Lensing convergence and anisotropic dark energy in galaxy redshift surveys

Analyses of upcoming galaxy surveys will require careful modelling of relevant observables such as the power spectrum of galaxy counts in harmonic space $C_\ell(z,z')$. We investigate the impact of disregarding relevant relativistic effects by considering a model of dark energy including constant sound speed $c_{\rm eff}^2$, constant equation of state $w$, and anisotropic stress sourced by matter perturbations $\pi$. Cosmological constraints were computed using cosmic microwave background anisotropies, baryon acoustic oscillations, supernovae type Ia, and redshift space distortions. Our results are consistent with $w=-1$, $c_{\rm eff}^2=1$, and $\pi=0$. Then, a forecast for the performance of an Euclid-like galaxy survey was carried out also adding information from other probes. Here we show that, regardless of the galaxy survey configuration, neglecting the effect of lensing convergence will lead to substantial shifts in the galaxy bias $b_0$ and the neutrino mass $\sum m_\nu$. Shifts in the dark energy sound speed and anisotropic stress also appear, but they depend on the survey configuration and hence lack robustness. While neglecting lensing convergence also leads to a Hubble constant $H_0$ moving downwards, the significance of the shift is not big enough to play a relevant part in the current $H_0$ tension.