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As an alternative explanation for the cosmic acceleration, $f(R)$ theories ofgravity can predict an almost identical expansion history to standard$\Lambda$CDM, yet make very different predictions for the growth ofcosmological structures. Measurements of the cosmic bulk flow provides a methodfor determining the strength of gravity over the history of structureformation. We use the modified gravity N-body code ECOSMOG to simulate darkmatter particles and make predictions for the bulk flow magnitude in both$\Lambda$CDM and $f(R)$ gravity. With the peculiar velocities output by ECOSMOGwe determine the bulk flow at depths ranging from $20h^{-1}$Mpc to$50h^{-1}$Mpc, following the redshift and sky distribution of the 2MASSTully-Fisher survey (2MTF). At each depth, we find that the $\Lambda$CDM and$f_{R0} = 10^{-5}$ simulations produce bulk flow measurements that areconsistent 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 $\Lambda$CDMpredictions at all depths considered. We conclude that $f_{R0}$ must beconstrained to a level no greater than $10^{-4}$ to agree with bulk flowmeasurements.

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