Quintessential Isocurvature in Separate Universe Simulations
  In a universe with quintessence isocurvature, or perturbations in dark energy
that are independent from the usual curvature perturbations, structure
formation is changed qualitatively. The existence of two independent fields,
curvature and isocurvature, causes the growth rate of matter perturbations to
depend on their initial conditions. The quintessence perturbations cause their
growth to depend on scale. We perform the first separate universe simulations
for this cosmology. We demonstrate that the power spectrum response and the
halo bias depend on scale and initial conditions and that the presence of the
isocurvature mode changes the mapping from these quantities to the halo auto-
and cross-power spectra, and the squeezed-limit bispectrum. We compare the bias
to several models, finding reasonable agreement with both a
power-spectrum-response model with one free parameter and a model that fits two
independent bias parameters for curvature and isocurvature sourced
fluctuations. We also verify that simulation responses to pure isocurvature and
pure curvature modes can be linearly combined to reproduce responses with
different ratios of isocurvature and curvature. This allows our results to be
used to predict the halo power spectrum and stochasticity with arbitrary
large-scale curvature and isocurvature power spectra. In an appendix, we study
the generation of quintessence isocurvature during inflation and show that a
modified kinetic term is typically required to produce observable isocurvature
modes in a field with $w_Q\approx -1$.
