Quintessential Scale Dependence from Separate Universe Simulations
  By absorbing fluctuations into a local background, separate universe
simulations provide a powerful technique to characterize the response of
small-scale observables to the long-wavelength density fluctuations, for
example those of the power spectrum and halo mass function which lead to the
squeezed-limit $n$-point function and halo bias, respectively. Using
quintessence dark energy as the paradigmatic example, we extend these
simulation techniques to cases where non-gravitational forces in other sectors
establish a Jeans scale across which the growth of density fluctuations becomes
scale dependent. By characterizing the separate universes with matching
background expansion histories, we show that the power spectrum and mass
function responses depend on whether the long-wavelength mode is above or below
the Jeans scale. Correspondingly, the squeezed bispectrum and halo bias also
become scale dependent. Models of bias that are effectively local in the
density field at a single epoch, initial or observed, cannot describe this
effect which highlights the importance of temporal nonlocality in structure
formation. Validated by these quintessence tests, our techniques are applicable
to a wide range of models where the complex dynamics of additional fields
affect the clustering of matter in the linear regime and it would otherwise be
difficult to simulate their impact in the nonlinear regime.
