Separate universe consistency relation and calibration of halo bias

The linear halo bias is the response of the dark matter halo number density to a long-wavelength fluctuation in the dark matter density. Using abundance matching between separate universe simulations which absorb the latter into a change in the background, we test the consistency relation between the change in a one-point function, the halo mass function, and a two-point function, the halo-matter cross-correlation in the long-wavelength limit. We find excellent agreement between the two at the 1%-2% level for average halo biases between 1 less than or similar to (h) over bar (1) less than or similar to 4 and no statistically significant deviations at the 4%-5% level out to (h) over bar (1) approximate to 8. The halo bias inferred assuming instead a universal mass function is significantly different and inaccurate at the 10% level or more. The separate universe technique provides a way of calibrating the linear halo bias efficiently for even highly biased rare halos in the. cold dark matter model. Observational violation of the consistency relation would indicate new physics, e.g. in the dark matter, dark energy, or primordial non-Gaussianity sectors.