Redshift-space 21-cm bispectrum multipoles as an SKA-era gravity test in the post-reionization Universe

TL;DR

This work develops a tree-level perturbation theory framework for the redshift-space 21-cm bispectrum in the post-reionization era, applied to ΛCDM and Hu-Sawicki f(R) gravity. By incorporating HI bias, Kaiser distortions, and FoG damping, the authors decompose the redshift-space signal into multipoles and quantify MG-induced deviations against a full covariance that includes cosmic variance and SKA-MID-like thermal noise. They find that the observable information is concentrated in the lowest multipoles, with the strongest gravity-test sensitivity arising from squeezed and stretched quasi-linear triangle configurations on scales k ~ 0.4–0.8 h/Mpc and redshifts z ~ 1–2, where MG effects produce percent-level enhancements relative to GR. The results demonstrate that 21-cm bispectrum multipoles offer a practical, SKA-ready observable for testing gravity beyond ΛCDM in the post-reionization Universe, while highlighting the need for more realistic modeling of bias, FoG, foregrounds, and survey systematics. Overall, this approach provides a promising complementary probe to power spectra for probing scale-dependent gravity and non-linear structure formation with upcoming 21-cm surveys.

Abstract

The redshifted 21-cm line from neutral hydrogen ($\textrm{H}\textsc{i}$) enables volumetric intensity mapping of large-scale structure in the post-reionization Universe. In anticipation of \texttt{SKA-MID}'s wide redshift coverage and high signal-to-noise clustering measurements, we study the redshift-space 21-cm bispectrum and its spherical-harmonic multipoles as probes of anisotropic non-linear structure formation and departures from General Relativity. Using a tree-level perturbative description for the 21-cm brightness-temperature field in redshift space, and adopting the Hu--Sawicki $f(R)$ model as a representative modified-gravity scenario, we forecast the detectability of configuration-dependent signatures with an \texttt{SKA-MID}--like survey. We derive the bispectrum-multipole covariance including sample variance and thermal noise and evaluate the expected signal-to-noise of deviations relative to $Λ$CDM. We find that the observable information is dominated by the lowest multipoles, while higher-order modes are strongly suppressed. This concentration in the lowest multipoles is well matched to \texttt{SKA-MID} sensitivity and to the quasi-linear modes that are expected to remain accessible in practice. The strongest modified-gravity sensitivity arises from squeezed and stretched triangle configurations on quasi-linear scales, where scale-dependent growth enhances the bispectrum relative to the total variance. Our results position 21-cm bispectrum multipoles as a practical, SKA-ready observable for testing gravity beyond $Λ$CDM in the post-reionization epoch.

Figures (9)

• Figure 1: Reduced redshift-space $\textrm{H}\textsc{i}$ bispectrum multipoles $Q_\ell^0(\mu,t)$ in the $(\mu,t)$ plane for a fiducial $\Lambda$CDM cosmology, evaluated at $k_1=0.1\,h\,\mathrm{Mpc}^{-1}$ and $z=2$. The reduced multipoles are defined as $Q_\ell^m \equiv B_\ell^m/B_{\text{H}\textsc{i}}^{\rm r}$, where $B_\ell^m$ are the spherical-harmonic multipoles of the redshift-space bispectrum (including Kaiser RSD and FoG damping), and $B_{\text{H}\textsc{i}}^{\rm r}$ is the real-space bispectrum. The monopole $Q_0^0$ shows a strong overall enhancement relative to real space across most of the allowed triangle domain, while the quadrupole $Q_2^0$ captures the leading anisotropic response and is largest toward nearly linear configurations ($\mu\to 1$), particularly for stretched triangles ($t\lesssim 0.8$). Higher-order $m=0$ multipoles ($\ell\ge 4$) are progressively suppressed and exhibit oscillatory structure across the $(\mu,t)$ plane, indicating that the dominant RSD-induced information is concentrated in the lowest multipoles.
• Figure 2: Reduced redshift-space $\textrm{H}\textsc{i}$ bispectrum multipoles $Q_\ell^m(\mu,t)$ in $\Lambda$CDM at $k_1=0.1\,h\,\mathrm{Mpc}^{-1}$ and $z=2$, shown for azimuthal modes $m=1$ (top row) and $m=2$ (bottom row) and for $\ell=2,4,6,8$ (left to right). For $m=1$, the dominant contribution is $Q_2^1$, with its largest amplitude localized near the squeezed/near-linear boundary of configuration space, while higher-$\ell$ modes are strongly suppressed by angular cancellations. For $m=2$, the leading signal arises from $Q_2^2$, with $\ell\ge 4$ multipoles exhibiting weaker, more oscillatory patterns and substantially smaller amplitudes. Overall, these panels illustrate that measurable azimuthal anisotropy is primarily carried by the lowest-order multipoles, motivating the focus on low $(\ell,m)$ in subsequent detectability forecasts.
• Figure 3: Scale dependence of linear growth in Hu--Sawicki $f(R)$ gravity. Left: the logarithmic growth rate $f(k)$ normalized by its large-scale value $f_0\equiv f(k=10^{-4}\,h\,\mathrm{Mpc}^{-1})$, shown for several $|f_{R0}|$ values. Right: the ratio of the linear matter power spectrum in $f(R)$ to that in $\Lambda$CDM for the same parameters. In both panels, solid and dotted curves correspond to $z=0$ and $z=2$, respectively. Deviations from $\Lambda$CDM increase toward smaller scales (larger $k$), while they are reduced at higher redshift. These trends reflect the Yukawa-like enhancement of gravity below the Compton wavelength in HS-$f(R)$ and motivate searching for modified-gravity signatures in quasi-linear and small-scale clustering statistics.
• Figure 4: Ratios of redshift-space $\textrm{H}\textsc{i}$ bispectrum multipoles in Hu--Sawicki $f(R)$ gravity relative to $\Lambda$CDM, evaluated at $z=2$ and $k_1=0.1\,h\,\mathrm{Mpc}^{-1}$ for $|f_{R0}|=10^{-5}$. Each heatmap shows $R_\ell^m(k_1,\mu,t)\equiv B_\ell^m|_{\rm HS}/B_\ell^m|_{\Lambda{\rm CDM}}$ across the allowed $(\mu,t)$ triangle domain. The lowest multipoles exhibit coherent percent-level departures, with the monopole and quadrupole ratios enhanced most strongly toward nearly linear configurations. Higher-order multipoles display more distinctive configuration dependence: in particular, the $\ell=4$ modes show localized regions of larger fractional deviations, including both enhancement and suppression depending on $(\mu,t)$.
• Figure 5: Signal-to-noise ratio (SNR) maps for modified-gravity signatures in redshift-space $\textrm{H}\textsc{i}$ bispectrum multipoles for an SKA-MID-like intensity-mapping survey, shown in the $(\mu,t)$ plane at $z=2$ and $k_1=0.1\,h\,\mathrm{Mpc}^{-1}$ for HS-$f(R)$ with $|f_{R0}|=10^{-5}$. The signal is defined as the multipole difference $\Delta B_\ell^m \equiv B_\ell^m|_{\rm HS}-B_\ell^m|_{\Lambda{\rm CDM}}$, and the noise is given by the diagonal covariance $C_{\ell\ell}^{mm}$ computed from Eq. \ref{['eq:cov']}. The detectability is concentrated toward nearly linear configurations ($\mu\to 1$), with stretched and squeezed triangles providing the highest SNR, while equilateral and L-isosceles configurations are strongly suppressed. The overall SNR is dominated by the $m=0$ multipoles, with azimuthal modes ($m=1,2$) contributing significantly only in localized regions near the high-$\mu$ boundary.