shows the ratio of the measured halo bias of MG models to the one in $\Lambda$CDM. As in previous plots, the errors are that of $\Lambda$CDM. As explained in previous plots, these errors are conservative upper limit. For this reason, the observed difference in the halo bias is statistically significant, despite the apparently large error bars. []{data-label="fig:bias"}](f4.eps){width="40.00000%"}

We define the bias of dark matter halos as the ratio of the halo mass cross-power spectrum to the dark matter power spectrum $$b(k,M_{200}) = \frac {P_{hm}(k,M_{200})}{P_{mm}(k)},$$ where $P_{hm}(k,M)$ denotes the cross-power spectrum with halos of mass $M_{200}$, and $P_{mm}(k)$ is the dark matter power spectrum. This measure dose not require a shot-noise correction, and it yields better statistics when the halos become sparse. The power spectrum is calculated using Daubechies wavelet mass assignment, which avoids the sampling effect. Although halo bias is scale dependent in the quasi-linear and nonlinear regime, here we focus on the large-scale bias, where $b$ is independent of $k$. We calculate $b$ as the average over the $5$ largest wavelength modes ($k\lesssim0.1 h/{\rm Mpc}$) in the simulation. We also check these results against bias as defined by $b_{hh}
= \sqrt {P_{hh}/P_{mm}}$, and we find that there is a 