Cosmological Implication of Cross-correlation between Galaxy Clustering and 21-cm Line Intensity Mapping

Technical Summary: Cosmological Implication of Cross-Correlation between Galaxy Clustering and 21-cm Line Intensity Mapping

Problem Statement
Current cosmological models face challenges in simultaneously constraining cosmic expansion and the growth of structure due to limitations in theoretical modeling and observational degeneracies. While anisotropic galaxy clustering in redshift space offers a probe for both the Alcock–Paczynski (AP) effect and redshift-space distortions (RSD), the applicability of standard perturbation theory is limited by non-perturbative smearing effects, specifically the "Fingers-of-God" (FoG) effect caused by virialized random motions within halos. This necessitates restricting analyses to large scales ($k \lesssim 0.1 \, h \, \text{Mpc}^{-1}$), which severely reduces statistical power. Furthermore, existing analyses of 21-cm line intensity mapping (LIM) often suffer from a strong degeneracy between the neutral hydrogen (HI) mass content ($\Omega_{\text{HI}}$) and the HI linear bias ($b_{\text{HI}}$), preventing precise measurements of post-reionization astrophysics. Standard linear-regime assumptions are insufficient to break this degeneracy, and current constraints on $\Omega_{\text{HI}}$ are limited by cosmic variance and selection biases in stacked emission studies.

Methodology
The authors propose a joint analysis framework combining galaxy clustering (specifically spectroscopic surveys like DESI) and 21-cm LIM. The core of their methodology is a generalized formalism for auto- and cross-correlation power spectra that extends RSD modeling into the quasi-nonlinear regime ($k \lesssim 2 \, h^{-1} \, \text{Mpc}$, with practical analysis up to $k_{\text{max}} \approx 0.2 \, h \, \text{Mpc}^{-1}$).

Key methodological components include:

• Hybrid RSD Model: The power spectrum is decomposed into perturbative terms (valid up to two-loop order) and a non-perturbative FoG damping factor ($D_{\text{FoG}}$). This model incorporates higher-order corrections ($A, B, T, F$ terms) derived from the product of density and velocity fields, allowing for the inclusion of nonlinear effects that break degeneracies between bias and growth parameters.
• Double-Tracer Formalism: The authors extend the formalism to a double-tracer case (galaxies $g$ and HI $H$), utilizing the fact that peculiar velocities are consistent across different tracers. This allows the cross-power spectrum ($P_{gH}$) to be constructed from the same underlying matter power spectra ($P_{\delta\delta}, P_{\delta\Theta}, P_{\Theta\Theta}$) but modulated by distinct bias parameters ($b_g, b_H$).
• Fisher Matrix Analysis: A Fisher forecast is performed for a survey configuration similar to DESI (focusing on Emission Line Galaxies at $z \sim 1$) combined with a 21-cm survey (modeled after SKA-MID). The analysis accounts for various noise sources, including shot noise, antenna temperature, and residual foregrounds (modeled via a fudge factor $f_r$). The parameter set includes cosmological parameters ($\alpha_\perp, \alpha_\parallel, f\sigma_8, \sigma_8, A_S$), nuisance parameters (biases $b_{1,2}$, FoG damping $\sigma_p$), and the astrophysical parameter $x_{\text{HI}}$ (neutral hydrogen fraction).

Key Contributions and Results
The study demonstrates that combining galaxy and 21-cm observables offers distinct advantages over single-tracer analyses:

1. Breaking Degeneracies in Structure Growth:

   • Single-tracer analyses (galaxy auto or HI auto) exhibit strong degeneracies between the linear growth rate ($f\sigma_8$) and the amplitude of fluctuations ($\sigma_8$), particularly when constrained by the FoG damping parameter.
   • The joint analysis (combining $P_{gg}$, $P_{HH}$, and $P_{gH}$) significantly breaks this degeneracy. The authors find that constraints on the growth of structure ($f\sigma_8$) and the amplitude of matter fluctuations ($\sigma_8$) are improved by a factor of two relative to galaxy auto-correlation alone.
   • Crucially, the velocity growth rate $f\sigma_8$ can be constrained to sub-percent precision, a result that remains robust even under conservative assumptions regarding foreground removal.

2. Precision Measurement of Neutral Hydrogen Content ($\Omega_{\text{HI}}$):

   • The most significant finding is the ability to constrain the neutral hydrogen fraction $x_{\text{HI}}$ (and thus $\Omega_{\text{HI}}$) to a sub-percent level (e.g., $\sim 0.3\%$ error for optimistic noise scenarios).
   • This precision is achieved by breaking the inherent degeneracy between $x_{\text{HI}}$ and $b_{\text{HI}}$. In the authors' formalism, $x_{\text{HI}}$ acts as a global amplitude multiplier, while $b_{\text{HI}}$ induces a distinct angular dependence in the redshift-space power spectrum. The nonlinear RSD effects allow these angular dependencies to be disentangled, a feat not possible with linear-regime analysis or HI auto-correlation alone.
   • This level of precision surpasses current constraints from stacked 21-cm emission and Lyman-$\alpha$ forest observations.

3. Cosmic Expansion Constraints:

   • Regarding geometric distances (AP effect), the joint analysis offers a modest improvement (roughly a factor of two) over the best single-tracer constraints.
   • The authors note that the constraining power for distances is driven primarily by the auto-power spectrum with the highest signal-to-noise ratio (typically the HI auto-correlation in ideal scenarios). The cross-correlation does not dramatically improve distance measurements compared to the growth parameter constraints.

Significance and Claims
The paper claims that the cross-correlation approach effectively compensates for the loss of constraining power when using galaxy clustering alone, particularly in the nonlinear regime. By fully incorporating nonlinear RSD and utilizing the statistical power of cross-correlation, the method unlocks the potential to probe post-reionization astrophysics with unprecedented precision.

Specifically, the authors assert that:

• The method breaks the degeneracy between $\Omega_{\text{HI}}$ and $b_{\text{HI}}$ inherent in linear power-spectrum analyses.
• The resulting sub-percent precision on $\Omega_{\text{HI}}$ would far surpass existing constraints and allow for the study of the temporal evolution of neutral hydrogen and the minimum mass of hydrogen clumps (related to Jeans-mass filtering).
• The approach provides a more robust and realistic forecast for future joint HI and galaxy analyses by remaining model-independent regarding the cosmological framework and explicitly accounting for residual radio foregrounds.

The authors conclude that while the improvement in distance measurements is modest, the dramatic improvement in measuring growth parameters and the neutral hydrogen content represents a major advancement for next-generation cosmology.