arXiv subjects

Matthias Bartelmann

Publications and source records attributed to Matthias Bartelmann.

At least 19 recordsLinked to original sources

arXiv2025

Phase-space perturbation theory for cosmic large-scale structure

We consider a perturbative approach to the Vlasov-Poisson system for cosmic structure formation that does not rely on any truncation of the momentum-cumulant hierarchy. The generally non-trivial linear solution is computed by solving a Volterra-type integral equation and higher orders are obtained recursively. As expected, the results of Eulerian standard perturbation theory are recovered for perfectly cold initial conditions. Deviating slightly from the latter by introducing a homogeneous and isotropic initial velocity dispersion, we show that all higher momentum cumulants are generated dynamically at any perturbative order. We support our numerical solutions by an analytical large-scale approximation. Our approach serves as a basis for exploring different background-perturbation splits of the phase-space density and non-perturbative techniques.

astro-ph.CO↗

arXiv2025

Kinetic field theory of compact systems

The kinetic field theory is developed without assumptions of statistical homogeneity and isotropy. In a solvable toy model with short-ranged interactions, we compare first-order perturbation theory to an iterated mean-field approximation scheme, demonstrating that the mean-field theory maintains positivity and captures collapse dynamics, allowing analytic estimates of blow-up times. In a self-gravitating sheet model, the first-order perturbation theory is shown to reproduce critical phenomena. This work suggests a path toward convergence analysis of the mean-field approximation and applications to more complex inhomogeneous systems.

astro-ph.CO↗

arXiv2025

Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory

We investigate cosmic structure formation in the framework of a path-integral formulation of an $N$-particle ensemble in phase space, dubbed Resummed Kinetic Field Theory (RKFT), up to one-loop perturbative order. In particular, we compute power spectra of the density contrast, the divergence and curl of the momentum density and arbitrary $n$-point cumulants of the stress tensor. In contrast to earlier works, we propose a different method of sampling initial conditions, with a Gaussian initial phase-space density. Doing so, we exactly reproduce the corresponding results from Eulerian standard perturbation theory (SPT) at one-loop order, showing that formerly found deviations can be fully attributed to inconsistencies in the previous sampling method. Since, in contrast to SPT, the full phase-space description does not assume a truncation of the Vlasov hierarchy, our findings suggest that nonperturbative techniques are required to accurately capture the physics of cosmic structure formation.

astro-ph.CO↗

arXiv2025

Free Cosmic Density Bispectrum on Small Scales

We study the asymptotic behaviour of the free, cold-dark matter density fluctuation bispectrum in the limit of small scales. From an initially Gaussian random field, we draw phase-space positions of test particles which then propagate along Zel'dovich trajectories. Only initial momentum-momentum correlation are considered, making the formulas identical to the typical Zel'dovich approximation. A suitable expansion of the initial momentum auto-correlations of these particles leads to an asymptotic series whose lower-order power-law exponents we calculate. The dominant contribution has an exponent of $-11/2$. For triangle configurations with zero surface area, this exponent is even enhanced to $-9/2$. These power laws can only be revealed by a non-perturbative calculation with respect to the initial power spectrum. They are valid for a general class of initial power spectra with a cut-off function, required to enforce convergence of its moments. We then confirm our analytic results numerically. Finally, we use this asymptotic behaviour to investigate the shape dependence of the bispectrum in the small-scale limit, and to show how different shapes grow over cosmic time. These confirm the usual model of gravitational collapse within the Zel'dovich picture.

astro-ph.CO↗

arXiv2025

Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum

The matter power spectrum, $P(k)$, is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in $d$ spatial dimensions, $P(k)$ has a universal $k^{-d}$ asymptotic scaling with the wave-number $k$, for $k \gg k_{\rm nl}$, where $k_{\rm nl}^{-1}$ denotes the length scale at which non-linearities in gravitational interactions become important. We propose a theoretical explanation for this scaling, based on a non-perturbative analysis of the system's phase-space structure. Gravitational collapse is shown to drive a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and non-linear time scales are balanced, and this balance dictates the $k$ dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The $k^{-d}$ scaling is also derived by expressing $P(k)$ as a phase-space integral in the framework of kinetic field theory, which is analysed by the saddle-point method; the dominant critical points of this integral are precisely those where the time scales are balanced. The coldness of the dark-matter distribution function - its non-vanishing only on a $d$-dimensional sub-manifold of phase-space - underpins both approaches. The theory is accompanied by $1\mathrm{D}$ Vlasov-Poisson simulations, which confirm it.

astro-ph.CO↗

arXiv2024

Kinetic Field Theory Applied to Planetesimal Formation I: Freely Streaming Dust Particles

Planet formation in the solar system was started when the first planetesimals were formed from the gravitational collapse of pebble clouds. Numerical simulations of this process, especially in the framework of streaming instability, produce various power laws for the initial mass function for planetesimals. While recent advances have shed light on turbulence and its role in particle clustering, a comprehensive theoretical framework linking turbulence characteristics to particle cluster properties and planetesimal mass function remains incomplete. Recently, a kinetic field theory for ensembles of point-like classical particles in or out of equilibrium has been applied to cosmic structure formation. This theory encodes the dynamics of a classical particle ensemble by a generating functional specified by the initial probability distribution of particles in phase space and their equations of motion. Here, we apply kinetic field theory to planetesimal formation. A model for the initial probability distribution of dust particles in phase space is obtained from a quasi-initial state for a three-dimensional streaming-instability simulation that is a particle distribution with velocities for gas and particles from the Nakagawa relations. The equations of motion are chosen for the simplest case of freely streaming particles. We calculate the non-linearly evolved density power spectrum of dust particles and find that it develops a universal $k^{-3}$ tail at small scales, suggesting scale-invariant structure formation below a characteristic and time-dependent length scale. Thus, the KFT analysis indicates that the initial state for streaming instability simulations does not impose a constraint on structure evolution during planetesimal formation.

astro-ph.EP↗

arXiv2024

Kinetic field theory: effects of modified gravity theories with screening mechanisms on non-linear cosmic density fluctuations

In a mean-field approximation within Kinetic Field Theory, it is possible to derive an accurate analytic expression for the power spectrum of present-day non-linear cosmic density fluctuations. It depends on the theory of gravity and the cosmological model via the expansion function of the background space-time, the growth factor derived from it, and the gravitational coupling strength, which may deviate from Newton's constant in a manner depending on time and spatial scale. In earlier work [1], we introduced a functional Taylor expansion around general relativity and the cosmological standard model to derive the effects of a wide class of modified-gravity theories on the non-linear power spectrum, assuming that such effects need to be small given the general success of the standard model. Here, we extend this class towards theories with small-scale screening, modeling screening effects by a suitably flexible interpolating function. We compare the Taylor expansion with full mean-field solutions and find good agreement where expected. We find typical relative enhancements of the non-linear power spectrum between a few and a few ten per cent in a broad range of wave numbers between $k\gtrsim0.1-10\,h\,\mathrm{Mpc}^{-1}$, in good qualitative agreement with results of numerical simulations. Taking nDGP gravity as a quantitative example we compare our results to N-body simulations and find percent-level agreement for wavenumbers $k\lesssim 2\,h\,\text{Mpc}^{-1}$, if the scale where screening sets in, $k^*$, is adapted appropriately. This extends the application of our analytic approach to non-linear cosmic structure formation to essentially all classes of modified-gravity theories.

astro-ph.CO↗

arXiv2023

On the sensitivity of weak gravitational lensing to the cosmic expansion function

We analyse the functional derivative of the cosmic-shear power spectrum $C_\ell^γ$ with respect to the cosmic expansion function. Our interest in doing so is two-fold: (i) In view of attempts to detect minor changes of the cosmic expansion function which may be due to a possibly time-dependent dark-energy density, we wish to know how sensitive the weak-lensing power spectrum is to changes in the expansion function. (ii) In view of recent empirical determinations of the cosmic expansion function from distance measurements, independent of specific cosmological models, we wish to find out how uncertainties in the expansion function translate to uncertainties in the cosmic-shear power spectrum. We find the following answers: Relative changes of the expansion function are amplified by the cosmic-shear power spectrum by a factor $\approx 2-6$, weakly depending on the scale factor where the change is applied, and the current uncertainty of one example for an empirically determined expansion function translates to a relative uncertainty of the cosmic-shear power spectrum of $\approx10\,\%$.

astro-ph.CO↗

arXiv2023

Kinetic field theory: generic effects of alternative gravity theories on non-linear cosmic density-fluctuations

Non-linear cosmic structures contain valuable information on the expansion history of the background space-time, the nature of dark matter, and the gravitational interaction. The recently developed kinetic field theory of cosmic structure formation (KFT) allows to accurately calculate the non-linear power spectrum of cosmic density fluctuations up to wave numbers of $k\lesssim10\,h\,\mathrm{Mpc}^{-1}$ at redshift zero. Cosmology and gravity enter this calculation via two functions, viz. the background expansion function and possibly a time-dependent modification of the gravitational coupling strength. The success of the cosmological standard model based on general relativity suggests that cosmological models in generalized theories of gravity should have observable effects differing only weakly from those in standard cosmology. Based on this assumption, we derive the functional, first-order Taylor expansion of the non-linear power spectrum of cosmic density fluctuations obtained from the mean-field approximation in KFT in terms of the expansion function and the gravitational coupling strength. This allows us to study non-linear power spectra expected in large classes of generalized gravity theories. To give one example, we apply our formalism to generalized Proca theories.

astro-ph.CO↗

arXiv2023

On the asymptotic behaviour of cosmic density-fluctuation power spectra

We study the small-scale asymptotic behaviour of the cosmic density-fluctuation power spectrum in the Zel'dovich approximation. For doing so, we extend Laplace's method in arbitrary dimensions and use it to prove that this power spectrum necessarily develops an asymptotic tail proportional to $k^{-3}$ , irrespective of the cosmological model and the power spectrum of the initial matter distribution. The exponent $-3$ is set only by the number of spatial dimensions. We derive the complete asymptotic series of the power spectrum and compare the leading- and next-to-leading-order terms to derive characteristic scales for the onset of non-linear structure formation, independent of the cosmological model and the type of dark matter. Combined with earlier results on the mean-field approximation for including particle interactions, this asymptotic behaviour is likely to remain valid beyond the Zel'dovich approximation. Due to their insensitivity to cosmological assumptions, our results are generally applicable to particle distributions with positions and momenta drawn from a Gaussian random field. We discuss an analytically solvable toy model to further illustrate the formation of the $k^{-3}$ asymptotic tail.

astro-ph.CO↗

arXiv2023

On the asymptotic behaviour of cosmic density-fluctuation power spectra of cold dark matter

We study the small-scale asymptotic behaviour of the cold dark matter density fluctuation power spectrum in the Zel'dovich approximation, without introducing an ultraviolet cut-off. Assuming an initially correlated Gaussian random field and spectral index $0 < n_s < 1$, we derive the small-scale asymptotic behaviour of the initial momentum-momentum correlations. This result is then used to derive the asymptotics of the power spectrum in the Zel'dovich approximation. Our main result is an asymptotic series, dominated by a $k^{-3}$ tail at large wave-numbers, containing higher-order terms that differ by integer powers of $k^{n_s-1}$ and logarithms of $k$. Furthermore, we show that dark matter power spectra with an ultraviolet cut-off develop an intermediate range of scales where the power spectrum is accurately described by the asymptotics of dark matter without a cut-off. These results reveal information about the mathematical structure that underlies the perturbative terms in kinetic field theory and thus the non-linear power spectrum. We also discuss the sensitivity of the small-scale asymptotics to the spectral index $n_s$.

astro-ph.CO↗

arXiv2023

Ultracold plasmas from strongly anti-correlated Rydberg gases in the Kinetic Field Theory formalism

The dynamics of correlated systems is relevant in many fields ranging from cosmology to plasma physics. However, they are challenging to predict and understand even for classical systems due to the typically large numbers of particles involved. Here, we study the evolution of an ultracold, correlated many-body system with repulsive interactions and initial correlations set by the Rydberg blockade using the analytical framework of Kinetic Field Theory (KFT). The KFT formalism is based on the path-integral formulation for classical mechanics and was first developed and successfully used in cosmology to describe structure formation in Dark Matter. The theoretical framework offers a high flexibility regarding the initial configuration and interactions between particles and, in addition, is computationally cheap. More importantly, the analytic approach allows us to gain better insight into the processes which dominate the dynamics. In this work we show that KFT can be applied in a much more general context and study the evolution of a correlated ion plasma. We find good agreement between the analytical KFT results for the evolution of the correlation function and results obtained from numerical simulations. We use the correlation functions obtained with KFT to compute the temperature increase in the ionic system due to disorder-induced heating. For certain choices of parameters we observe that the effect can be reversed, leading to correlation cooling. Due to its numerical efficiency as compared to numerical simulations, a detailed study using KFT can help to constrain parameter spaces where disorder-induced heating is minimal in order to reach the regime of strong coupling.

cond-mat.quant-gas↗

arXiv2023

Baryon-photon interactions in Resummed Kinetic Field Theory

We explore how interactions between baryons and photons can be incorporated into Kinetic Field Theory (KFT), a description of cosmic structure formation based on classical Hamiltonian particle dynamics. In KFT, baryons are described as effective mesoscopic particles which represent fluid elements governed by the hydrodynamic equations. In this paper, we modify the mesoscopic particle model to include pressure effects exerted on baryonic matter through interactions with photons. As a proof of concept, we use this extended mesoscopic model to describe the tightly coupled baryon-photon fluid between matter-radiation equality and recombination. We show that this model can qualitatively reproduce the formation of baryon-acoustic oscillations in the cosmological power spectrum.

astro-ph.CO↗

arXiv2022

Kinetic Field Theory: Perturbation theory beyond first order

We present recent improvements in the perturbative treatment of particle interactions in Kinetic Field Theory (KFT) for inertial Zel'dovich trajectories. KFT has been developed for the systematic analytical calculation of non-linear cosmic structure formation on the basis of microscopic phase-space dynamics. We improve upon the existing treatment of the interaction operator by deriving a more rigorous treatment of phase-space trajectories of particles in an expanding universe. We then show how these results can be applied to KFT perturbation theory by calculating corrections to the late-time dark matter power spectrum at second order in the interaction operator. We find that the modified treatment of interactions w.r.t. inertial Zel'dovich trajectories improves the agreement of KFT with simulation results on intermediate scales compared to earlier results. Additionally, we illustrate that including particle interactions up to second order leads to a systematic improvement of the non-linear power spectrum compared to the first-order result.

astro-ph.CO↗

arXiv2022

Kinetic Field Theory for Cosmic Structure Formation

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 $k^{-3}$ for $k\to\infty$, 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 $k^{-11/2}$ under the same general conditions.

astro-ph.CO↗

arXiv2022

Triaxiality in galaxy clusters: Mass versus Potential reconstructions

Accounting for the triaxial shapes of galaxy clusters will become important in the context of upcoming cosmological surveys. We show that, compared to the gas density distribution, the cluster gravitational potential can be better characterised by a simple 3D model and is more robust against fluctuations. Perturbations in the gas density distribution can have a substantial influence on the derived thermodynamic properties, while cluster potentials are smooth and well-approximated by a spheroidal model. We use a statistical sample of 85 galaxy clusters from a large cosmological hydrodynamical simulation to investigate cluster shapes as a function of radius. In particular, we examine the shape of isodensity and isopotential shells and analyze how it is affected by the choice of component (gas vs. potential), substructure removal (for the gas density) and the definition of the computation domain (interior vs. shells). We find that the orientation and axis ratios of gas isodensity contours are degenerate with the presence of substructures and unstable against fluctuations. We observe that, as the derived cluster shape depends on the method used for removing the substructures, thermodynamic properties extracted from e.g. X-ray emissivity profiles suffer from this additional, often underestimated bias. In contrast, the shape reconstruction of the potential is largely unaffected by these factors and converges towards simple geometric models for both relaxed and dynamically active clusters. The observation that cluster potentials are better represented by simple geometrical models and reconstructed with a low level of systematics for both dynamically active and relaxed clusters suggests that by characterising galaxy clusters by their potential rather than by their mass, dynamically active and relaxed clusters could be combined in cosmological studies, improving statistics and lowering scatter.

astro-ph.CO↗

arXiv2021

Gravitational wave induced baryon acoustic oscillations

We study the impact of gravitational waves originating from a first order phase transition on structure formation. To do so, we perform a second order perturbation analysis in the $1+3$ covariant framework and derive a wave equation in which second order, adiabatic density perturbations of the photon-baryon fluid are sourced by the gravitational wave energy density during radiation domination and on sub-horizon scales. The scale on which such waves affect the energy density perturbation spectrum is found to be proportional to the horizon size at the time of the phase transition times its inverse duration. Consequently, structure of the size of galaxies and bigger can only be affected in this way by relatively late phase transitions at $\ge 10^{6}\,\text{s}$. Using cosmic variance as a bound we derive limits on the strength $α$ and the relative duration $(β/H_*)^{-1}$ of phase transitions as functions of the time of their occurrence which results in a new exclusion region for the energy density in gravitational waves today. We find that the cosmic variance bound forbids only relative long lasting phase transitions, e.g. $β/H_*\lesssim 6.8$ for $t_*\approx 5\times10^{11}\,\text{s}$, which exhibit a substantial amount of supercooling $α>20$ to affect the matter power spectrum.

gr-qc↗

arXiv2021

A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory

We present a detailed comparison of the newly developed particle-based Kinetic Field Theory framework for cosmic large-scale structure formation with the established formalism of Eulerian Standard Perturbation Theory. We highlight the qualitative differences of both approaches by a comparative analysis of the respective equations of motion and implementation of initial conditions. A natural starting point for a first quantitative comparison is given by the non-interacting regime of free-streaming kinematics. Our results suggest that Kinetic Field Theory contains a complete resummation of Standard Perturbation Theory in this regime. We further show that the exact free-streaming solution of Kinetic Field Theory can not be recovered in any finite order of Standard Perturbation Theory. Kinetic Field Theory should therefore provide a better starting point for perturbative treatments of non-linear structure formation.

astro-ph.CO↗