# The Helmholtz Hierarchy: phase space statistics of cold dark matter

@article{Tassev2011TheHH, title={The Helmholtz Hierarchy: phase space statistics of cold dark matter}, author={Svetlin Valentinov Tassev}, journal={Journal of Cosmology and Astroparticle Physics}, year={2011}, volume={2011}, pages={022-022} }

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the ``Helmholtz Hierarchy'') of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys… Expand

#### 12 Citations

Schrödinger method as $N$-body double and UV completion of dust

- Physics
- 2014

We investigate large-scale structure formation of collisionless dark matter in the phase space description based on the Vlasov equation whose nonlinearity is induced solely by gravitational… Expand

The mildly non-linear regime of structure formation

- Physics
- 2011

We present a simple physically motivated picture for the mildly non-linear regime of structure formation, which captures the effects of the bulk flows. We apply this picture to develop a method to… Expand

Impact of a warm dark matter late-time velocity dispersion on large-scale structures

- Physics
- 2012

We investigate whether the late-time (at $z\leq 100$) velocity dispersion expected in Warm Dark Matter scenarios could have some effect on the cosmic web (i.e., outside of virialized halos). We… Expand

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

- Physics
- 2017

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schr\"odinger method (ScM). With the ScM, one solves the… Expand

Models of large scale structure formation in cosmology

- Physics
- 2014

Combining all knowledge we have gathered about the origin, evolution and current state of the universe it appears indisputable that 95% of the mass-energy density in today's universe is comprised of… Expand

Matter power spectrum from a Lagrangian-space regularization of perturbation theory

- Physics
- 2013

We present a new approach to computing the matter density power spectrum, from large linear scales to small highly nonlinear scales. Instead of explicitly computing a partial series of high-order… Expand

Large-scale structure perturbation theory without losing stream crossing

- Physics
- 2018

Author(s): McDonald, P; Vlah, Z | Abstract: © 2018 American Physical Society. We suggest an approach to perturbative calculations of large-scale clustering in the Universe that includes from the… Expand

Estimating CDM particle trajectories in the mildly non-linear regime of structure formation. Implications for the density field in real and redshift space

- Physics
- 2012

We obtain approximations for the CDM particle trajectories starting from Lagrangian Perturbation Theory. These estimates for the CDM trajectories result in approximations for the density in real and… Expand

Solving large scale structure in ten easy steps with COLA

- Physics
- 2013

We present the COmoving Lagrangian Acceleration (COLA) method: an N-body method for solving for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories… Expand

AN APPLICATION OF THE WIENER HERMITE EXPANSION TO THE NONLINEAR EVOLUTION OF DARK MATTER

- Physics
- 2012

We apply the Wiener Hermite (WH) expansion to the nonlinear evolution of the large-scale structure and obtain an approximate expression for the matter power spectrum in the full order of the… Expand

#### References

SHOWING 1-10 OF 36 REFERENCES

A COSMOLOGICAL KINETIC THEORY FOR THE EVOLUTION OF COLD DARK MATTER HALOS WITH SUBSTRUCTURE: QUASI-LINEAR THEORY

- Physics
- 2004

We present a kinetic theory for the evolution of the phase-space distribution of dark matter particles in galaxy halos in the presence of a cosmological spectrum of fluctuations. This theory… Expand

Renormalized cosmological perturbation theory

- Physics
- 2006

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is… Expand

Large-N expansions applied to gravitational clustering

- Physics
- 2006

We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive… Expand

Non-perturbative renormalization flow in quantum field theory and statistical physics

- Physics
- 2002

Abstract We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the… Expand

Memory of initial conditions in gravitational clustering

- Physics
- 2006

We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it… Expand

The Evolution of Correlation Functions in the Zeldovich Approximation and Its Implications for the Validity of Perturbation Theory

- Physics
- 1996

We investigate whether it is possible to study perturbatively the transition in cosmological clustering from a single-streamed flow to a multistreamed flow. We do this by considering a system whose… Expand

How to generate a significant effective temperature for cold dark matter, from first principles

- Physics
- 2009

I show how to reintroduce velocity dispersion into perturbation theory (PT) calculations of structure in the Universe, i.e., how to go beyond the pressureless fluid approximation, starting from first… Expand

Lagrangian dynamics in non-flat universes and non-linear gravitational evolution

- Physics
- 1995

We present a new formalism which allows to derive the general Lagrangian dynamical equations for the motion of gravitating particles in a non--flat Friedmann universe with arbitrary density parameter… Expand

Cosmological non-linearities as an effective fluid

- Physics
- 2012

The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that… Expand

Baryonic Acoustic Oscillations via the Renormalization Group

- Physics
- 2008

Renormalization Group techniques, successfully employed in quantum field theory and statistical physics, are applied to study the dynamics of structure formation in the Universe. A semi-analytic… Expand