Relativistic effects in the large-scale structure with effective dark
  energy fluids
  We study the imprints of an effective dark energy fluid in the large scale
structure of the universe through the observed angular power spectrum of
galaxies in the relativistic regime. We adopt the phenomenological approach
that introduces two parameters $\{Q,\eta\}$ at the level of linear
perturbations and allow to take into account the modified clustering (or
effective gravitational constant) and anisotropic stress appearing in models
beyond $\Lambda$CDM. We characterize the effective dark energy fluid by an
equation of state parameter $w=-0.95$ and various sound speed cases in the
range $10^{-6}\leq c^2_s\leq 1$, thus covering K-essence and quintessence
cosmologies. We calculate the angular power spectra of standard and
relativistic effects for these scenarios under the $\{Q,\eta\}$
parametrization, and we compare these relative to a fiducial $\Lambda$CDM
cosmology. We find that, overall, deviations relative to $\Lambda$CDM are
stronger at low redshift since the behavior of the dark energy fluid can mimic
the cosmological constant during matter domination era but departs during dark
energy domination. In particular, at $z=0.1$ the matter density fluctuations
are suppressed by up to $\sim3\%$ for the quintessence-like case, while
redshift-space distortions and Doppler effect can be enhanced by $\sim15\%$ at
large scales for the lowest sound speed scenario. On the other hand, at $z=2$
we find deviations of up to $\sim5\%$ in gravitational lensing, whereas the
Integrated Sachs-Wolfe effect can deviate up to $\sim17\%$. Furthermore, when
considering an imperfect dark energy fluid scenario, we find that all effects
are insensitive to the presence of anisotropic stress at low redshift, and only
the Integrated Sachs-Wolfe effect can detect this feature at $z=2$ and very
large scales.
