We use 1-dimensional numerical simulations to study spherical collapse in the f(R) gravity models. We include the nonlinear coupling of the gravitational potential to the scalar field in the theory and use a relaxation scheme to follow the collapse. We find an unusual enhancement in density near the virial radius which may provide observable tests of gravity. We also use the estimated collapse time to calculate the critical overdensity $δ_c$ used in calculating the mass function and bias of halos. We find that analytical approximations previously used in the literature do not capture the complexity of nonlinear spherical collapse.
We give a set of exact nonlinear closed--form solutions for the non-spherical collapse of pressure-less matter in Newtonian gravity, and indicate their possible cosmological applications. Keywords: Newtonian gravitation: free collapse, large-scale cosmic structures
We study the spherical collapse in the Parametrized Post-Friedmannian (PPF) scheme. We use a general form of the PPF parameter related to the Poisson equation and found the equations to solve that includes a non-trivial fifth force coming from the convolution of the modified gravity term in the k-space. In order to compute a concrete model, we use the parametrization proposed by Bertschinger and Zukin. The equations of the spherical collapse are solved assuming a Gaussian density profile and we show there is no shell crossing before reaching the turn around point. We show that the fifth force …
Under the commonly used spherical collapse model, we study how dark energy affects the growth of large scale structures of the Universe in the context of agegraphic dark energy models. The dynamics of the spherical collapse of dark matter halos in nonlinear regimes is determined by the properties of the dark energy model. We show that the main parameters of the spherical collapse model are directly affected by the evolution of dark energy in the agegraphic dark energy models. We compute the spherical collapse quantities for different values of agegraphic model parameter $α$ in two different sc…
We study the spherical collapse of non-top-hat matter fluctuations in the presence of dark energy with arbitrary sound speed. The model is described by a system of partial differential equations solved using a pseudo-spectral method with collocation points. This method can reproduce the known analytical solutions in the linear regime with an accuracy better than $10^{-6}\%$ and better than $10^{-2}\%$ for the virialization threshold given by the usual spherical collapse model. We show the impact of nonlinear dark energy fluctuations on matter profiles, matter peculiar velocity and gravitationa…
We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modi…
The effect of background dynamics of the universe on formation of large scale structures in the framework of Modified Newtonian Dynamics (MOND) is investigated. A spherical collapse model is used for modeling the formation of the structures. This study is done in two extreme cases: ({\it i}) assuming a universe with a low-density baryonic matter without any cold dark matter and dark energy; ({\it ii}) a dark energy dominated universe with baryonic matter, without cold dark matter. We show that for the case ({\it ii}) the structures virialize at lower redshifts with larger radii compared to the…
We study the non-linear spherical "top hat" collapse for Chaplygin and viscous unified cosmologies. The term unified refers to models where dark energy and dark matter are replaced by one single component. For the generalized Chaplygin gas (GCG) we extend previous results of [R. A. A. Fernandes {\it et al}. Physical Review D 85, 083501 (2012)]. We discuss the differences at non-linear level between the GCG with $α=0$ and the $Λ$CDM model. We show that both are indeed different. The bulk viscous model which differs from the GCG due to the existence of non-adiabatic perturbations is also studied…
We explore the real solutions to the Spherical Collapse Model in a non-flat Universe with a Cosmological Constant, and observe a possible situation for a fake or Ghost Collapse, in which an expanding overdense spherical region, turns around and begins to collapse, turns around again after a finite time and starts expanding. To make such a situation of spurious collapse feasible, we make a linear redshift dependent correction to the standard Dark Energy density term which is originally in the form of a cosmological constant. There is good reason to believe in such a correction based on recent r…
Considering perturbation growth in spherical Top-Hat model of structure formation in a generalized Chaplygin gas dominated universe, we want to study this scenario with a modified Chaplygin gas model. The evolution of background and collapsed region parameters are found for different cases. The stability of the model and the collapse time rate are considered in different cases. The turn-around redshifts are also computed; the results are in relatively good agreement with current observational data.
The nonlinear collapse for viscous generalized Chaplygin gas Model (VGCG) was analyzed in the framework of spherical top-hat collapse. As the VGCG and baryons are essential to form the large scale structure, we focused on their nonlinear collapse in this paper. We discussed the influence of model parameters $α$ and $ζ_{0}$ on the spherical collapse by varying their values and compare with $ΛCDM$. The results show that, for the VGCG model, smaller $ζ_{0}$ and larger $α$ make the structure formation earlier and faster, and the collapse curves of VGCG model is almost distinguished with the $ΛCDM$…
We study the evolution of inhomogeneous spherical perturbations in the universe in a way that generalizes the spherical top hat collapse in a straightforward manner. For that purpose we derive a dynamical equation for the evolution of the density contrast in the context of a Lemaitre-Tolman-Bondi metric and construct solutions with and without a cosmological constant for the evolution of a spherical perturbation with a given initial radial profile.
We study gravitational collapse of a spherically symmetric inhomogeneous dust cloud in the Lovelock theory without cosmological constant. We show that the final fate of gravitational collapse in this theory depends on the spacetime dimensions. In odd dimensions the naked singularities formed are found to be massive. In the even dimensions,on the other hand, the naked singularities are found to be massless. We also show that the curvature strength of naked singularity is independent of the spacetime dimensions in odd dimensions. However, it depends on the spacetime dimensions in even dimension.
In this paper, we test the spherical collapse of a viscous unified dark fluid (VUDF) which has constant adiabatic sound speed and show the nonlinear collapse for VUDF, baryons, and dark matter which are important to form the large scale structure of our Universe. By varying the values of model parameters $α$ and $ζ_{0}$, we discuss their effects on the nonlinear collapse of the VUDF model, and compare its result to $ΛCDM$ model. The analyzed results show that, within the spherical top-hat collapse framework, larger values of $α$ and smaller values of $ζ_{0}$ make the structure formation earlie…
The spherical collapse model is often used to follow the evolution of overdensities into the nonlinear regime. We describe the correct approach to be used in coupled dark energy cosmologies, where a fifth force, different from gravity and mediated by the dark energy scalar field, influences the collapse. We reformulate the spherical collapse description by deriving it directly from the set of nonlinear hydrodynamical Navier Stokes equations. By comparing with the corresponding relativistic equations, we show how the fifth force should be taken into account within the spherical collapse picture…
In this paper, we test the spherical collapse of a unified dark fluid (UDF) which has constant adiabatic sound speed. By choosing the different values of model parameters $B_s$ and $α$, we show the nonlinear collapse for UDF and baryons which are considered for their formation of the large scale structure of our Universe. The analyzed results show that larger values of $α$ and $B_s$ make the structure formation faster and earlier.
We numerically study spherical gravitational collapse in shift symmetric Einstein dilaton Gauss Bonnet (EdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from hyperbolic to elliptic type in a compact region of the spacetime. In these cases evolution of the system, treated as a hyperbolic initial boundary value problem, leads to the equations of motion becoming ill-posed when the elliptic region forms. No singularities or discontinuities are encountered on the corresponding effective "Cauchy horizon". Therefore it…
The influence of the shear stress and angular momentum on the nonlinear spherical collapse model is discussed in the framework of the Einstein-de Sitter (EdS) and $Λ$CDM models. By assuming that the vacuum component is not clustering within the homogeneous nonspherical overdensities, we show how the local rotation and shear affects the linear density threshold for collapse of the non-relativistic component ($δ_\mathrm{c}$) and its virial overdensity ($Δ_\mathrm{V}$). It is also found that the net effect of shear and rotation in galactic scale is responsible for higher values of the linear over…
We study, for the first time, how shear and angular momentum modify typical parameters of the spherical collapse model, in dark energy dominated universes. In particular, we study the linear density threshold for collapse $δ_\mathrm{c}$ and the virial overdensity $Δ_\mathrm{V}$, for several dark-energy models and its influence on the cumulative mass function. The equations of the spherical collapse are those obtained in Pace et al. (2010), who used the fully nonlinear differential equation for the evolution of the density contrast derived from Newtonian hydrodynamics, and assumed that dark ene…
We investigate the virialization of cosmic structures in the framework of flat FLRW cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, "turn around" and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, $Λ=Λ(H)$. A particularly well motivated model of this type is the so-called quantum field vacuum, in which $Λ(H)$ is a quadratic function, $Λ(H)=n_0+n_2\…
Traditionally the spherical collapse of objects is studied with respect to a uniform background density, yielding the critical over-density $δ_\mathrm{c}$ as key ingredient to the mass function of virialized objects. Here we investigate the shear and rotation acting on a peak in a Gaussian random field. By assuming that collapsing objects mainly form at those peaks, we use this shear and rotation as external effects changing the dynamics of the spherical collapse, which is described by the Raychaudhuri equation. We therefore assume that the shear and rotation have no additional dynamics on top…
We report the findings of new exact analytical solutions to the cosmological fluid equations, namely for the case where the initial conditions are perturbatively close to a spherical top-hat profile. To do so we enable a fluid description in a Lagrangian-coordinates approach, and prove the convergence of the Taylor-series representation of the Lagrangian displacement field until the time of collapse ("shell-crossing"). This allows the determination of the time for quasi-spherical collapse, which is shown to happen generically earlier than in the spherical case. For pedagogical reasons, calcula…
Here we present a simple, parameter-free, non-perturbative algorithm that gives low-redshift cosmological particle realizations accurate to few-Megaparsec scales, called MUSCLE (MUltiscale Spherical ColLapse Evolution). It has virtually the same cost as producing N-body-simulation initial conditions, since it works with the 'stretch' parameter ψ, the Lagrangian divergence of the displacement field. It promises to be useful in quickly producing mock catalogs, and to simplify computationally intensive reconstructions of galaxy surveys. MUSCLE applies a spherical-collapse prescription on multiple…
We compute the critical density of collapse for spherically symmetric overdensities in a class of f(R) modified gravity models. For the first time we evolve the Einstein, scalar field and non-linear fluid equations, making the minimal simplifying assumptions that the metric potentials and scalar field remain quasi-static throughout the collapse. Initially evolving a top hat profile, we find that the density threshold for collapse depends significantly on the initial conditions imposed, specifically the choice of size and shape. By imposing `natural' initial conditions, we obtain a fitting func…
Understanding the influence of dark energy on the formation of structures is currently a major challenge in Cosmology, since it can distinguish otherwise degenerated viable models. In this work we consider the Top-Hat Spherical-Collapse (SC) model with dark energy, which can partially (or totally) cluster, according to a free parameter $γ$. The {\it lack of} energy conservation has to be taken into account accordingly, as we will show. We determine characteristic quantities for the SC model, such as the critical contrast density and radius evolution, with particular emphasis on their dependenc…
We expand previous works on the spherical `top-hat' collapse (SC-TH) framework in generalized Chaplygin gas (gCg) dominated universes. Here we allow the collapse in all energetic components within the system. We analyze the non-linear stages of collapse for various choices of parameter αof the gCg model introducing an exact formulation for the so-called effective sound speed, $c_{eff}^2$. We show that, within the SC-TH framework, the growth of the structure becomes faster with increasing values of α.
The DGP (Dvali, Gabadaze and Porrati) braneworld cosmology gives an alternative to dark energy. In DGP cosmology the alleged cosmic acceleration is generated by the modification of gravity theory. Nonlinear evolution of matter density contrast in DGP braneworld cosmology is studied in the present work. The semi-analytic approach of spherical collapse of matter overdensity is adopted in the present context to study the nonliner evolution. Further, the number count of galaxy clusters along the redshift is studied for the DGP cosmology using Press-Schechter and Sheth-Tormen mass function formalis…
We study the gravitational clustering of spherically symmetric overdensities and the statistics of the resulting dark matter halos in the "symmetron model", in which a new long range force is mediated by a $Z_2$ symmetric scalar field. Depending on the initial radius of the overdensity, we identify two distinct regimes: for small initial radii the symmetron mediated force affects the spherical collapse at all redshifts; for initial radii larger than some critical size this force vanishes before collapse because of the symmetron screening mechanism. In both cases overdensities collapse earlier …
We investigate the effects of a disformal coupling between dark energy and dark matter in the predictions of the spherical collapse and its signatures in galaxy cluster number counts. We find that the disformal coupling has no significant effects on spherical collapse at high redshifts, and in particular during matter domination epoch. However, at lower redshifts, the extrapolated linear density contrast at collapse close to redshift $z \lesssim 1$ and overdensity at virialization can be strongly suppressed by a disformal coupling between dark energy and dark matter. We also find that disforma…
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…
I examine differences in non-linear structure formation between cosmological models that share a $z=0$ linear power spectrum in both shape and amplitude, but that differ via their growth history. $N$-body simulations of these models display an approximately identical large-scale-structure skeleton, but reveal deeply non-linear differences in the demographics and properties of haloes. I investigate to what extent the spherical-collapse model can help in understanding these differences, in both real and redshift space. I discuss how this is difficult to do if one attempts to identify haloes dire…
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a co…
Accretion shocks around galaxy clusters mark the position where the infalling diffuse gas is significantly slowed down, heated up, and becomes a part of the intracluster medium (ICM). They play an important role in setting the ICM properties. Hydrodynamical simulations have found an intriguing result that the radial position of this accretion shock tracks closely the position of the `splashback radius' of the dark matter, despite the very different physical processes that gas and dark matter experience. Using the self-similar spherical collapse model for dark matter and gas, we find that an al…
We study, using $N$-body simulation, the shape evolution in gravitational collapse of cold uniform spherical system. The central interest is on how the deviation from spherical symmetry depends on particle number $N$. By revisit of the spherical collapse model, we hypothesize that the departure from spherical symmetry is regulated by the finite-$N$ density fluctuation. Following this assumption, the estimate of the flattening of relaxed structures is derived to be $N^{-1/3}$. In numerical part, we find that the virialized states can be characterized by the core-halo structures and the flatteni…
