# How smooth are particle trajectories in a ΛCDM Universe

@article{Rampf2015HowSA, title={How smooth are particle trajectories in a $\Lambda$CDM Universe}, author={Cornelius Rampf and Barbara Villone and Uriel Frisch}, journal={Monthly Notices of the Royal Astronomical Society}, year={2015}, volume={452}, pages={1421-1436} }

It is shown here that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant ($\Lambda$), modelled in terms of a Newtonian and collisionless fluid, particle trajectories are analytical in time (representable by a convergent Taylor series) until at least a finite time after decoupling. The time variable used for this statement is the cosmic scale factor, i.e., the "$a$-time", and not the cosmic time. For this, a Lagrangian-coordinates formulation of the Euler…

## 27 Citations

### Cosmological perturbations for two cold fluids in ΛCDM

- Physics
- 2020

The cosmic large-scale structure of our Universe is comprised of baryons and cold dark matter (CDM). Yet it is customary to treat these two components as a combined single-matter fluid with vanishing…

### Semiclassical path to cosmic large-scale structure

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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…

### Perturbation theory of large scale structure in the ΛCDM Universe: Exact time evolution and the two-loop power spectrum

- PhysicsPhysical Review D
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We derive exact analytic solutions for density and velocity ﬁelds to all orders in Eulerian standard perturbation theory for ΛCDM cosmology. In particular, we show that density and velocity ﬁeld…

### Lagrangian Cosmological Perturbation Theory at Shell Crossing.

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This work examines the convergence properties of a high-order perturbative expansion in the vicinity of shell crossing by comparing the analytical results with state-of-the-art high resolution Vlasov-Poisson simulations and finds that it slows down when going from quasi-one-dimensional initial conditions to quasitriaxial symmetry.

### Cosmological N -body simulations including radiation perturbations

- Physics
- 2017

Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of…

### Shell-crossing in a ΛCDM Universe

- PhysicsMonthly Notices of the Royal Astronomical Society: Letters
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Perturbation theory is an indispensable tool for studying the cosmic large-scale structure, and establishing its limits is therefore of utmost importance. One crucial limitation of perturbation…

### Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

- PhysicsPhysical Review D
- 2023

Cosmological perturbation theory is known to converge poorly for predicting the spherical collapse and void evolution of collisionless matter. Using the exact parametric solution as a testing ground,…

### Shell-crossing in quasi-one-dimensional flow

- Physics
- 2017

Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid. At this…

### On General-Relativistic Lagrangian Perturbation Theory and Its Non-Perturbative Generalization

- PhysicsUniverse
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The Newtonian Lagrangian perturbation theory is a widely used framework to study structure formation in cosmology in the nonlinear regime. We review a general-relativistic formulation of such a…

### Mechanisms of Lagrangian Analyticity in Fluids

- MathematicsArchive for Rational Mechanics and Analysis
- 2019

Certain systems of inviscid fluid dynamics have the property that for solutions that are only slightly better than differentiable in Eulerian variables, the corresponding Lagrangian trajectories are…

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