Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics

Lilow, Robert; Fabis, Felix; Kozlikin, Elena; Viermann, Celia; Bartelmann, Matthias

doi:10.1088/1475-7516/2019/04/001

Cited by 19 publications

(67 citation statements)

References 21 publications

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“…In lowest order in the initial power spectrum P (i) δ , using growing mode initial conditions δ (i) = − ∇ · p (i) , and ignoring shot-noise contributions, the free 2-point cumulants for our cosmological framework are given by where we have used the abbreviations g jk := g qp (η j , η k )θ(η j − η k ), (C.4) g j := g qp (η j , 0), (C.5) with g qp given in (2.42), and P (i) δ (k) denotes the power spectrum at initial time. Note that the contributions of higher orders in the initial power spectrum can be safely neglected in the qualitative analysis presented in this paper, as they only affect scales below the particles' mean free-streaming length [31].…”

Section: Explicit Expressions For Free 2-point Cumulantsmentioning

confidence: 99%

Resummed Kinetic Field Theory: using Mesoscopic Particle Hydrodynamics to describe baryonic matter in a cosmological framework

Geiß

Lilow²,

Fabis³

et al. 2019

J. Cosmol. Astropart. Phys.

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We present a new analytical description of baryonic matter in a cosmological framework, using the formalism of 'Kinetic Field Theory' (KFT) -a statistical field theory approach to structure formation based on the dynamics of classical particles. So far, only the purely gravitational dynamics of dark matter had been considered in KFT, but an accurate description of cosmic structure formation requires to also take into account the baryonic gas dynamics. In this paper, we propose to achieve this by incorporating an effective mesoscopic particle model of hydrodynamics into the recently developed framework of Resummed KFT. Our main result is the baryonic density contrast power spectrum computed to lowest perturbative order, assuming a simplified isothermal fluid model. Compared to the spectrum of dark matter, the baryonic spectrum shows a suppression of power as well as an oscillatory behaviour associated with sound waves on scales smaller than the Jeans length. We further compare our result to the linear spectrum of an isothermal fluid obtained from Eulerian perturbation theory (EPT), finding good quantitative agreement within the approximations we made in the EPT calculation. A subsequent paper will resolve the problem of coupling both dark and baryonic matter, to gain a full model of cosmic matter. Applying the mesoscopic particle approach to more general ideal or viscous fluids will also be subject of upcoming work.

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Section: Explicit Expressions For Free 2-point Cumulantsmentioning

confidence: 99%

Resummed Kinetic Field Theory: using Mesoscopic Particle Hydrodynamics to describe baryonic matter in a cosmological framework

Geiß

Lilow²,

Fabis³

et al. 2019

J. Cosmol. Astropart. Phys.

Self Cite

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“…The presentation here is based on the more detailed and general derivation in ref. [64] which uses the full phase-space density rather than the spatial density to preserve momentum information.…”

Section: Macroscopic Reformulation Of Kftmentioning

confidence: 99%

“…Since we will use this macroscopic reformulation of KFT in Section 9.4 to treat Newtonian dynamics, whose Green's function (54) is limited from above, we have to take the complete expression for the initial probability distribution (64) into account, which includes all correlations between the initial phase-space coordinates of particles. This means that the lengthy polynomial C( p) introduced in (64) must be included.…”

Section: Including Density-density and Density-momentum Correlationsmentioning

confidence: 99%

“…For further detail on the general properties of the macroscopic perturbation theory, we refer the reader to ref. [64], where we introduce a Feynman-diagram language to compute the higher-order perturbative contributions-that is, the so-called loop-contributionssystematically. To find expressions for the inverse propagator −1 and the ver-…”

Section: Macroscopic Perturbation Theorymentioning

confidence: 99%

“…[45] In ref. [64], we describe how R , A , and ρρ can be computed explicitly for a given physical system. But even without specifying the system, it is always possible to express (167) formally in terms of a Neumann series by expanding the functional inverse www.advancedsciencenews.com www.ann-phys.org…”

Section: Macroscopic Perturbation Theorymentioning

confidence: 99%

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Cosmic Structure Formation with Kinetic Field Theory

et al. 2019

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Kinetic Field Theory (KFT) is a statistical field theory for an ensemble of point-like classical particles in or out of equilibrium. We review its application to cosmological structure formation. Beginning with the construction of the generating functional of the theory, we describe in detail how the theory needs to be adapted to reflect the expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, we develop three main approaches to non-linear, late-time cosmic structures, which rest either on the Taylor expansion of an interaction operator, suitable averaging procedures for the interaction term, or a resummation of perturbation terms. We show how an analytic, parameterfree equation for the non-linear cosmic power spectrum can be derived.We explain how the theory can be used to derive the density profile of gravitationally bound structures and use it to derive power spectra of cosmic velocity densities. We further clarify how KFT relates to the BBGKY hierarchy. We then proceed to apply kinetic field theory to fluids, introduce a reformulation of KFT in terms of macroscopic quantities which leads to a resummation scheme, and use this to describe mixtures of gas and dark matter. We discuss how KFT can be applied to study cosmic structure formation with modified theories of gravity. As an example for an application to a noncosmological particle ensemble, we show results on the spatial correlation function of cold Rydberg atoms derived from KFT.

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Kinetic field theory for cosmic structure formation

Konrad

Bartelmann

2022

Riv. Nuovo Cim.

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We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are drawn from a Gaussian random field. We place particular emphasis on the late-time, asymptotic behaviour on small spatial scales of low-order statistical measures for the distribution of particles in configuration and velocity space. Our main result is that the power spectra for density and velocity fluctuations in ensembles of particles freely streaming along Zel’dovich trajectories asymptotically fall off with wave number k like $$k^{-3}$$ k - 3 for $$k\rightarrow \infty $$ k → ∞ , irrespective of the cosmological model and the type of dark matter assumed, with the exponent set only by the number of spatial dimensions. This conclusion remains valid for density-fluctuation power spectra if particle interactions are taken into account in a mean-field approximation. We also show that the bispectrum of freely streaming particles falls off asymptotically like $$k^{-11/2}$$ k - 11 / 2 under the same general conditions.

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Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics

Cited by 19 publications

References 21 publications

Resummed Kinetic Field Theory: using Mesoscopic Particle Hydrodynamics to describe baryonic matter in a cosmological framework

Resummed Kinetic Field Theory: using Mesoscopic Particle Hydrodynamics to describe baryonic matter in a cosmological framework

Cosmic Structure Formation with Kinetic Field Theory

Kinetic field theory for cosmic structure formation

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