Spherical Overdensities Research Articles

Evolution of spherical overdensities in energy-momentum-squared gravity

Evolution of spherical overdensities in energy-momentum-squared gravity

Compaso: A new halo finder for competitive assignment to spherical overdensities

ABSTRACT We describe a new method (compaso) for identifying groups of particles in cosmological N-body simulations. compaso builds upon existing spherical overdensity (SO) algorithms by taking into consideration the tidal radius around a smaller halo before competitively assigning halo membership to the particles. In this way, the compaso finder allows for more effective deblending of haloes in close proximity as well as the formation of new haloes on the outskirts of larger ones. This halo-finding algorithm is used in the abacussummit suite of N-body simulations, designed to meet the cosmological simulation requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. compaso is developed as a highly efficient on-the-fly group finder, which is crucial for enabling good load-balancing between the GPU and CPU and the creation of high-resolution merger trees. In this paper, we describe the halo-finding procedure and its particular implementation in abacus, accompanying it with a qualitative analysis of the finder. We test the robustness of the compaso catalogues before and after applying the cleaning method described in an accompanying paper and demonstrate its effectiveness by comparing it with other validation techniques. We then visualize the haloes and their density profiles, finding that they are well fit by the NFW formalism. Finally, we compare other properties such as radius–mass relationships and two-point correlation functions with that of another widely used halo finder, rockstar.

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.

Gravitational Collapse and Structure Formation in an Expanding Universe with Dark Energy

Observations show that the expansion of the Universe is accelerating. This requires that the dominant constituent of matter in the Universe has some unusual properties like negative pressure. This exotic component has been given the name dark energy. We work with the simplest model of dark energy, the cosmological constant introduced by Einstein. We study the evolution of spherical over-densities in such a model and show that there is a minimum over-density required for collapse; perturbations with a smaller amplitude do not collapse. This threshold is interesting as even perturbations with a positive over-density and negative energy do not collapse in finite time. Further, we show that perturbations with an amplitude larger than, but comparable to the threshold value, take a very long time to collapse. We compare the solutions with the case when dark energy is absent.

Machine learning cosmological structure formation

We train a machine learning algorithm to learn cosmological structure formation from N-body simulations. The algorithm infers the relationship between the initial conditions and the final dark matter haloes, without the need to introduce approximate halo collapse models. We gain insights into the physics driving halo formation by evaluating the predictive performance of the algorithm when provided with different types of information about the local environment around dark matter particles. The algorithm learns to predict whether or not dark matter particles will end up in haloes of a given mass range, based on spherical overdensities. We show that the resulting predictions match those of spherical collapse approximations such as extended Press-Schechter theory. Additional information on the shape of the local gravitational potential is not able to improve halo collapse predictions; the linear density field contains sufficient information for the algorithm to also reproduce ellipsoidal collapse predictions based on the Sheth-Tormen model. We investigate the algorithm's performance in terms of halo mass and radial position and perform blind analyses on independent initial conditions realisations to demonstrate the generality of our results.

Spherical collapse models with clustered dark energy

We investigate the clustering effect of dark energy (DE) in the formation of galaxy clusters using the spherical collapse model. Assuming a fully clustered DE component, the spherical overdense region is treated as an isolated system which conserves the energy separately for both matter and DE inside the spherical region. Then, by introducing a parameter $r$ to characterize the degree of DE clustering, which is defined by the nonlinear density contrast ratio of matter to DE at turnaround in the recollapsing process, i.e. $r\equiv \nld_{\de,\ta}/\nld_{\m,\ta}$, we are able to uniquely determine the spherical collapsing process and hence obtain the virialized overdensity $\Dvir$ through a proper virialization scheme. Estimation of the virialized overdensities from current observation on galaxy clusters suggests that $0.5 < r < 0.8$ at $1\sigma$ level for the clustered DE with $w < -0.9$. Also, we compare our method to the linear perturbation theory that deals with the growth of DE perturbation at early times. While both results are consistent with each other, our method is practically simple and it shows that the collapse process is rather independent of initial DE perturbation and its evolution at early times.

Evolution of spherical over-densities in tachyon scalar field model

We study the tachyon scalar field model in flat FRW cosmology with the particular potential ϕ−2 and the scale factor behavior a(t)=tn. We consider the spherical collapse model and investigate the effects of the tachyon scalar field on the structure formation in flat FRW universe. We calculate δc(zc), λ(zc), ξ(zc), ΔV(zc), log⁡[νf(ν)] and log⁡[n(k)] for the tachyon scalar field model and compare the results with the results of EdS model and ΛCDM model. It is shown that in the tachyon scalar field model the structure formation may occur earlier, in comparison to the other models.

Evolution of spherical overdensities in new agegraphic dark energy model

We study the structure formation by investigating the spherical collapse model in the context of new agegraphic dark energy (NADE) model in flat FRW cosmology. We compute the perturbational quantities [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for the NADE model and compare the results with those of EdS and [Formula: see text] models. We find that there is a dark energy-dominated universe at low redshifts and a matter-dominated universe at high redshifts in agreement with the observations. Also, the size of structures, the overdense spherical region, and the halo size in the NADE model are found to be smaller, denser, and larger than those of EdS and [Formula: see text] models. We compare our results with the results of tachyon scalar field and holographic dark energy models.

Spherical collapse model and cluster number counts in power-lawf(T) gravity

We study the spherical collapse model (SCM) in the framework of spatially flat power law $f(T) \propto (-T)^{b}$ gravity model. We find that the linear and non-linear growth of spherical overdensities of this particular $f(T)$ model are affected by the power-law parameter $b$. Finally, we compute the predicted number counts of virialized haloes in order to distinguish the current $f(T)$ model from the expectations of the concordance $\Lambda$ cosmology. Specifically, the present analysis suggests that the $f(T)$ gravity model with positive (negative) $b$ predicts more (less) virialized objects with respect to those of $\Lambda$CDM.

Growth of spherical overdensities in scalar–tensor cosmologies

The accelerated expansion of the universe is a rather established fact in cosmology and many different models have been proposed as a viable explanation. Many of these models are based on the standard general relativistic framework of non-interacting fluids or more recently of coupled (interacting) dark energy models, where dark energy (the scalar field) is coupled to the dark matter component giving rise to a fifth-force. An interesting alternative is to couple the scalar field directly to the gravity sector via the Ricci scalar. These models are dubbed non-minimally coupled models and give rise to a time-dependent gravitational constant. In this work we study few models falling into this category and describe how observables depend on the strength of the coupling. We extend recent work on the subject by taking into account also the effects of the perturbations of the scalar field and showing their relative importance on the evolution of the mass function. By working in the framework of the spherical collapse model, we show that perturbations of the scalar field have a limited impact on the growth factor (for small coupling constant) and on the mass function with respect to the case where perturbations are neglected.

Effects of ghost dark energy perturbations on the evolution of spherical overdensities

While in the standard cosmological model the accelerated expansion of the Universe is explained by invoking the presence of the cosmological constant term, it is still unclear the true origin of this stunning observational fact. It is therefore interesting to explore alternatives to the simplest scenario, in particular by assuming a more general framework where the fluid responsible of the accelerated expansion is characterised by a time-dependant equation of state. Usually these models, dubbed dark energy models, are purely phenomenological, but in this work we concentrate on a theoretically justified model, the ghost dark energy model. Within the framework of the spherical collapse model, we evaluate effects of dark energy perturbations both at the linear and non-linear level and transfer these results into an observable quantity, the mass function, by speculatively taking into account contributions of dark energy to the mass of the halos. We showed that the growth rate is higher in ghost models and that perturbations enhance the number of structures with respect to the $\Lambda$CDM model, with stronger effects when the total mass takes into account dark energy clumps.

Evolution of spherical overdensities in holographic dark energy models

In this work we investigate the spherical collapse model in flat FRW dark energy universes. We consider the Holographic Dark Energy (HDE) model as a dynamical dark energy scenario with a slowly time-varying equation-of-state (EoS) parameter $w_{\rm de}$ in order to evaluate the effects of the dark energy component on structure formation in the universe. We first calculate the evolution of density perturbations in the linear regime for both phantom and quintessence behavior of the HDE model and compare the results with standard Einstein-de Sitter (EdS) and $\Lambda$CDM models. We then calculate the evolution of two characterizing parameters in the spherical collapse model, i.e., the linear density threshold $\delta_{\rm c}$ and the virial overdensity parameter $\Delta_{\rm vir}$. We show that in HDE cosmologies the growth factor $g(a)$ and the linear overdensity parameter $\delta_{\rm c}$ fall behind the values for a $\Lambda$CDM universe while the virial overdensity $\Delta_{\rm vir}$ is larger in HDE models than in the $\Lambda$CDM model. We also show that the ratio between the radius of the spherical perturbations at the virialization and turn-around time is smaller in HDE cosmologies than that predicted in a $\Lambda$CDM universe. Hence the growth of structures starts earlier in HDE models than in $\Lambda$CDM cosmologies and more concentrated objects can form in this case. It has been shown that the non-vanishing surface pressure leads to smaller virial radius and larger virial overdensity $\Delta_{\rm vir}$. We compare the predicted number of halos in HDE cosmologies and find out that in general this value is smaller than for $\Lambda$CDM models at higher redshifts and we compare different mass function prescriptions. Finally, we compare the results of the HDE models with observations.

ON PHYSICAL SCALES OF DARK MATTER HALOS

It is common practice to describe formal size and mass scales of dark matter halos as spherical overdensities with respect to an evolving density threshold. Here, we critically investigate the evolutionary effects of several such commonly used definitions and compare them to the halo evolution within fixed physical scales as well as to the evolution of other intrinsic physical properties of dark matter halos. It is shown that, in general, the traditional way of characterizing sizes and masses of halos dramatically overpredicts the degree of evolution in the last 10 Gyr, especially for low-mass halos. This pseudo-evolution leads to the illusion of growth even though there are no major changes within fixed physical scales. Such formal size definitions also serve as proxies for the virialized region of a halo in the literature. In general, those spherical overdensity scales do not coincide with the virialized region. A physically more precise nomenclature would be to simply characterize them by their very definition instead of calling such formal size and mass definitions 'virial'. In general, we find a discrepancy between the evolution of the underlying physical structure of dark matter halos seen in cosmological structure formation simulations and pseudo-evolving formal virial quantities. We question the importance of the role of formal virial quantities currently ubiquitously used in descriptions, models and relations that involve properties of dark matter structures. Concepts and relations based on pseudo-evolving formal virial quantities do not properly reflect the actual evolution of dark matter halos and lead to an inaccurate picture of the physical evolution of our universe.

Evolution of spherical over-density in thawing dark energy models

In this paper, we have studied the general evolution of spherical over-densities for thawing class of scalar field dark energy (DE) models. We have considered the scalar fields having canonical as well as non-canonical kinetic energy (particularly the Born-Infeld form of kinectic term) with various type of potentials, and also investigated the situation where DE is homogeneous as well as the case where DE virializes together with matter (inhomogeneous). Our study has shown that models with linear potential, in particular, can have significant deviation from the ΛCDM model in terms of density contrast at the time of virialization, and further study of the cluster number counts has shown that the total cluster number counts of different DE models can have substantial deviation from ΛCDM, and this deviation is most significant for all the models we have considered.

Separate universes do not constrain primordial black hole formation

Carr and Hawking showed that the proper size of a spherical overdense region surrounded by a flat Friedmann Robertson Walker (FRW) universe cannot be arbitrarily large as otherwise the region would close up on itself and become a separate universe. From this result, they derived a condition connecting size and density of the overdense region ensuring that it is part of our universe. Carr used this condition to obtain an upper bound for the density fluctuation amplitude with the property that for smaller amplitudes the formation of a primordial black hole is possible, while larger ones indicate a separate universe. In contrast, we find that the appearance of a maximum is not a consequence of avoiding separate universes but arises naturally from the geometry of the chosen slicing. Using instead of density a volume fluctuation variable reveals that a fluctuation is a separate universe if this variable diverges on superhorizon scales. Hence, Carr's and Hawking's condition does not pose a physical constraint on density fluctuations. The dynamics of primordial black hole formation with an initial curvature fluctuation amplitude larger than the one corresponding to the maximum density fluctuation amplitude was previously not considered in detail and so we compare it to the well-known case where the amplitude is smaller by presenting embedding and conformal diagrams of both types in dust spacetimes.

Evolution of spherical overdensity in thawing dark energy models

We study the general evolution of spherical over-densities for thawing class of dark energy models. We model dark energy with scalar fields having canonical as well as non-canonical kinetic energy. For non-canonical case, we consider models where the kinetic energy is of the Born-Infeld Form. We study various potentials like linear, inverse-square, exponential as well as PNGB-type. We also consider the case when dark energy is homogeneous as well as the case when it is inhomogeneous and virializes together with matter. Our study shows that models with linear potential in particular with Born-Infeld type kinetic term can have significant deviation from the $\Lambda$CDM model in terms of density contrast at the time of virialization. Although our approach is a simplified one to study the nonlinear evolution of matter overdensities inside the cluster and is not applicable to actual physical situation, it gives some interesting insights into the nonlinear clustering of matter in the presence of thawing class of dark energy models.

A theory of a spot

We present a simple inflationary scenario that can produce arbitrarily large spherical underdense or overdense regions embedded in a standard Λ cold dark matter paradigm, which we refer to as bubbles. We analyze the effect such bubbles would have on the Cosmic Microwave Background (CMB). For super-horizon sized bubble in the vicinity of the last scattering surface, a signal is imprinted onto CMB via a combination of Sach-Wolfe and an early integrated Sach-Wolfe (ISW) effects. Smaller, sub-horizon sized bubbles at lower redshifts (during matter domination and later) can imprint secondary anisotropies on the CMB via Rees-Sciama, late-time ISW and Ostriker-Vishniac effects. Our scenario, and arguably most similar inflationary models, produce bubbles which are over/underdense in potential: in density such bubbles are characterized by having a distinct wall with the interior staying at the cosmic mean density. We show that such models can potentially, with only moderate fine tuning, explain the cold spot, a non-Gaussian feature identified in the Wilkinson Microwave Anisotropy Probe (WMAP) data by several authors. However, more detailed comparisons with current and future CMB data are necessary to confirm (or rule out) this scenario.

Spherical collapse model in dark-energy cosmologies

We study the spherical collapse model for several dark energy scenarios using the fully nonlinear differential equation for the evolution of the density contrast within homogeneous spherical overdensities derived from Newtonian hydrodynamics. While mathematically equivalent to the more common approach based on the differential equation for the radius of the perturbation, this approach has substantial conceptual as well as numerical advantages. Among the most important are that no singularities at early times appear, which avoids numerical problems in particular in applications to cosmologies with dynamical and early dark energy, and that the assumption of time-reversal symmetry can easily be dropped where it is not strictly satisfied. We use this approach to derive the two parameters characterising the spherical-collapse model, i.e.~the linear density threshold for collapse $\delta_\mathrm{c}$ and the virial overdensity $\Delta_\mathrm{V}$, for a broad variety of dark-energy models and to reconsider these parameters in cosmologies with early dark energy. We find that, independently of the model under investigation, $\delta_\mathrm{c}$ and $\Delta_\mathrm{V}$ are always very close to the values obtained for the standard $\Lambda$CDM model, arguing that the abundance of and the mean density within non-linear structures are quite insensitive to the differences between dark-energy cosmologies. Regarding early dark energy, we thus arrive at a different conclusion than some earlier papers, including one from our group, and we explain why.

Second-order Lagrangian perturbation theory initial conditions for resimulations

We describe and test a new method for creating initial conditions for cosmological N-body dark matter simulations based on second-order Lagrangian perturbation theory (2lpt). The method can be applied to multi-mass particle distributions making it suitable for creating resimulation, or `zoom' initial conditions. By testing against an analytic solution we show that the method works well for a spherically symmetric perturbation with radial features ranging over more than three orders of magnitude in linear scale and eleven orders of magnitude in particle mass. We apply the method and repeat resimulations of the rapid formation of a high mass halo at redshift fifty and the formation of a Milky-Way mass dark matter halo at redshift zero. In both cases we find that many properties of the final halo show a much smaller sensitivity to the start redshift with the 2lpt initial conditions, than simulations started from Zel'dovich initial conditions. For spherical overdense regions structure formation is erroneously delayed in simulations starting from Zel'dovich initial conditions, and we demonstrate for the case of the formation the high redshift halo that this delay can be accounted for using the spherical collapse model. In addition to being more accurate, 2lpt initial conditions allow simulations to start later, saving computer time.

Dark energy and the evolution of spherical overdensities

We use the non-linear spherical model in cold dark matter (CDM) cosmologies with dark energy to investigate the effects of dark energy on the growth of structure and the formation of virialised structures. We consider dark energy models with a constant equation of state parameter w. For -1<w<-1/3, clusters form earlier and are more concentrated in quintessence than in LambdaCDM models, but they form later and are less concentrated than in the corresponding open model with the same matter density and no dark energy. We point out some confusion in the literature around the expression of the collapse factor (ratio of the radius of the sphere at virialisation to that at turn-around) derived from the virial theorem. We use the Sheth & Tormen extension of the Press-Schechter framework to calculate the evolution of the cluster abundance in different models and show the sensitivity of the cluster abundance to both the amplitude of the mass fluctuations, sigma8, and the sigma8-w normalisation, selected to match either the cosmic microwave background observations or the abundance of X-ray clusters.