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

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 $\Lambda$CDM Universe, with the inclusion of a cosmological constant $\Lambda >0$.

v1: 9 pages, 5 figures; v2: 13 pages, 7 figures. Major revision: results unchanged, however generalised the calculations to a LCDM Universe (upon request from the referee) and extended the discussion; changed title

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Cited by in corpus (12)

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• Semiclassical path to cosmic large-scale structure
• Shell-crossing in a $\Lambda$CDM Universe
• Unveiling the singular dynamics in the cosmic large-scale structure
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Cold dark matter protohalo structure around collapse: Lagrangian cosmological perturbation theory versus Vlasov simulations
• Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation
• Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon
• Fast and accurate collapse-time predictions for collisionless matter
• The gravitational force field of proto-pancakes
• Starting Cosmological Simulations from the Big Bang