-1}$), sinks dominate, delaying the end of reionization.

Takeaway: We are entering an era where we can use the 3D map of neutral hydrogen to probe the physics of inflation. If SKA detects a "fragmented" reionization history, it may be the first direct evidence that our inflationary models need a "sudden transition" upgrade.

Limitations: The study assumes linear power spectrum evolution at small scales. In reality, non-linear growth and relative streaming velocities between dark matter and baryons could further complicate the minihalo gas content, potentially amplifying the "sink" effect even further.