Halo mass function in clustering dark energy models with an extended spherical collapse model

The halo mass function is a key tool for analysing halo abundance within a given cosmological model. Its evaluation requires both a suitable functional form and the solution of the spherical collapse equations, which encode the relevant cosmological dependence. We consider quintessence and phantom dark energy models, solving both the standard and extended spherical collapse models, the latter including an additional velocity-dependent term in the Euler equation. For each case, we compute the halo mass function in its standard formulation and in a corrected version accounting for dark energy clustering. Our results show that the extended spherical collapse model induces corrections of a few percent in both formulations.