Quasi-spherical collapse of matter in $\Lambda$CDM

Understand

We report the findings of new exact analytical solutions to the cosmological fluid equations, namely for the case where the initial conditions are perturbatively close to a spherical top-hat profile.

• To do so we enable a fluid description in a Lagrangian-coordinates approach, and prove the convergence of the Taylor-series representation of the Lagrangian displacement field until the time of collapse ("shell-crossing").
• This allows the determination of the time for quasi-spherical collapse, which is shown to happen generically earlier than in the spherical case.
• For pedagogical reasons, calculations are first given for a spatially flat universe that is only filled with a non-relativistic component of cold dark matter (CDM).