Spherical collapse of non-top-hat profiles in the presence of dark energy with arbitrary sound speed

We study the spherical collapse of non-top-hat matter fluctuations in the presence of dark energy with arbitrary sound speed. The model is described by a system of partial differential equations solved using a pseudo-spectral method with collocation points. This method can reproduce the known analytical solutions in the linear regime with an accuracy better than 10-6% and better than 10-2% for the virialization threshold given by the usual spherical collapse model. We show the impact of nonlinear dark energy fluctuations on matter profiles, matter peculiar velocity and gravitational potential. We also show that phantom dark energy models with low sound speed can develop a pathological behaviour around matter halos, namely negative energy density. The dependence of the virialization threshold density for collapse on the dark energy sound speed is also computed, confirming and extending previous results in the limit for homogeneous and clustering dark energy.

Automated summary

We study the spherical collapse of non-top-hat matter fluctuations in the presence of dark energy with arbitrary sound speed. We use a pseudo-spectral method with collocation points to solve a system of partial differential equations. This method accurately reproduces known analytical solutions in the linear regime and the virialization threshold given by the usual spherical collapse model. Our findings show the impact of nonlinear dark energy fluctuations on matter profiles, matter peculiar velocity, and gravitational potential. We also highlight the pathological behavior of phantom dark energy models with low sound speed, such as negative energy density around matter halos. Additionally, we calculate the dependence of the virialization threshold density for collapse on the dark energy sound speed, confirming and extending previous results for both homogeneous and clustering dark energy.