Separate Universe Consistency Relation and Calibration of Halo Bias

TL;DR

This paper tests the consistency relation for linear halo bias using separate universe simulations, confirming its accuracy and proposing a calibration method, which could reveal new physics if violated observationally.

Contribution

It demonstrates the validity of the separate universe approach for calibrating halo bias and highlights its potential to detect new physics through observational tests.

Findings

Excellent agreement with the consistency relation at 1-2% level

Universal mass function assumption is inaccurate by 10% or more

Method effectively calibrates halo bias for rare halos in  cosmology

Abstract

Linear halo bias is the response of 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 $1 \lesssim \bar b_1 \lesssim 4$ and no statistically significant deviations at the $4-5\%$ level out to $\bar b_1 \approx 8$. 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 linear halo bias efficiently for even highly biased rare halos in the $\Lambda$CDM model. Observational violation of the consistency relation would indicate new physics, e.g.~in the dark matter, dark energy or primordial non-Gaussianity sectors.