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Analyses of upcoming galaxy surveys will require careful modelling ofrelevant observables such as the power spectrum of galaxy counts in harmonicspace $C_\ell(z,z')$. We investigate the impact of disregarding relevantrelativistic effects by considering a model of dark energy including constantsound speed $c_{\rm eff}^2$, constant equation of state $w$, and anisotropicstress sourced by matter perturbations $\pi$. Cosmological constraints werecomputed using cosmic microwave background anisotropies, baryon acousticoscillations, supernovae type Ia, and redshift space distortions. Our resultsare consistent with $w=-1$, $c_{\rm eff}^2=1$, and $\pi=0$. Then, a forecastfor the performance of an Euclid-like galaxy survey was carried out also addinginformation from other probes. Here we show that, regardless of the galaxysurvey configuration, neglecting the effect of lensing convergence will lead tosubstantial 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, butthey depend on the survey configuration and hence lack robustness. Whileneglecting lensing convergence also leads to a Hubble constant $H_0$ movingdownwards, the significance of the shift is not big enough to play a relevantpart in the current $H_0$ tension.

Lensing convergence and anisotropic dark energy in galaxy redshift surveys