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

As an alternative explanation for the cosmic acceleration, $f(R)$ theories of gravity can predict an almost identical expansion history to standard $\Lambda$CDM, yet make very different predictions for the growth of cosmological structures. Measurements of the cosmic bulk flow provides 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 $\Lambda$CDM and $f(R)$ gravity. With the peculiar velocities output by ECOSMOG we determine the bulk flow at depths ranging from $20h^{-1}$Mpc to $50h^{-1}$Mpc, following the redshift and sky distribution of the 2MASS Tully-Fisher survey (2MTF). At each depth, we find that the $\Lambda$CDM and $f_{R0} = 10^{-5}$ simulations produce bulk flow measurements that are consistent with $\Lambda$CDM predictions and the 2MTF survey at a $1\sigma$ level. We also find that adopting an $f(R)$ strength of $f_{R0} = 10^{-3}$ predict a much larger value for the bulk flow, which disagree with $\Lambda$CDM predictions at all depths considered. We conclude that $f_{R0}$ must be constrained to a level no greater than $10^{-4}$ to agree with bulk flow measurements.