Testing the cosmological Euler equation: viscosity, equivalence principle, and gravity beyond general relativity

TL;DR

This paper explores how to test the cosmological Euler equation considering viscous dark matter, violations of the equivalence principle, and modified gravity, proposing new observables and forecasting constraints from upcoming surveys.

Contribution

It introduces a generalized observable for EP violation, identifies a model-independent measure of dark matter viscosity, and forecasts tight constraints from future cosmological surveys.

Findings

$C_{vis,0}$ can be constrained to $ ext{O}(10^{-6})$ with upcoming surveys.

SKA2 provides the most stringent forecast, with a $1\sigma$ uncertainty of $1.08 \times 10^{-7}$.

EP violation can still be tested in the small-viscosity limit.

Abstract

We investigate how the cosmological Euler equation can be tested in the presence of viscous dark matter, violations of the equivalence principle (EP), and modifications of gravity, while relying on minimal theoretical assumptions. Extending the previous analysis, we generalize the observable $E_P$, which quantifies EP violation, to $\tilde{E}_P$, discuss the degeneracy between bulk and shear viscosities and EP-violating effects, and explicitly show that the EP can still be tested in the small-viscosity limit. In addition, we identify a model-independent observable, $C_{\rm vis,0}$, which characterizes the present-day dark matter viscosity and can be measured from relativistic galaxy number counts by cross-correlating two galaxy populations. We perform forecasts for three forthcoming Stage-IV surveys: DESI, Euclid, and SKA Phase 2 (SKA2), and find that $C_{\rm vis,0}$ can be tightly constrained, at the level of $\mathcal{O}(10^{-6})$ or better in all cases. Among these surveys, SKA2 provides the tightest constraint, with a $1\sigma$ uncertainty of $1.08 \times 10^{-7}$ on $C_{\rm vis,0}$.