Fingerprinting Dark Energy II: weak lensing and galaxy clustering tests

TL;DR

This paper investigates how future large-scale structure surveys can constrain dark energy properties, especially its sound speed, by analyzing weak lensing and galaxy clustering data within a perturbation framework.

Contribution

It introduces an analytical approach to assess the potential of upcoming surveys in constraining dark energy perturbations, focusing on sound speed and equation of state.

Findings

Weak lensing and galaxy surveys can constrain small sound speeds (c_s ≲ 0.01).

For larger sound speeds, constraints become very weak or non-informative.

Surveys can detect non-relativistic ('cold') dark energy but not canonical scalar fields with sound speed unity.

Abstract

The characterization of dark energy is a central task of cosmology. To go beyond a cosmological constant, we need to introduce at least an equation of state and a sound speed and consider observational tests that involve perturbations. If dark energy is not completely homogeneous on observable scales then the Poisson equation is modified and dark matter clustering is directly affected. One can then search for observational effects of dark energy clustering using dark matter as a probe. In this paper we exploit an analytical approximate solution of the perturbation equations in a general dark energy cosmology to analyze the performance of next-decade large scale surveys in constraining equation of state and sound speed. We find that tomographic weak lensing and galaxy redshift surveys can constrain the sound speed of the dark energy only if the latter is small, of the order of $c_{s}\lesssim0.01$ (in units of $c$). For larger sound speeds the error grows to 100% and more. We conclude that large scale structure observations contain very little information about the perturbations in canonical scalar field models with a sound speed of unity. Nevertheless, they are able to detect the presence of "cold" dark energy, i.e. a dark energy with non-relativistic speed of sound.