High-redshift test of gravity using enhanced growth of small structures probed by the neutral hydrogen distribution

Future 21-cm intensity mapping surveys such as SKA can provide precise information on the spatial distribution of the neutral hydrogen (HI) in the postreionization epoch. This information will allow us to test the standard $\mathrm{\Lambda }$ cold dark matter paradigm and with that the nature of gravity. In this work, we employ the shybone simulations, which model galaxy formation in $f(R)$ modified gravity using the IllustrisTNG model, to study the effects of modified gravity on HI abundance and power spectra. We find that the enhanced growth low-mass dark matter halos experience in $f(R)$ gravity at high redshifts alters the HI power spectrum and can be observable through 21-cm intensity mapping. Our results suggest that the HI power spectrum is suppressed by $\sim 13\%$ on scales $k\lesssim 2h{\mathrm{Mpc}}^{-1}$ at $z=2$ for F6, a $f(R)$ model which passes most observational constraints. We show that this suppression can be detectable by SKA1-MID with 1000 hours of exposure time, making HI clustering a novel test of gravity at high redshift.

Figure 1

Top panel: Overall HI abundance, ${\mathrm{\Omega }}_{\mathrm{HI}}(z)={\overline{\rho }}_{\mathrm{HI}}(z)/{\rho }_{\mathrm{c}0}$, where ${\overline{\rho }}_{\mathrm{HI}}(z)$ is the mean HI density, from GR (black), F6 (blue), and F5 (green), compared with observationally measured values (symbols). Solid lines refer to S25 simulations, while dashed lines refer to S62 simulations. Bottom panel: The relative differences of the simulation predictions from F6 (blue) and F5 (green) with respect to GR.

Figure 2

HI mass contained in each halo at $z=3$ and $z=2$ measured from the S25 simulations for GR, F6, and F5, respectively (as labeled). The green solid line in each panel shows the best-fit curve obtained from Eq. (9). The best-fit values of the free parameters are displayed in Table 1. The cyan dotted line indicates the best-fit curve of Eq. (9) found in [34] for GR. The blue vertical line indicates the mass of halos with around 50 DM (simulation) particles in S25.

Figure 3

Neutral hydrogen power spectra and halo mass functions at $z=2$ (upper panels) and $z=3$ (lower panels) for GR (black), F6 (blue), and F5 (green). Left panels: Real-space HI power spectra $P_{\mathrm{HI}}$. Dashed lines show the results for S62, while solid lines show those for S25. The real-space power spectra are taken from Ref. [46]. Central panels: Same as the left panels but for the redshift space (monopole) HI power spectra. The cyan shaded areas in the lower subpanels represent the expected errors for SKA1-MID measurements for GR, assuming 1000 observing hours. The error bars are calculated using the GR redshift space power spectrum measured from S25. Right panels: Differential halo mass functions as shown in [69], for comparison. Solid (dashed) lines show the results from full-physics S25 (S62) simulations. Symbols indicate the results from DMO S62 simulations. The lower subpanels show the relative differences to GR.

Figure 4

The ratios of the F5 (green) and F6 (blue) HI power spectra with respect to GR for the actual real-space HI power spectrum (symbols) and the halo HI power spectrum (lines), $P_{\mathrm{HI},\text{halo}}$, as defined in the text, at $z=2.0$ (upper panel) and $z=3.0$ (lower panel). Solid lines and full circles show the results from S25, while dashed lines and empty circles show the results from S62.

Figure 5

Number density of halos with HI mass $\ge M_{\mathrm{HI}}^{\star }={10}^6{\mathrm{M}}_{\odot }$, for GR (black), F6 (blue), and F5 (green) at $z=2.0$ (left panel) and 3.0 (right panel). Solid lines show the results for S25, while dashed lines represent those from S62. The vertical grey dashed lines indicate halos with $\sim 50$ particles in S62. We do not show the corresponding limit for S25 because it is at around $\sim 6\times {10}^8{\mathrm{M}}_{\odot }$, so it is outside the halo mass range shown in the figure.