Clustering dark energy imprints on cosmological observables of the gravitational field

ABSTRACT We study cosmological observables on the past light-cone of a fixed observer in the context of clustering dark energy. We focus on observables that probe the gravitational field directly, namely the integrated Sachs–Wolfe and non-linear Rees–Sciama effect (ISW-RS), weak gravitational lensing, gravitational redshift, and Shapiro time delay. With our purpose-built N-body code ‘k-evolution’ that tracks the coupled evolution of dark matter particles and the dark energy field, we are able to study the regime of low speed of sound cs where dark energy perturbations can become quite large. Using ray tracing, we produce two-dimensional sky maps for each effect and we compute their angular power spectra. It turns out that the ISW-RS signal is the most promising probe to constrain clustering dark energy properties coded in $w-c_\mathrm{ s}^2$, as the linear clustering of dark energy would change the angular power spectrum by ${\sim}30{{\ \rm per\ cent}}$ at low ℓ when comparing two different speeds of sound for dark energy. Weak gravitational lensing, Shapiro time delay, and gravitational redshift are less sensitive probes of clustering dark energy, showing variations of only a few per cent. The effect of dark energy non-linearities in all the power spectra is negligible at low ℓ, but reaches about $2{{\ \rm per\ cent}}$ and $3{{\ \rm per\ cent}}$, respectively, in the convergence and ISW-RS angular power spectra at multipoles of a few hundred when observed at redshift ∼0.85. Future cosmological surveys achieving per cent precision measurements will allow us to probe the clustering of dark energy to a high degree of confidence.