Clear and Measurable Signature of Modified Gravity in the Galaxy Velocity Field

The velocity field of dark matter and galaxies reflects the continued action of gravity throughout cosmic history. We show that the low-order moments of the pairwise velocity distribution $v_{12}$ are a powerful diagnostic of the laws of gravity on cosmological scales. In particular, the projected line-of-sight galaxy pairwise velocity dispersion ${\sigma }_{12}(r)$ is very sensitive to the presence of modified gravity. Using a set of high-resolution $N$-body simulations, we compute the pairwise velocity distribution and its projected line-of-sight dispersion for a class of modified gravity theories: the chameleon $f(R)$ gravity and Galileon gravity (cubic and quartic). The velocities of dark matter halos with a wide range of masses would exhibit deviations from general relativity at the $(5–10)\sigma$ level. We examine strategies for detecting these deviations in galaxy redshift and peculiar velocity surveys. If detected, this signature would be a “smoking gun” for modified gravity.

Figure 1

The scale dependence of the pairwise velocity moments extracted from HOD mock galaxy catalogs. The black solid lines show the GR case, whereas the red dashed lines show the $F4$ model. The thin red and black lines show minus the mean streaming velocity $-v_{12}(r)$, scaled down by factor of 2 for clarity; the lines with filled circles show the dispersion ${\sigma }_{12}(r)$. The shaded region represents an illustrative error as in Refs. [3] and [4]. The dotted green line shows the Hubble velocity $H_{0}r$, also scaled down for comparison.

Figure 2

Comparison of absolute values (top panel in each pair) and the relative deviation from the GR case (bottom panel in each pair) of the 2-point correlation function ${\xi }_2(r)$ (top-left panels); minus the mean streaming velocity $-v_{12}(r)$ (top-right panels); the pairwise velocity dispersion ${\sigma }_{\parallel }(r)$ (bottom-left panels); and the projected pairwise velocity dispersion ${\sigma }_{12}(r)$ (bottom-right panels). The data are binned in halo mass $M_{200}$ and shown at two different pair separations: 1 and $5h^{-1}\mathrm{Mpc}$. The legend in the panel for ${\xi }_2(5h^{-1}\mathrm{Mpc})$ gives the colors and symbols that we use to distinguish the different models. Top panels show only the LCDM and $f(R)$ cases; the QCDM and Galileon cases were omitted for clarity.