Effects of tidal gravitational fields in clustering dark energy models

We extend a previouswork by Reischke et al. 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 selfconsistent, our treatment is valid only on linear scales since we do not intend to introduce any heuristic models. This approach makes the linear overdensity δc 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 per cent 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 cold dark matter evolution of perturbations. We also showed that effects on the comoving number density of haloes are small and qualitatively and quantitatively in agreement with what were previously found for smooth dark energy models.