Scale-dependent bias and bispectrum in neutrino separate universe
  simulations
  Cosmic background neutrinos have a large velocity dispersion, which causes
the evolution of long-wavelength density perturbations to depend on scale. This
scale-dependent growth leads to the well-known suppression in the linear theory
matter power spectrum that is used to probe neutrino mass. In this paper, we
study the impact of long-wavelength density perturbations on small-scale
structure formation. By performing separate universe simulations where the
long-wavelength mode is absorbed into the local expansion, we measure the
responses of the cold dark matter (CDM) power spectrum and halo mass function,
which correspond to the squeezed-limit bispectrum and halo bias. We find that
the scale-dependent evolution of the long-wavelength modes causes these
quantities to depend on scale and provide simple expressions to model them in
terms of scale and the amount of massive neutrinos. Importantly, this
scale-dependent bias reduces the suppression in the linear halo power spectrum
due to massive neutrinos by 13 and 26% for objects of bias $\bar{b}=2$ and
$\bar{b} \gg1$, respectively. We demonstrate with high statistical significance
that the scale-dependent halo bias ${\it cannot}$ be modeled by the CDM and
neutrino density transfer functions at the time when the halos are identified.
This reinforces the importance of the temporal nonlocality of structure
formation, especially when the growth is scale dependent.
