arXiv subjects

Gábor Rácz

Publications and source records attributed to Gábor Rácz.

13 recordsLinked to original sources

arXiv2026

Cylindrical cosmological simulations with StePS

The global topology of the Universe can affect long-range gravitational forces via boundary conditions. Detailed studies of non-trivial topologies require simulations that natively adopt such geometries. Cosmological $N$-body simulations typically evolve matter in a periodic cubic box. While numerically convenient, this imposes a non-trivial three-torus topology that affects long-range gravitational forces, potentially biasing large-scale statistics. We introduce a compactified simulation framework that is only periodic along a single axis, characterised by an infinite topology with isotropic boundary conditions towards the perpendicular directions, namely, a $\mathrm{S}^1\times\mathbb{R}^2$ (slab) topology. This new simulation geometry is ideal for simulating systems with cylindrical symmetries such as filaments or certain anisotropic cosmological models. We compactified the comoving space via an inverse stereographic projection along the radial direction of a periodic cylinder. Then, we evolved the particles based on Newtonian dynamics. A smoothly varying spatial and mass resolution with radius suppresses edge artefacts at the free outer boundary. Our implementation in the StePS (STEreographically Projected cosmological Simulations) framework uses a direct force calculation that maps efficiently to GPUs, as well as an Octree force calculation for use on large CPU clusters. The cylindrical domain's topology enables fully self-consistent simulations to be run in the $\mathrm{S}^1\times\mathbb{R}^2$ manifold, while mitigating any periodic-image artefacts with respect to targets whose symmetries are mismatched to a cubic box. The main trade-off is a radially varying resolution with distinct systematics and analysis requirements. Finally, we demonstrate the accuracy of the new simulation method via a standard lambda cold dark matter cosmological simulation.

astro-ph.CO↗

arXiv2026

STEPSIC: Initial condition generator for stereographic cosmological simulations

Conventional cosmological initial condition generators are designed exclusively for fully periodic cubic domains and cannot produce the non-periodic, observer-centric configurations required by stereographically projected N-body codes such as StePS. We present STEPSIC, an open-source initial condition generator that extends Lagrangian perturbation theory-based initial conditions to the spherical and cylindrical geometries used by StePS, while also supporting cuboid domains with arbitrary aspect ratios. The code constructs Gaussian random density fields on anisotropy-free Fourier grids with cubic voxels, applies first- and second-order LPT to obtain displacement and velocity fields, and interpolates these onto particles via B-spline mass-assignment kernels with Fourier-space deconvolution. For stereographic geometries, a multiresolution scheme maps displacement fields across the radially varying particle mass resolution intrinsic to the projection. Both standard and paired-and-fixed variance-reduced realizations are supported. In periodic cubic boxes, the recovered matter power spectrum agrees with the input linear theory prediction to better than 0.5% up to half the Nyquist wavenumber, independent of box aspect ratio (tested up to 10:1). Cross-validation against monofonic using identical white noise fields yields sub-percent power spectrum agreement, with a small residual offset consistent with differences between two independent implementations. Full N-body evolution of matched cylindrical StePS runs confirms that second-order LPT correctly suppresses the 2-3% transient power excess present in first-order initial conditions.

astro-ph.CO↗

arXiv2025

Constraints on AvERA Cosmologies from Cosmic Chronometers and Type Ia Supernovae

We constrain AvERA cosmologies in comparison with the flat $Λ$CDM model using cosmic chronometer (CC) data and the Pantheon+ sample of type Ia supernovae (SNe Ia). The analysis includes fits to both CC and SN datasets using the \texttt{dynesty} dynamic nested sampling algorithm. For model comparison, we use the Bayesian model evidences and Anderson-Darling tests applied to the normalized residuals to assess consistency with a standard normal distribution. Best-fit parameters are derived within the redshift ranges $z \leq 2$ for CCs and $z \leq 2.3$ for SNe. For the baseline AvERA cosmology, we obtain best-fit values of the Hubble constant of ${H_0=68.32_{-3.27}^{+3.21}~\mathrm{km~s^{-1}~Mpc^{-1}}}$ from the CC analysis and ${H_0=71.99_{-1.03}^{+1.05}~\mathrm{km~s^{-1}~Mpc^{-1}}}$ from the SN analysis, each consistent within $1σ$ with the corresponding AvERA simulation value of $H(z=0)$. While both the CC and SN datasets yield higher Bayesian evidence for the flat $Λ$CDM model, they favor the AvERA cosmologies according to the Anderson-Darling test. We have identified signs of overfitting in each model, which suggests the possibility of overestimating the uncertainties in the Pantheon+ covariance matrix.

astro-ph.CO↗

arXiv2024

Simulating Rotating Newtonian Universes

We present the results of a novel type of numerical simulation that realizes a rotating Universe with a shear-free, rigid body rotation inspired by a Gödel-like metric. We run cosmological simulations of unperturbed glasses with various degrees of rotation in the Einstein-de Sitter and the $Λ$CDM cosmologies. To achieve this, we use the StePS N-body code capable of simulating the infinite Universe, overcoming the technical obstacles of classical toroidal (periodic) topologies that would otherwise prevent us from running such simulations. Results show a clear anisotropy between the polar and equatorial expansion rates with more than $1\%$ deviation from the isotropic case for maximal rotation without closed timeline curves within the horizon, $ω_{0} \approx 10^{-3}$ Gyr$^{-1}$; a considerable effect in the era of precision cosmology.

astro-ph.CO↗

arXiv2023

Complementary Cosmological Simulations

Cosmic variance limits the accuracy of cosmological N-body simulations, introducing bias in statistics such as the power spectrum, halo mass function, or the cosmic shear. We provide new methods to measure and reduce the effect of cosmic variance in existing and new simulations. We ran pairs of simulations using phase-shifted initial conditions with matching amplitudes. We set the initial amplitudes of the Fourier modes to ensure that the average power spectrum of the pair is equal to the cosmic mean power spectrum from linear theory. The average power spectrum of a pair of such simulations remains consistent with the estimated nonlinear spectra of the state-of-the-art methods even at late times. We also show that the effect of cosmic variance on any analysis involving a cosmological simulation can be estimated using the complementary pair of the original simulation. To demonstrate the effectiveness of our novel technique, we simulated a complementary pair of the original Millennium run and quantified the degree to which cosmic variance affected its the power spectrum. The average power spectrum of the original and complementary Millennium simulation was able to directly resolve the baryon acoustic oscillation features.

astro-ph.CO↗

arXiv2022

An empirical nonlinear power spectrum overdensity-response

Context. The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the response function. Aims. Our aim is to provide a new, simple, and accurate formula for the power spectrum overdensity response at highly nonlinear scales based on the results of cosmological simulations and paying special attention to the lognormal nature of the density field. Methods. We measured the dark matter power spectrum amplitude as a function of the overdensity ($δ_W$) in $N$-body simulation subsamples. We show that the response follows a power-law form in terms of $(1+δ_W)$, and we provide a new fit in terms of the variance, $σ(L)$, of a sub-volume of size $L$. Results. Our fit has a similar accuracy and a comparable complexity to second-order standard perturbation theory on large scales, but it is also valid for nonlinear (smaller) scales, where perturbation theory needs higher-order terms for a comparable precision. Furthermore, we show that the lognormal nature of the overdensity distribution causes a previously unidentified bias: the power spectrum amplitude for a subsample with an average density is typically underestimated by about $-2σ^2$. Although this bias falls to the sub-percent level above characteristic scales of $200Mpch^{-1}$, taking it into account improves the accuracy of estimating power spectra from zoom-in simulations and smaller high-resolution surveys embedded in larger low-resolution volumes.

astro-ph.CO↗

arXiv2021

The anisotropy of the power spectrum in periodic cosmological simulations

The classical gravitational force on a torus is anisotropic and always lower than Newton's $1/r^2$ law. We demonstrate the effects of periodicity in dark matter only $N$-body simulations of spherical collapse and standard $Λ$CDM initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations are a consequence of the missing large scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale $Λ$CDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

astro-ph.CO↗

arXiv2020

A common explanation of the Hubble tension and anomalous cold spots in the CMB

The standard cosmological paradigm narrates a reassuring story of a universe currently dominated by an enigmatic dark energy component. Disquietingly, its universal explaining power has recently been challenged by, above all, the $\sim4σ$ tension in the values of the Hubble constant. Another, less studied anomaly is the repeated observation of integrated Sachs-Wolfe imprints $\sim5\times$ stronger than expected in the $Λ$CDM model from R>100 $Mpc/h$ super-structures. Here we show that the inhomogeneous AvERA model of emerging curvature is capable of telling a plausible albeit radically different story that explains both observational anomalies without dark energy. We demonstrate that while stacked imprints of R>100 $Mpc/h$ supervoids in cosmic microwave background temperature maps can discriminate between the AvERA and $Λ$CDM models, their characteristic differences may remain hidden using alternative void definitions and stacking methodologies. Testing the extremes, we then also show that the CMB Cold Spot can plausibly be explained in the AvERA model as an ISW imprint. The coldest spot in the AvERA map is aligned with multiple low-$z$ supervoids with R>100 $Mpc/h$ and central underdensity $δ_{0}\approx-0.3$, resembling the observed large-scale galaxy density field in the Cold Spot area. We hence conclude that the anomalous imprint of supervoids may well be the canary in the coal mine, and existing observational evidence for dark energy should be re-interpreted to further test alternative models.

astro-ph.CO↗

arXiv2019

StePS: A Multi-GPU Cosmological N-body Code for Compactified Simulations

We present the multi-GPU realization of the StePS (Stereographically Projected Cosmological Simulations) algorithm with MPI-OpenMP-CUDA hybrid parallelization and nearly ideal scale-out to multiple compute nodes. Our new zoom-in cosmological direct N-body simulation method simulates the infinite universe with unprecedented dynamic range for a given amount of memory and, in contrast to traditional periodic simulations, its fundamental geometry and topology match observations. By using a spherical geometry instead of periodic boundary conditions, and gradually decreasing the mass resolution with radius, our code is capable of running simulations with a few gigaparsecs in diameter and with a mass resolution of $\sim 10^{9}M_{\odot}$ in the center in four days on three compute nodes with four GTX 1080Ti GPUs in each. The code can also be used to run extremely fast simulations with reasonable resolution for fitting cosmological parameters. These simulations are useful for prediction needs of large surveys. The StePS code is publicly available for the research community.

astro-ph.CO↗

arXiv2018

Compactified Cosmological Simulations of the Infinite Universe

We present a novel $N$-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low $k$ modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically Projected Cosmological Simulations. It uses stereographic projection for space compactification and naive $\mathcal{O}(N^2)$ force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P$^3$M) algorithm with similar spatial and mass resolution. The $N^2$ force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 \citep{Gadget2_2005MNRAS.364.1105S} running matching initial conditions.

astro-ph.CO↗

arXiv2018

The integrated Sachs-Wolfe effect in the AvERA cosmology

The recent AvERA cosmological simulation of Rácz et al. (2017) has a $Λ\mathrm{CDM}$-like expansion history and removes the tension between local and Planck (cosmic microwave background) Hubble constants. We contrast the AvERA prediction of the integrated Sachs--Wolfe (ISW) effect with that of $Λ\mathrm{CDM}$. The linear ISW effect is proportional to the derivative of the growth function, thus it is sensitive to small differences in the expansion histories of the respective models. We create simulated ISW maps tracing the path of light-rays through the Millennium XXL cosmological simulation, and perform theoretical calculations of the ISW power spectrum. AvERA predicts a significantly higher ISW effect than $Λ\mathrm{CDM}$, $A=1.93-5.29$ times larger depending on the $l$ index of the spherical power spectrum, which could be utilized to definitively differentiate the models. We also show that AvERA predicts an opposite-sign ISW effect in the redshift range $z \approx 1.5 - 4.4$, in clear contrast with $Λ\mathrm{CDM}$. Finally, we compare our ISW predictions with previous observations. While at present these cannot distinguish between the two models due to large error bars, and lack of internal consistency suggesting systematics, ISW probes from future surveys will tightly constrain the models.

astro-ph.CO↗

arXiv2017

Accurate and Efficient Profile Matching in Knowledge Bases

A profile describes a set of properties, e.g. a set of skills a person may have, a set of skills required for a particular job, or a set of abilities a football player may have with respect to a particular team strategy. Profile matching aims to determine how well a given profile fits to a requested profile. The approach taken in this article is grounded in a matching theory that uses filters in lattices to represent profiles, and matching values in the interval [0,1]: the higher the matching value the better is the fit. Such lattices can be derived from knowledge bases exploiting description logics to represent the knowledge about profiles. An interesting first question is, how human expertise concerning the matching can be exploited to obtain most accurate matchings. It will be shown that if a set of filters together with matching values by some human expert is given, then under some mild plausibility assumptions a matching measure can be determined such that the computed matching values preserve the rankings given by the expert. A second question concerns the efficient querying of databases of profile instances. For matching queries that result in a ranked list of profile instances matching a given one it will be shown how corresponding top-k queries can be evaluated on grounds of pre-computed matching values, which in turn allows the maintenance of the knowledge base to be decoupled from the maintenance of profile instances. In addition, it will be shown how the matching queries can be exploited for gap queries that determine how profile instances need to be extended in order to improve in the rankings. Finally, the theory of matching will be extended beyond the filters, which lead to a matching theory that exploits fuzzy sets or probabilistic logic with maximum entropy semantics. It will be shown that added fuzzy links can be captured by extending the underlying lattice.

cs.LO↗

arXiv2017

Concordance cosmology without dark energy

According to the separate universe conjecture, spherically symmetric sub-regions in an isotropic universe behave like mini-universes with their own cosmological parameters. This is an excellent approximation in both Newtonian and general relativistic theories. We estimate local expansion rates for a large number of such regions, and use a scale parameter calculated from the volume-averaged increments of local scale parameters at each time step in an otherwise standard cosmological $N$-body simulation. The particle mass, corresponding to a coarse graining scale, is an adjustable parameter. This mean field approximation neglects tidal forces and boundary effects, but it is the first step towards a non-perturbative statistical estimation of the effect of non-linear evolution of structure on the expansion rate. Using our algorithm, a simulation with an initial $Ω_m=1$ Einstein--de~Sitter setting closely tracks the expansion and structure growth history of the $Λ$CDM cosmology. Due to small but characteristic differences, our model can be distinguished from the $Λ$CDM model by future precision observations. Moreover, our model can resolve the emerging tension between local Hubble constant measurements and the Planck best-fitting cosmology. Further improvements to the simulation are necessary to investigate light propagation and confirm full consistency with cosmic microwave background observations.

astro-ph.CO↗