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

The apparent anisotropies of galaxy clustering and 21-cm mapping in redshift space offer a unique opportunity to simultaneously probe cosmic expansion and gravity on cosmological scales through the Alcock-Paczynski (AP) effect and redshift-space distortions (RSD). Although improved theoretical models exist for anisotropic clustering, their applicability is limited by the non-perturbative smearing effect caused by the randomness of relative velocities. Here, we consider an alternative approach using the statistical power of cross-correlation between galaxy clustering and 21-cm line intensity mapping. Based on Fisher matrix analysis, fully incorporating nonlinear RSD, we estimate the benefit of combining both observables. We find that, for spectroscopy surveys like DESI combined with 21-cm line-intensity mapping surveys, the constraint on the growth of structure is improved by a factor of two relative to the galaxy auto-correlation, while the constraint on the cosmic expansion is only slightly improved. Crucially, such an observation can strongly constrain the neutral hydrogen (HI) content Omega_HI to a sub-percent level. This level of precision unlocks the potential of this method to probe post-reionization astrophysics with enhanced precision. It would far surpass existing constraints from stacked 21-cm emission (resulting in ~ 50%-100% uncertainties) and break the degeneracy between Omega_HI and the HI bias b_HI inherent in linear-regime power spectrum analysis. This cross-correlation approach effectively compensates for the loss of constraining power when using galaxy clustering alone.

💡 Research Summary

This paper presents a novel cosmological probe by leveraging the cross-correlation between galaxy clustering surveys and 21-cm line intensity mapping (LIM). The primary goal is to simultaneously constrain cosmic expansion history and the growth of structure with enhanced precision, while also breaking long-standing degeneracies in astrophysical parameters related to neutral hydrogen (HI).

The authors begin by outlining the cosmological significance of anisotropic clustering in redshift space, which encodes information via the Alcock-Paczynski (AP) effect (sensitive to geometry: H(z), D_A(z)) and redshift-space distortions (RSD) (sensitive to dynamics: growth rate f). However, traditional analyses using galaxy auto-correlation alone are limited. Theoretical models struggle to accurately describe the non-perturbative “Finger-of-God” (FoG) effect caused by random virial motions within halos, forcing analyses to use only large, linear scales (k < 0.1 h/Mpc) and thus sacrificing considerable statistical power.

To overcome this, the paper proposes using the cross-power spectrum between a spectroscopic galaxy survey (like DESI) and a 21-cm LIM survey. The key methodological advance is the development of a comprehensive model for the anisotropic power spectrum that fully incorporates nonlinear RSD effects, including the FoG effect, for both auto- and cross-correlations. The model decomposes the power spectrum into linear terms, higher-order perturbative terms (A, B, T, F), and a non-perturbative FoG damping factor. For the galaxy field, a nonlinear bias model is adopted. This formalism allows the FoG parameter (σ_p, the line-of-sight velocity dispersion) to be marginalized over, isolating the cosmological signal.

Using Fisher matrix forecasting, the authors quantify the benefits of this cross-correlation approach for a representative survey combination at z ~ 1. The main findings are threefold:

1. Improved Growth Constraints: The constraint on the growth of structure parameter (f σ8) is improved by a factor of approximately two compared to using the galaxy auto-correlation alone. The cross-correlation helps break the degeneracy between the coherent infall motion (which probes growth) and the FoG damping.
2. Precise HI Astrophysics: The method can constrain the cosmic density of neutral hydrogen, Ω_HI, to a sub-percent level of precision (~1%). This is a dramatic improvement over existing methods: stacking of 21-cm emission from individual galaxies yields uncertainties of 50-100%, while linear-theory analysis of the 21-cm auto-power spectrum suffers from a perfect degeneracy between Ω_HI and the HI bias b_HI. The nonlinear RSD modeling in the cross-correlation effectively breaks this degeneracy.
3. Modest Gain on Geometry: Constraints on the geometric AP parameters (H(z), D_A(z)) see only a slight improvement over the galaxy-only case.

The paper concludes that this cross-correlation technique represents a powerful synergy between upcoming optical and radio surveys. It not only compensates for the loss of constraining power in galaxy-only analyses due to nonlinear systematics but also unlocks a new, precise window into post-reionization HI astrophysics. By delivering simultaneous, tight constraints on cosmology and astrophysics, this approach will be instrumental in testing theories of dark energy, modified gravity, and the evolution of neutral gas in the universe.