Probing initial isocurvature perturbation with 21cm one-point statistics

Technical Summary: Probing Initial Isocurvature Perturbation with 21cm One-Point Statistics

Problem Statement
While the Cosmic Microwave Background (CMB) has provided precise constraints on primordial adiabatic perturbations, the existence of isocurvature perturbations—predicted by multi-field inflation models and cosmic defects—remains weakly constrained, particularly on small scales. Standard CMB constraints are primarily applicable to large-scale (low-$k$) modes; however, if the isocurvature spectrum is blue-tilted (large spectral index), its contribution at small scales can be significantly enhanced. The paper addresses the need to probe these small-scale isocurvature modes during the Cosmic Dawn (CD) and the Epoch of Reionization (EoR), where the 21cm hydrogen line offers a unique three-dimensional probe of the Intergalactic Medium (IGM). While previous work (e.g., Minoda et al.) suggested the global 21cm signal could constrain isocurvature, this work investigates the specific constraining power of one-point statistics (variance and skewness) of the 21cm brightness temperature, offering a complementary approach to traditional power spectrum analyses.

Methodology
The authors employ semi-numerical simulations using the 21cmFAST code to model the evolution of the 21cm signal from redshift $z=30$ to $z=6$.

• Physical Modeling: The simulations incorporate both adiabatic and Cold Dark Matter (CDM) isocurvature perturbations. The initial power spectra are defined by amplitudes ($A_{adi}, A_{iso}$) and spectral indices ($n_{adi}, n_{iso}$). The total matter power spectrum is constructed as the sum of uncorrelated adiabatic and isocurvature contributions, modulated by their respective transfer functions. The study focuses on the isocurvature fraction $r_{CDM}$ and the isocurvature spectral index $n_{iso}$.
• Astrophysical Models: To account for astrophysical uncertainties, three distinct models are tested, constrained by HERA observations. These models vary parameters governing the stellar-to-halo mass relation ($\alpha_*$), minimum halo mass for star formation ($M_{turn}$), star formation timescale ($t_*$), and the X-ray luminosity-to-star formation rate ratio ($\ell_X$).
• Statistical Observables: The study focuses on the redshift evolution of the variance ($\sigma^2$) and skewness ($\gamma$) of the 21cm brightness temperature ($\delta T_b$). These are calculated from pixelized maps (simulated at $1.5 \text{ cMpc}$ resolution) and smoothed to a $12 \text{ Mpc}$ scale to match the expected beam of the Square Kilometre Array (SKA).
• Noise and Forecasting: Realistic instrumental thermal noise, based on SKA Phase 1 configurations, is included. A Fisher matrix analysis is performed using only the redshift evolution of the variance and skewness (excluding the full power spectrum) to forecast constraints on six parameters: $r_{CDM}$, $n_{iso}$, and the four astrophysical parameters.

Key Contributions

1. Systematic Forecast: The paper provides the first systematic forecast of CDM isocurvature constraints derived specifically from 21cm one-point statistics under realistic SKA-like noise conditions.
2. Diagnostic Utility: It establishes the 21cm power spectrum as a physical diagnostic for understanding the impact of isocurvature on structure formation timing, while utilizing one-point statistics as the primary basis for parameter inference.
3. Degeneracy Analysis: The work explicitly quantifies the interplay between cosmological isocurvature parameters and astrophysical uncertainties (star formation and X-ray heating efficiency) in the context of one-point statistics.

Results

• Impact on Structure Formation: Isocurvature perturbations, particularly with blue-tilted spectra, enhance small-scale density fluctuations. This accelerates the formation of the first stars and galaxies, leading to an earlier onset of Wouthuysen-Field coupling, X-ray heating, and reionization.
• Variance vs. Skewness:
  • Variance: Highly sensitive to the timing of cosmic events. Increasing $r_{CDM}$ or $n_{iso}$ shifts the characteristic peaks in the variance (associated with reionization and X-ray heating) to higher redshifts ($\Delta z \approx 2.8$ for reionization and $\Delta z \approx 8.7$ for X-ray heating when $r_{CDM}$ increases from 0 to 0.1). The amplitude of these peaks remains largely unchanged, indicating that isocurvature primarily affects the timing of events. Variance provides tight constraints on parameters.
  • Skewness: More sensitive to localized, non-Gaussian features (e.g., patchy heating). While it also shifts to higher redshifts with increased isocurvature, it is significantly more affected by astrophysical uncertainties and observational noise.
• Forecasted Constraints:
  • Using a joint analysis of variance and skewness, the authors forecast that the isocurvature fraction ($r_{CDM}$) can be constrained to the percent level ($\Delta r_{CDM} \simeq 1.8 \times 10^{-3}$) and the spectral index ($n_{iso}$) to $\Delta n_{iso} \simeq 8.4 \times 10^{-3}$, assuming SKA Phase 1 sensitivity and 1000 hours of integration.
  • Degeneracy: A strong degeneracy exists between $r_{CDM}$ and $n_{iso}$. Both parameters enhance small-scale power and shift 21cm features to higher redshifts, making them difficult to disentangle using 21cm one-point statistics alone.
  • Astrophysical Impact: Astrophysical parameters (like $M_{turn}$ and X-ray efficiency) affect both the timing and the amplitude/shape of the variance peaks, distinguishing their impact from the primarily timing-driven effect of isocurvature.

Significance and Claims
The paper claims that 21cm one-point statistics serve as robust and independent tools for probing early-Universe physics beyond the reach of traditional power spectrum analyses.

• Complementarity: The work highlights that while variance offers high signal-to-noise constraints on the timing of cosmic milestones, skewness provides complementary information on non-Gaussian features, though it is more noise-limited.
• Limitations and Future Directions: The authors modestly note that the strong degeneracy between $r_{CDM}$ and $n_{iso}$ cannot be fully broken by 21cm one-point statistics alone. They suggest that complementary probes, such as the 21cm forest and galaxy surveys, are necessary to resolve these parameter degeneracies.
• Methodological Scope: The study acknowledges that the Fisher formalism assumes Gaussian likelihoods and may not fully capture information in non-Gaussian statistics; thus, simulation-based inference methods are recommended for future work to exploit higher-order moments fully. The paper concludes that precision 21cm measurements will become a powerful probe of fundamental physics, including primordial non-Gaussianity and exotic dark matter scenarios, in the coming decade.