Quasi-spherical collapse of matter in ΛCDM

Rampf, Cornelius

doi:10.1093/mnras/stz372

Cited by 19 publications

(27 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Deviating from 1D, we have generically V eff = 0, and, as a result, the ZA performs rather poorly as gravitational tidal effects become non-negligible. In particular, this reflects in inaccurate predictions of the ZA for the shell-crossing time that worsen successively when deviating more and more from the 1D collapse [15][16][17]. Very similar performance issues are expected for the propagator method.…”

Section: Results Beyond 1d Collapsementioning

confidence: 78%

“…The central quantity is the Lagrangian displacement field that encodes how fluid elements are displaced as a function of time and initial (Lagrangian) position. The corresponding perturbative framework is usually called Lagrangian perturbation theory (LPT), and, although a challenge, allows to investigate the instance of shell-crossing by analytic means [12][13][14][15][16][17]. However, to update the gravitational potential that is responsible for displacing the fluid elements, one still requires, effectively, the Eulerian density.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Semiclassical path to cosmic large-scale structure

et al. 2019

Self Cite

View full text Add to dashboard Cite

We chart a path toward solving for the nonlinear gravitational dynamics of cold dark matter by relying on a semiclassical description using the propagator. The evolution of the propagator is given by a Schrödinger equation, where the small parameter acts as a softening scale that regulates singularities at shell-crossing. The leading-order propagator, called free propagator, is the semiclassical equivalent of the Zel'dovich approximation (ZA), that describes inertial particle motion along straight trajectories. At next-to-leading order, we solve for the propagator perturbatively and obtain, in the classical limit the displacement field from second-order Lagrangian perturbation theory (LPT). The associated velocity naturally includes an additional term that would be considered as third order in LPT. We show that this term is actually needed to preserve the underlying Hamiltonian structure, and ignoring it could lead to the spurious excitation of vorticity in certain implementations of second-order LPT. We show that for sufficiently small the corresponding propagator solutions closely resemble LPT, with the additions that spurious vorticity is avoided and the dynamics at shell-crossing is regularised. Our analytical results possess a symplectic structure that allows us to advance numerical schemes for the large-scale structure. For times shortly after shell-crossing, we explore the generation of vorticity, which in our method does not involve any explicit multi-stream averaging, but instead arises naturally as a conserved topological charge.

show abstract

Section: Results Beyond 1d Collapsementioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Semiclassical path to cosmic large-scale structure

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…We remark that, so far, the mathematical convergence of the SPT series until shell-crossing has not been explicitly demonstrated, except for the simplified cases of one-dimensional (McQuinn and White 2016) and spherical collapse (Rampf 2019). Nonetheless, convergence for cosmological initial conditions until-but excluding-shell-crossing is likely, mainly as a consequence of the analyticity results in Lagrangian coordinates Schmidt 2021).…”

Section: Perturbative Methods and Overview Of Applicationsmentioning

confidence: 94%

“…By applying equivalent multi-scaling techniques in Lagrangian coordinates as reviewed above, it has been shown that the matter collapse of arbitrary small departures from spherical symmetry also constitutes an exact solution of (19) until shellcrossing (Rampf 2019). In that case, the initial gravitational potential can be taken to be…”

Section: Analytical Shell-crossing Solutions For Simplified Initial Conditionsmentioning

confidence: 99%

Cosmological Vlasov–Poisson equations for dark matter

Rampf

2021

Rev. Mod. Plasma Phys.

Self Cite

View full text Add to dashboard Cite

The cosmic large-scale structures of the Universe are mainly the result of the gravitational instability of initially small-density fluctuations in the dark-matter distribution. Dark matter appears to be initially cold and behaves as a continuous and collisionless medium on cosmological scales, with evolution governed by the gravitational Vlasov–Poisson equations. Cold dark matter can accumulate very efficiently at focused locations, leading to a highly non-linear filamentary network with extreme matter densities. Traditionally, investigating the non-linear Vlasov–Poisson equations was typically reserved for massively parallelised numerical simulations. Recently, theoretical progress has allowed us to analyse the mathematical structure of the first infinite densities in the dark-matter distribution by elementary means. We review related advances, as well as provide intriguing connections to classical plasma problems, such as the beam–plasma instability.

show abstract

“…Because they follow elements of fluid along the motion, Zel'dovich ap-proximation and higher-order LPT provide us with a rather accurate description of the large scale matter distribution, even in the nonlinear regime, shortly after shell crossing. The families of singularities that form at shell-crossing and after have been examined in detail in the Lagrangian dynamics framework (Arnold et al 1982;Hidding et al 2014;Feldbrugge et al 2018), and the structure of cosmological systems at shell-crossing has been investigated for specific initial conditions (Novikov 1969;Rampf & Frisch 2017;Saga et al 2018;Rampf 2019) and for random initial conditions ).…”

Section: Introductionmentioning

confidence: 99%

Cold dark matter protohalo structure around collapse: Lagrangian cosmological perturbation theory versus Vlasov simulations

Saga,

Taruya,

Colombi

2021

Preprint

View full text Add to dashboard Cite

We explore the structure around shell-crossing time of cold dark matter protohaloes seeded by two or three crossed sine waves of various relative initial amplitudes, by comparing Lagrangian perturbation theory (LPT) up to 10th order to high-resolution cosmological simulations performed with the public Vlasov code ColDICE. Accurate analyses of the density, the velocity, and related quantities such as the vorticity are performed by exploiting the fact that ColDICE can follow locally the phase-space sheet at the quadratic level. To test LPT predictions beyond shell-crossing, we employ a ballistic approximation, which assumes that the velocity field is frozen just after shell-crossing. In the generic case, where the amplitudes of the sine waves are all different, high-order LPT predictions match very well the exact solution, even beyond collapse. As expected, convergence slows down when going from quasi-1D dynamics where one wave dominates over the two others, to the axial-symmetric configuration, where all the amplitudes of the waves are equal. It is also noticed that LPT convergence is slower when considering velocity related quantities. Additionally, the structure of the system at and beyond collapse given by LPT and the simulations agrees very well with singularity theory predictions, in particular with respect to the caustic and vorticity patterns that develop beyond collapse. Again, this does not apply to axial-symmetric configurations, that are still correct from the qualitative point of view, but where multiple foldings of the phase-space sheet produce very high density contrasts, hence a strong backreaction of the gravitational force.

show abstract

Quasi-spherical collapse of matter in ΛCDM

Cited by 19 publications

References 51 publications

Semiclassical path to cosmic large-scale structure

Semiclassical path to cosmic large-scale structure

Cosmological Vlasov–Poisson equations for dark matter

Cold dark matter protohalo structure around collapse: Lagrangian cosmological perturbation theory versus Vlasov simulations

Contact Info

Product

Resources

About