Quintessential Scale Dependence from Separate Universe Simulations

TL;DR

This paper extends separate universe simulations to models with scale-dependent growth, such as those with a Jeans scale, revealing how long-wavelength modes influence small-scale observables differently across scales.

Contribution

It introduces a method to incorporate scale dependence in separate universe simulations, accounting for non-gravitational forces and Jeans scales, which was not previously addressed.

Findings

Power spectrum and mass function responses depend on the scale relative to the Jeans scale.

Squeezed bispectrum and halo bias become scale dependent.

Local bias models cannot fully describe the scale-dependent effects.

Abstract

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.