Cosmological Structure Formation Research Articles

N-body simulations for parametrized modified gravity

ABSTRACT We present MG-evolution, an N-body code simulating the cosmological structure formation for parametrized modifications of gravity. It is built from the combination of parametrized linear theory with a parametrization of the deeply non-linear cosmological regime extrapolated from modified spherical collapse computations that cover the range of known screening mechanisms. We test MG-evolution, which runs at the speed of conventional ΛCDM simulations, against a suit of existing exact model-specific codes, encompassing linearized and chameleon f(R) gravity as well as the normal branch of the Dvali–Gabadadz–Porrati braneworld model, hence covering both large-field value and large-derivative screening effects. We compare the non-linear power spectra produced by the parametrized and model-specific approaches over the full range of scales set by the box size and resolution of our simulations, k = (0.05 − 2.5) $h\, \mathrm{Mpc}^{-1}$, and for two redshift slices, z = 0 and z = 1. We find sub-percent to one-percent level recovery of all the power spectra generated with the model-specific codes for the full range of scales. MG-evolution can be used for generalized and accurate tests of gravity and dark energy with the increasing wealth of high-precision cosmological survey data becoming available over the next decade.

Numerical solutions to Einstein’s equations in a shearing-dust universe: a code comparison

A number of codes for general-relativistic simulations of cosmological structure formation have been developed in recent years. Here we demonstrate that a sample of these codes produce consistent results beyond the Newtonian regime. We simulate solutions to Einstein’s equations dominated by gravitomagnetism—a vector-type gravitational field that does not exist in Newtonian gravity and produces frame-dragging, the leading-order post-Newtonian effect. We calculate the coordinate-invariant effect on intersecting null geodesics by performing ray tracing in each independent code. With this observable quantity, we assess and compare each code’s ability to compute relativistic effects.

Predicting dark matter halo formation in N-body simulations with deep regression networks

ABSTRACT Dark matter haloes play a fundamental role in cosmological structure formation. The most common approach to model their assembly mechanisms is through N-body simulations. In this work, we present an innovative pathway to predict dark matter halo formation from the initial density field using a Deep Learning algorithm. We implement and train a Deep Convolutional Neural Network to solve the task of retrieving Lagrangian patches from which dark matter haloes will condense. The volumetric multilabel classification task is turned into a regression problem by means of the Euclidean distance transformation. The network is complemented by an adaptive version of the watershed algorithm to form the entire protohalo identification pipeline. We show that splitting the segmentation problem into two distinct subtasks allows for training smaller and faster networks, while the predictive power of the pipeline remains the same. The model is trained on synthetic data derived from a single full N-body simulation and achieves deviations of ∼10 per cent when reconstructing the dark matter halo mass function at z = 0. This approach represents a promising framework for learning highly non-linear relations in the primordial density field. As a practical application, our method can be used to produce mock dark matter halo catalogues directly from the initial conditions of N-body simulations.

Inflaton clusters and inflaton stars

In a broad class of scenarios, inflation is followed by an extended era of matter-dominated expansion during which the inflaton condensate is nonrelativistic on subhorizon scales. During this phase density perturbations grow to the point of nonlinearity and collapse into bound structures. This epoch strongly resembles structure formation with ultra-light axion-like particles. This parallel permits us to adapt results from studies of cosmological structure formation to describe the nonlinear dynamics of this post-inflationary epoch. We show that the inflaton condensate fragments into “inflaton clusters”, analogues of axion dark matter halos in present-day cosmology. Moreover, solitonic objects or “inflaton stars” can form inside these clusters, leading to density contrasts as large as 106 in the post-inflationary universe.

Collapse of spherical overdensities in superfluid models of dark matter

Aims. We intend to understand cosmological structure formation within the framework of superfluid models of dark matter with finite temperatures. Of particular interest is the evolution of small-scale structures where the pressure and superfluid properties of the dark matter fluid are prominent. We compare the growth of structures in these models with the standard cold dark matter paradigm and non-superfluid dark matter. Methods. The equations for superfluid hydrodynamics were computed numerically in an expanding ΛCDM background with spherical symmetry; the effect of various superfluid fractions, temperatures, interactions, and masses on the collapse of structures was taken into consideration. We derived the linear perturbation of the superfluid equations, giving further insights into the dynamics of the superfluid collapse. Results. We found that while a conventional dark matter fluid with self-interactions and finite temperatures experiences a suppression in the growth of structures on smaller scales, as expected due to the presence of pressure terms, a superfluid can collapse much more efficiently than was naively expected due to its ability to suppress the growth of entropy perturbations and thus gradients in the thermal pressure. We also found that the cores of the dark matter halos initially become more superfluid during the collapse, but eventually reach a point where the superfluid fraction falls sharply. The formation of superfluid dark matter halos surrounded by a normal fluid dark matter background is therefore disfavored by the present work.

Amending the halo model to satisfy cosmological conservation laws

One of the most powerful tools in the arsenal of theoretical cosmologists is the halo model of large scale structure, which provides a phenomenological description of nonlinear structure in our universe. However, it is well known that there is no simple way to impose conservation laws in the halo model. This can severely impair the predictions on large scales for observables such as weak lensing or the kinematic Sunyaev-Zel'dovich effect, which should satisfy mass and momentum conservations, respectively. For example, the standard halo model overpredicts weak lensing power spectrum by $> 8\%$ on scales $>20$ degrees. To address this problem, we present an $Amended ~ Halo ~ Model$, explicitly separating the linear perturbations from $compensated$ halo profiles. This is guaranteed to respect conservation laws, as well as linear theory predictions on large scales. We then provide a simple fitting function for the compensated halo profiles, and discuss the modified predictions for 1-halo and 2-halo terms, as well as other cosmological observations such weak lensing power spectrum. Furthermore, we argue that the amended halo model provides a more accurate framework to capture physical effects that happen in the process of cosmological structure formation.

Trans-Planckian censorship and inflationary cosmology

We study the implications of the recently proposed Trans-Planckian Censorship Conjecture (TCC) for early universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a successful scenario for cosmological structure formation, the energy scale of inflation has to be lower than $10^9$ GeV. Demanding the correct amplitude of the cosmological perturbations then forces the generalized slow-roll parameter $\epsilon$ of the model to be very small ($<10^{-31}$). This leads to the prediction of a negligible amplitude of primordial gravitational waves. For slow-roll inflation models, it also leads to severe fine tuning of initial conditions.

The Schrödinger-Poisson method for Large-Scale Structure

We study the Schrödinger-Poisson (SP) method in the context of cosmological large-scale structure formation in an expanding background. In the limit 0ℏ → , the SP technique can be viewed as an effective method to sample the phase space distribution of cold dark matter that remains valid on non-linear scales. We present results for the 2D and 3D matter correlation function and power spectrum at length scales corresponding to the baryon acoustic oscillation (BAO) peak. We discuss systematic effects of the SP method applied to cold dark matter and explore how they depend on the simulation parameters. In particular, we identify a combination of simulation parameters that controls the scale-independent loss of power observed at low redshifts, and discuss the scale relevant to this effect.

Gamma-Ray and Neutrino Emissions due to Cosmic-Ray Protons Accelerated at Intracluster Shocks in Galaxy Clusters

Abstract We examine the cosmic-ray protons (CRp) accelerated at collisionless shocks in galaxy clusters using cosmological structure formation simulations. We find that in the intracluster medium (ICM) within the virial radius of simulated clusters, only ∼7% of shock kinetic energy flux is dissipated by the shocks that are expected to accelerate CRp—that is, supercritical, quasi-parallel (Q ∥) shocks with sonic Mach number M s ≥ 2.25. The rest is dissipated at subcritical shocks and quasi-perpendicular shocks, both of which may not accelerate CRp. Adopting the diffusive shock acceleration (DSA) model recently presented in Ryu et al., we quantify the DSA of CRp in simulated clusters. The average fraction of the shock kinetic energy transferred to CRp via DSA is assessed at ∼(1–2) × 10−4. We also examine the energization of CRp through reacceleration using a model based on the test-particle solution. Assuming that the ICM plasma passes through shocks three times on average through the history of the universe and that CRp are reaccelerated only at supercritical Q ∥-shocks, the CRp spectrum flattens by ∼0.05–0.1 in slope and the total amount of CRp energy increases by ∼40%–80% from reacceleration. We then estimate diffuse γ-ray and neutrino emissions, resulting from inelastic collisions between CRp and thermal protons. The predicted γ-ray emissions from simulated clusters lie mostly below the upper limits set by Fermi-LAT for observed clusters. The neutrino fluxes toward nearby clusters would be ≲10−4 of the IceCube flux at E ν = 1 PeV and ≲10−6 of the atmospheric neutrino flux in the energy range of E ν ≤ 1 TeV.

Cosmological signatures of dark sector physics: the evolution of haloes and spin alignment

ABSTRACT The standard cosmological paradigm currently lacks a detailed account of physics in the dark sector, the dark matter and energy that dominate cosmic evolution. In this paper, we consider the distinguishing factors between three alternative models – warm dark matter, quintessence, and coupled dark matter–energy – and lambda cold dark matter (ΛCDM) through numerical simulations of cosmological structure formation. Key halo statistics – halo spin/velocity alignment between large-scale structure and neighbouring haloes, halo formation time, and migration – were compared across cosmologies within the redshift range 0 ≤ z ≤ 2.98. We found the alignment of halo motion and spin to large-scale structures and neighbouring haloes to be similar in all cosmologies for a range of redshifts. The search was extended to low-density regions, avoiding non-linear disturbances of halo spins, yet very similar alignment trends were found between cosmologies, which are difficult to characterize and use as a probe of cosmology. We found that haloes in quintessence cosmologies form earlier than their ΛCDM counterparts. Relating this to the fact that such haloes originate in high-density regions, such findings could hold clues to distinguishing factors for the quintessence cosmology from the standard model. However, in general, halo statistics are not an accurate probe of the dark sector physics.

The perturbed FLRW metric on all scales: Newtonian limit and top-hat collapse

Abstract The applicability of a linearized perturbed FLRW metric to the late, lumpy universe has been subject to debate. We consider in an elementary way the Newtonian limit of the Einstein equations with this ansatz for the case of structure formation in late-time cosmology, on small and on large scales, and argue that linearizing the Einstein tensor produces only a small error down to arbitrarily small, decoupled scales (e.g. solar system scales). On subhorizon patches, the metric scale factor becomes a coordinate choice equivalent to choosing the spatial curvature, and not a sign that the FLRW metric cannot perturbatively accommodate very different local physical expansion rates of matter; we distinguish these concepts, and show that they merge on large scales for the Newtonian limit to be globally valid. Furthermore, on subhorizon scales, a perturbed FLRW metric ansatz does not already imply assumptions on isotropy, and effects beyond a FLRW background, including those potentially caused by nonlinearities of GR, may be encoded into nontrivial boundary conditions. The corresponding cosmologies have already been developed in a Newtonian setting by Heckmann and Schücking and none of these boundary conditions can explain the accelerated expansion of the universe. Our analysis of the field equations is confirmed on the level of solutions by an example of pedagogical value, comparing a collapsing top-hat overdensity (embedded into a cosmological background) treated in such perturbative manner to the corresponding exact solution of GR, where we find good agreement even in the regimes of strong density contrast

Cosmic Structure Formation with Kinetic Field Theory

AbstractKinetic field theory (KFT) is a statistical field theory for an ensemble of classical point particles in or out of equilibrium. Its application to cosmological structure formation is reviewed. Beginning with the construction of a generating functional, it is described in detail how the theory needs to be adapted to an expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, three approaches are developed to nonlinear cosmic structures, which rest either on expanding an interaction operator, averaging the interaction term, or resumming perturbation terms. An analytic, parameter‐free equation for the nonlinear cosmic power spectrum is presented. It is explained how density profiles of bound structures and velocity power spectra can be derived from the theory. It is clarified how KFT relates to the BBGKY hierarchy. Kinetic field theory is then applied to fluids, reformulating KFT in terms of macroscopic quantities. The resulting resummation scheme is used to describe mixtures of gas and dark matter. Finally, it is discussed how KFT can be combined with modified theories of gravity. As an example for a noncosmological application, results are shown on the spatial correlation function of cold Rydberg atoms derived from KFT.

Origin and impacts of the first cosmic rays

Nonthermal phenomena are ubiquitous in the Universe, and cosmic rays (CRs) play various roles in different environments. When, where, and how CRs are first generated since the Big Bang? We argue that blast waves from the first cosmic explosions at z~20 lead to Weibel mediated nonrelativistic shocks and CRs can be generated by the diffusive shock acceleration mechanism. We show that protons are accelerated at least up to sub-GeV energies, and the fast velocity component of supernova ejecta is likely to allow CRs to achieve a few GeV in energy. We discuss other possible accelerators of the first CRs, including accretion shocks due to the cosmological structure formation. These CRs can play various roles in the early universe, such as the ionization and heating of gas, the generation of magnetic fields, and feedbacks on the galaxy formation.

The dark matter bispectrum from effective viscosity and one-particle irreducible vertices

Dark matter evolution during the process of cosmological structure formation can be described in terms of a one-particle irreducible effective action at a characteristic scale km and a loop expansion below this scale, based on the effective propagators and vertices. We calculate the form of the effective vertices and compute the bispectrum of density perturbations within a one-loop approximation. We find that the effective vertices play a subdominant role as compared to the effective viscosity and sound velocity that modify the (inverse) propagators. For the bispectrum we reproduce the results of standard perturbation theory in the range where it is applicable, and find a slightly improved agreement with N-body simulations at larger wavenumbers.

Brief Review on Scalar Field Dark Matter Models

The existence of dark matter in the Universe has been solidly established in the last decades, after the arrival of accurate cosmological and astrophysical observations, and some consider it the most challenging problem in modern physics. Given the magnitude of the problem, one cannot discard the existence of new particles with properties that may look exotic in comparison with our current understanding of ordinary matter. This is the case for the so-called scalar field dark matter model, which assumes the existence of a (probably fundamental) scalar field with a very tiny mass that can have observable consequences in the formation of cosmological structure. We present here a brief account of the main properties of an ultra-light scalar field (with masses of the order of $10^{-22} \, \mathrm{eV}/c^2$) and how different observations have been used in the last two decades to put constraints on its physical parameters. Among other topics, we review the cosmological solutions of the model, discuss the features of its self-gravitating equilibrium configurations, revisit the gravitational collapse for the formation of galaxies, and revise the possibility to find a soliton structure in the center of dark matter halos.

Unification of the standard model and dark matter sectors in [SU(5) \xd7 U(1)

A simple model of dark matter contains a light Dirac field charged under a hidden U(1) gauge symmetry. When a chiral matter content in a strong dynamics satisfies the t’Hooft anomaly matching condition, a massless baryon is a natural candidate of the light Dirac field. One realization is the same matter content as the standard SU(5) × U(1)(B−L) grand unified theory. We propose a chiral [SU(5) × U(1)]4 gauge theory as a unified model of the SM and DM sectors. The low-energy dynamics, which was recently studied, is governed by the hidden U(1)4 gauge interaction and the third-family mathrm{U}{(1)}_{{left(B-Lright)}_3} gauge interaction. This model can realize self-interacting dark matter and alleviate the small-scale crisis of collisionless cold dark matter in the cosmological structure formation. The model can also address the semi-leptonic B-decay anomaly reported by the LHCb experiment.

Learning to predict the cosmological structure formation

Matter evolved under the influence of gravity from minuscule density fluctuations. Nonperturbative structure formed hierarchically over all scales and developed non-Gaussian features in the Universe, known as the cosmic web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and use a large ensemble of computer simulations to compare with the observed data to extract the full information of our own Universe. However, to evolve billions of particles over billions of years, even with the simplest physics, is a daunting task. We build a deep neural network, the Deep Density Displacement Model ([Formula: see text]), which learns from a set of prerun numerical simulations, to predict the nonlinear large-scale structure of the Universe with the Zel'dovich Approximation (ZA), an analytical approximation based on perturbation theory, as the input. Our extensive analysis demonstrates that [Formula: see text] outperforms the second-order perturbation theory (2LPT), the commonly used fast-approximate simulation method, in predicting cosmic structure in the nonlinear regime. We also show that [Formula: see text] is able to accurately extrapolate far beyond its training data and predict structure formation for significantly different cosmological parameters. Our study proves that deep learning is a practical and accurate alternative to approximate 3D simulations of the gravitational structure formation of the Universe.

Structure formation in dark energy cosmologies described by PADE parametrization

We study the imprints on the formation of cosmic structures of a particular class of dark energy parameterizations dubbed PADE parameterization. Here we investigate how dark energy can affect the growth of large scale structures of the universe in framework of spherical collapse model. The dynamics of the spherical collapse of a dark matter halo depends on the properties of the dark energy model. We show that the properties of spherical collapse scenario are directly affected by the evolution of dark energy. We obtain the main parameters of spherical collapse for two different DE parameterizations in two different approaches: first the homogeneous DE approach, in which dark energy does not exhibit fluctuations on cluster scales and the other, clustered DE scenario in which, dark energy components inside the overdense region collapses similar to dark matter. Using the Sheth-Tormen mass function, we investigate the abundance of virialized halos in the framework of PADE parameterizations. Specifically, the present analysis shows that the number count of dark matter halos depends on the evolution of DE parameterizations and clustering properties of dark energy. Also we show that perturbations in phantom DE components enhance the growth of matter perturbations. This result were obtained in the literature for dark energy parameterizations that are phantom at all redshifts. But we obtained same results for dark energy parameterizations which are in phantom regime and enter in quintessence region at relatively low redshifts. We also show that in parameterizations under study, low mass halos were formed before massive halos.

Effects of neutrino mass and asymmetry on cosmological structure formation

Light but massive cosmological neutrinos do not cluster significantly on small scales, due to their high thermal velocities. With finite masses, cosmological neutrinos become part of the total matter field and contribute to its smoothing. Structure formation in the presence of massive neutrinos is therefore impeded compared to that in the standard ΛCDM cosmology with massless neutrinos. Neutrinos' masses also distort the anisotropy power spectrum of cosmic microwave background (CMB). Furthermore, a finite chemical potential μ for cosmological neutrinos, still allowed by current data, would have a non-negligible impact on CMB and structure formation. We consistently evaluate effects of neutrino masses and chemical potentials on the matter power spectrum by use of a neutrino-involved N-body simulation, with cosmological parameters obtained from a Markov-Chain Monte-Carlo (MCMC) refitting of CMB data. Our results show that while a finite averaged neutrino mass mν tends to suppress the matter power spectrum in a range of wave numbers, the neutrino degeneracy parameters ξi ≡ μi /T (i= 1, 2, 3) enhance the latter, leading to a large parameter degeneracy between mν and ξi. We provide an empirical formula for the effects on the matter power spectrum in a selected range of wave numbers induced by mν and η ≡ √∑i ξ2i. Observing a strong correlation between mν and η, we propose a single redshift-independent parameter mν − 4/3 η2 to characterize the neutrino effects on the matter power spectrum.

Dust scaling relations in a cosmological simulation

To study the dust evolution in the cosmological structure formation history, we perform a smoothed particle hydrodynamic simulation with a dust enrichment model in a cosmological volume. We adopt the dust evolution model that represents the grain size distribution by two sizes and takes into account stellar dust production and interstellar dust processing. We examine the dust mass function and the scaling properties of dust in terms of the characteristics of galaxies. The simulation broadly reproduces the observed dust mass functions at redshift $z = 0$, except that it overproduces the massive end at dust mass $M_\mathrm{d} \gtrsim 10^{8}$ ${\rm M}_\odot$. This overabundance is due to overproducing massive gas/metal-rich systems, but we also note that the relation between stellar mass and gas-phase metallicity is reproduced fairly well by our recipe. The relation between dust-to-gas ratio and metallicity shows a good agreement with the observed one at $z=0$, which indicates successful implementation of dust evolution in our cosmological simulation. Star formation consumes not only gas but also dust, causing a decreasing trend of the dust-to-stellar mass ratio at the high-mass end of galaxies. We also examine the redshift evolution up to $z \sim~ 5$, and find that the galaxies have on average the highest dust mass at $z = 1-2$. For the grain size distribution, we find that galaxies with metallicity $\sim 0.3~ Z_\odot$ tend to have the highest small-to-large grain abundance ratio; consequently, the extinction curves in those galaxies have the steepest ultraviolet slopes.