Subhalo Abundance Matching in $f(R)$ Gravity

Using the liminality $N$-body simulations of Shi et al., we present the first predictions for galaxy clustering in $f(R)$ gravity using subhalo abundance matching. We find that, for a given galaxy density, even for an $f(R)$ model with $f_{R0}=-{10}^{-6}$, for which the cold dark matter clustering is very similar to the cold dark matter model with a cosmological constant ($\mathrm{\Lambda }\mathrm{CDM}$), the predicted clustering of galaxies in the $f(R)$ model is very different from $\mathrm{\Lambda }\mathrm{CDM}$. The deviation can be as large as 40% for samples with mean densities close to that of $L_{*}$ galaxies. This large deviation is testable given the accuracy that future large-scale galaxy surveys aim to achieve. Our result demonstrates that galaxy surveys can provide a stringent test of general relativity on cosmological scales, which is comparable to the tests from local astrophysical observations.

Figure 1

The global cumulative subhalo abundance as a function of halo mass $M_{200}$ (left), and the current maximum circular velocity $v_{\max }$ and $v_{\mathrm{peak}}$ (right). Here the subhalo catalogs include both satellite and main subhalos. In $\mathrm{\Lambda }\mathrm{CDM}$, the cumulative subhalo number counts as a function of mass are well approximated by a power law. However, the mass function in the $f(R)$ model is more complicated. At the high mass end, $M>10^{13}{h}^{-1}{M}_{\odot }$, due to the efficient screening, the cumulative subhalo number counts in the $f(R)$ model are very close to those in $\mathrm{\Lambda }\mathrm{CDM}$. However, at the low mass end, the abundance of subhalos in the $f(R)$ model is higher than in $\mathrm{\Lambda }\mathrm{CDM}$ due to the enhanced gravity in unscreened halos. The enhancement is more significant in the effective halo catalog of the $f(R)$ model since the effective mass is used in this case. For the subhalo abundance plotted in terms of $v_{\max }$ and $v_{\mathrm{peak}}$ (right), compared with $v_{\max }$ (dashed lines), using $v_{\mathrm{peak}}$ (solid lines) enhances the overall abundance of subhalos in the $f(R)$ model even for the most massive ones. In the right panel, the dotted lines show the abundance of satellite subhalos (excluding main subhalos) selected using $v_{\mathrm{peak}}$ for $\mathrm{\Lambda }\mathrm{CDM}$ (black), the $f(R)$ standard halo catalog (blue) and the $f(R)$ effective halo catalog (red). The abundance of satellite subhalos is relatively complete for the full subhalo samples investigated with mean number densities $⟨n_g⟩=0.01[\mathrm{Mpc}/h{]}^{-3}$ and $⟨n_g⟩=0.02[\mathrm{Mpc}/h{]}^{-3}$.

Figure 2

The mean number of selected satellite subhalos (excluding main subhalos) per host halo as a function of the mass of their host halo for $\mathrm{\Lambda }\mathrm{CDM}$ (black points), the $f(R)$ standard halo catalog (blue points), and the $f(R)$ effective halo catalog (red points), respectively. Left: subhalos are selected by their current maximum circular velocity $v_{\max }>100\mathrm{km}/\mathrm{s}$. At the high mass end, $M>10^{13}{h}^{-1}{M}_{\odot }$, due to the screening mechanism in the $f(R)$ model, the mean satellite subhalo occupations of the $f(R)$ model and $\mathrm{\Lambda }\mathrm{CDM}$ are very similar to one another and the mean number of selected satellite subhalos per host halo is proportional to the mass of their host halos $⟨N_{\mathrm{sub}}⟩\propto M$. However, at the low mass end, using $v_{\max }$ tends to select more satellite subhalos per host halo in the $f(R)$ model than in $\mathrm{\Lambda }\mathrm{CDM}$ since unscreened halos in the $f(R)$ model experience enhanced gravity and therefore a boosted value of $v_{\max }$. Right: similar to the left panel but subhalos are selected by $v_{\mathrm{peak}}$. In contrast to $v_{\max }$, using $v_{\mathrm{peak}}$ enhances the overall selection of subhalos in the $f(R)$ model even for the most massive ones.

Figure 3

The predicted three-dimensional two-point galaxy correlation functions from the SHAM model (upper panels). The shaded regions represent the $1\sigma$ Poisson errors. The lower panels show the fractional differences between the $f(R)$ model and $\mathrm{\Lambda }\mathrm{CDM}$. The left panels show the results for a galaxy density $⟨n_g⟩=0.01[\mathrm{Mpc}/h{]}^{-3}$ and the right panels are for $⟨n_g⟩=0.02[\mathrm{Mpc}/h{]}^{-3}$. For comparison, the dashed lines show the results obtained using the current maximum circular velocity $v_{\max }$.