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We study cosmological observables on the past light cone of a fixed observerin the context of clustering dark energy. We focus on observables that probethe gravitational field directly, namely the integrated Sachs-Wolfe andnon-linear Rees-Sciama effect (ISW-RS), weak gravitational lensing,gravitational redshift and Shapiro time delay. With our purpose-built $N$-bodycode "$k$-evolution" that tracks the coupled evolution of dark matter particlesand the dark energy field, we are able to study the regime of low speed ofsound $c_s$ where dark energy perturbations can become quite large. Using raytracing we produce two-dimensional sky maps for each effect and we computetheir angular power spectra. It turns out that the ISW-RS signal is the mostpromising probe to constrain clustering dark energy properties coded in$w-c_s^2$, as the $\textit{linear}$ clustering of dark energy would change theangular power spectrum by $\sim 30\%$ at low $\ell$ when comparing twodifferent speeds of sound for dark energy. Weak gravitational lensing, Shapirotime-delay and gravitational redshift are less sensitive probes of clusteringdark energy, showing variations of a few percent only. The effect of darkenergy $\textit{non-linearities}$ in all the power spectra is negligible at low$\ell$, but reaches about $2\%$ and $3\%$, respectively, in the convergence andISW-RS angular power spectra at multipoles of a few hundred when observed atredshift $\sim 0.85$. Future cosmological surveys achieving percent precisionmeasurements will allow to probe the clustering of dark energy to a high degreeof confidence.

Clustering dark energy imprints on cosmological observables of the gravitational field