Effects of tidal gravitational fields in clustering dark energy models

We extend a previous work by Reischke et al., 2016 by studying the effects of tidal shear on clustering dark energy models within the framework of the extended spherical collapse model and using the Zel'dovich approximation. As in previous works on clustering dark energy, we assumed a vanishing effective sound speed describing the perturbations in dark energy models. To be self-consistent, our treatment is valid only on linear scales since we do not intend to introduce any heuristic models. This approach makes the linear overdensity $\delta_{\rm c}$ mass dependent and similarly to the case of smooth dark energy, its effects are predominant at small masses and redshifts. Tidal shear has effects of the order of percent or less, regardless of the model and preserves a well known feature of clustering dark energy: When dark energy perturbations are included, the models resemble better the $\Lambda$CDM evolution of perturbations. We also showed that effects on the comoving number density of halos are small and qualitatively and quantitatively in agreement with what previously found for smooth dark energy models.