Using measurements of the cosmic bulk flow to constrain $f(R)$ Gravity

As an alternate explanation for the cosmic acceleration, f(R) theories of gravity can predict an almost identical expansion history to standard λ cold dark matter (λCDM), yet make very different predictions for the growth of cosmological structures. Measurements of the cosmic bulk flow provide a method for determining the strength of gravity over the history of structure formation. We use the modified gravity N-body code ECOSMOG to simulate dark matter particles and make predictions for the bulk flow magnitude in both λCDM and f(R) gravity. With the peculiar velocities output by ECOSMOG, we determine the bulk flow at depths ranging from 20 to 50 hMpc, following the redshift and sky distribution of the 2MASS Tully-Fisher survey (2MTF). At each depth, we find that the λCDM and fR0 = 10 simulations produce bulk flow measurements that are consistent with λCDM predictions and the 2MTF survey at a 1σ level. We also find that adopting an f(R) strength of fR0 = 10 predict a much larger value for the bulk flow, which disagree with λCDM predictions at all depths considered. We conclude that fR0 must be constrained to a level no greater than 10 to agree with bulk flow measurements.