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arXiv · 1712.01878

Quasi-spherical collapse of matter in $Λ$CDM

Cornelius Rampf
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Abstract

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). Then, the methodology is updated to a $Λ$CDM Universe, with the inclusion of a cosmological constant $Λ>0$.

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Cornelius Rampf. 2019-02-27. Quasi-spherical collapse of matter in $Λ$CDM. https://doi.org/10.1093/mnras%2Fstz372

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