A future test of gravitation using galaxy cluster velocities

The accelerating expansion of the Universe at recent epochs has called into question the validity of general relativity on cosmological scales. One probe of gravity is a comparison of expansion history of the Universe with the history of structure growth via gravitational instability: general relativity predicts a specific relation between these two observables. Here we show that the mean pairwise streaming velocity of galaxy clusters provides a useful method of constraining this relation. Galaxy cluster velocities can be measured via the kinetic Sunyaev-Zeldovich distortion of the cosmic microwave background radiation. Future surveys can provide large enough catalogs of cluster velocities to discriminate between general relativity and other proposed gravitational theories.

Figure 1

The $1\mathrm{\text{−}}\sigma$ constraint on the growth index $\gamma$ in a seven-parameter spatially flat cosmological model, constrained by a galaxy cluster velocity survey of 4000 clusters chosen via the Sunyaev-Zeldovich effect, as a function of assumed velocity errors. Prior parameter constraints anticipated from the Planck satellite measurement of the primary microwave background power spectrum [32], plus the current Hubble parameter constraint $H_0=74.2\pm 3.6\mathrm{km}/\mathrm{s}{\mathrm{Mpc}}^{-1}$ [33] are included.