We investigate generic perturbed scenarios for the spherical collapse of a top-hat matter overdensity. For this we enable a fluid description in a Lagrangian-coordinates approach, derive simple all-order recursion relations for the time-Taylor coefficients of the Lagrangian displacement field and prove the convergence of its series representation until the time of collapse (“shell-crossing”). As to the nature of the perturbed initial conditions, its amplitude must be sufficiently small in comparison to the one of the pure spherical collapse, but besides that they are kept fairly general in our description: they could be of geometrical origin (“ellipsoidal collapse”), or due to the presence of another clustering fluid component (e.g., massive neutrinos or clustering dark energy). Then, we derive an exact and simple analytical expression for the time of perturbed matter collapse, which is shown to happen generically earlier than in the spherical case. Although the linear matter density receives an additive correction proportional to the perturbation, we show, due to the decreased collapse time, that the threshold of the linear matter density at collapse is reduced — irrespective of the sign of the perturbation. This could have important consequences for models that predict the abundance of biased tracers of matter, such as halos and galaxies.
Thu, 7 Dec 17
Comments: 9 pages, 5 figures