Separating the Universe into the Real and Fake

TL;DR

This paper extends the separate universe technique to include non-gravitational forces and Jeans scales, enabling accurate modeling of small-scale matter observables in complex cosmologies.

Contribution

It introduces a method to incorporate scale-dependent effects of non-gravitational forces into the separate universe framework, improving modeling of cosmological observables.

Findings

The technique accurately models matter fluctuations across the Jeans scale.

It demonstrates the approach with scalar field dark energy scenarios.

The method accounts for temporal nonlocality and scale dependence in observables.

Abstract

The separate universe technique provides a means of establishing consistency relations between short wavelength observables and the long wavelength matter density fluctuations within which they evolve by absorbing the latter into the cosmological background. We extend it to cases where non-gravitational forces introduce a Jeans scale in other species like dynamical dark energy or massive neutrinos. The technique matches the synchronous gauge matter density fluctuations to the local expansion using the acceleration equation and accounts for the temporal nonlocality and scale dependence of the long wavelength response of small scale matter observables, e.g. the nonlinear power spectrum, halo abundance and the implied halo bias, and $N$-point correlation functions. Above the Jeans scale, the local Friedmann equation relates the expansion to real energy densities and a curvature that is constant in comoving coordinates. Below the Jeans scale, the curvature evolves and acts like a fake density component. In all cases, the matter evolution on small scales is correctly modeled as we illustrate using scalar field dark energy with adiabatic or isocurvature initial conditions across the Jeans scale set by its finite sound speed.