Linear response to long wavelength fluctuations using curvature
  simulations
  We study the local response to long wavelength fluctuations in cosmological
$N$-body simulations, focusing on the matter and halo power spectra, halo
abundance and non-linear transformations of the density field. The long
wavelength mode is implemented using an effective curved cosmology and a
mapping of time and distances. The method provides an alternative, most
probably more precise, way to measure the isotropic halo biases. Limiting
ourselves to the linear case, we find generally good agreement between the
biases obtained from the curvature method and the traditional power spectrum
method at the level of a few percent. We also study the response of halo counts
to changes in the variance of the field and find that the slope of the relation
between the responses to density and variance differs from the naive derivation
assuming a universal mass function by 18%. This has implications for
measurements of the amplitude of local non-Gaussianity using scale dependent
bias. We also analyze the halo power spectrum and halo-dark matter
cross-spectrum response to long wavelength fluctuations and derive second order
halo bias from it, as well as the super-sample variance contribution to the
galaxy power spectrum covariance matrix.
