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 $w-c_s^2$, as the linear clustering of dark energy would change the angular power spectrum by $\sim 30\%$ 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 a few percent only. The effect of dark energy non-linearities in all the power spectra is negligible at low ℓ, but reaches about $2\%$ and $3\%$, 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 percent precision measurements will allow to probe the clustering of dark energy to a high degree of confidence.

Accurate relativistic observables from post-processing light cone catalogues

“…8. All of the schemes show agreement with the linear ISW power spectrum at low and begin to deviate from the linear result at > 60, consistent with previous studies [50,52,55]. The interpolation scheme based on 16 snapshots significantly overestimates the power compared to the on-the-fly reference spectrum.…”

“…This is especially true when computing the ISW signal in the highly nonlinear regime, and when post-processing simulation data. Various techniques have been studied in past literature to this end [50][51][52][53][54][55]. These all require either output from a large number of snapshots or on-the-fly raytracing, and so are not directly applicable as a post-processing step, which is especially important for fast emulators.…”

A Short Review on Clustering Dark Energy

“…However, this implementation can introduce a small error in the determination of δ c . From Equations ( 34) and (35), we can see that, for small x, the linear and nonlinear values of matter contrast differ by O x 4 . Thus, their initial values are slightly different.…”

“…Having solved the system, one has to determine a criterion to find the moment of collapse. In the standard SCM, the collapse threshold can be found analytically by computing the value of the linearly evolved density contrast (35) at the time of collapse, R → 0 or δ NL m → ∞. This suggests that, in general, the determination of δ c can be done by defining a numerical threshold value for δ NL m , above which the halo is considered to be formed.…”

“…The obvious approach of using full-blown General Relativity to include DE fluctuations in structure formation studies is undoubtedly challenging. In fact, relativistic studies of structure formation with Clustering Dark Energy (CDE) were developed quite recently Dakin et al [33], Hassani et al [34,35].…”