  Using N-body simulations, we measure the power spectrum of the effective dark
matter density field, which is defined through the modified Poisson equation in
$f(R)$ cosmologies. We find that when compared to the conventional dark matter
power spectrum, the effective power spectrum deviates more significantly from
the $\Lambda$CDM model. For models with $f_{R0}=-10^{-4}$, the deviation can
exceed 150\% while the deviation of the conventional matter power spectrum is
less than 50\%. Even for models with $f_{R0}=-10^{-6}$, for which the
conventional matter power spectrum is very close to the $\Lambda$CDM
prediction, the effective power spectrum shows sizeable deviations. Our results
indicate that traditional analyses based on the dark matter density field may
seriously underestimate the impact of $f(R)$ gravity on galaxy clustering. We
therefore suggest the use of the effective density field in such studies. In
addition, based on our findings, we also discuss several possible methods of
making use of the differences between the conventional and effective dark
matter power spectra in $f(R)$ gravity to discriminate the theory from the
$\Lambda$CDM model.
