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

Cornelius Rampf (1)

1 LAGRANGE - Joseph Louis LAGRANGE

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 ΛCDM Universe, with the inclusion of a cosmological constant Λ > 0.

Mots clés: cosmology: theory; large-scale structure of Universe; dark matter

Domaines: Astrophysique [astro-ph]

Cornelius Rampf. Quasi-spherical collapse of matter in $\Lambda$CDM. Monthly Notices of the Royal Astronomical Society, 2019, 484, pp.5223-5235. ⟨10.1093/mnras/stz372⟩. ⟨hal-02058592⟩