Cosmological Initial Conditions Research Articles

Second-order cosmological perturbation theory and initial conditions forN-body simulations

We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.

Angular momentum distribution during the collapse of primordial star-forming clouds

It is generally believed that angular momentum is distributed during the gravitational collapse of the primordial star forming cloud. However, so far there has been little understanding of the exact details of the distribution. We use the modified version of the Gadget-2 code, a three-dimensional smoothed-particle hydrodynamics simulation, to follow the evolution of the collapsing gas in both idealized as well as more realistic minihalos. We find that, despite the lack of any initial turbulence and magnetic fields in the clouds the angular momentum profile follows the same characteristic power-law that has been reported in studies that employed fully self-consistent cosmological initial conditions. The fit of the power-law appears to be roughly constant regardless of the initial rotation of the cloud. We conclude that the specific angular momentum of the self-gravitating rotating gas in the primordial minihalos maintains a scaling relation with the gas mass as $L \propto M^{1.125}$. We also discuss the plausible mechanisms for the power-law distribution.

Mean maps for cosmic web structures in cosmological initial conditions

Halos, filaments, sheets and voids in the cosmic web can be defined in terms of the eigenvalues of the smoothed shear tensor and a threshold $\lambda_{\rm th}$. Using analytic methods, we construct mean maps centered on these types of structures for Gaussian random fields corresponding to cosmological initial conditions. Each map also requires a choice of shear at the origin; we consider three possibilities. We find characteristic sizes, shapes and other properties of the central objects in these mean maps and explore how these properties change with varying the threshold and smoothing scale, i.e. varying the separation of the cosmic web into different kinds of components. The mean maps become increasingly complex as the threshold $\lambda_{\rm th}$ decreases to zero. We also describe scatter around these mean maps, subtleties which can arise in their construction, and some comparisons between halos in the maps and collapsed halos at final times.

Origin of inflation in CFT driven cosmology: $$R^2$$ R 2 -gravity and non-minimally coupled inflaton models

We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology $S^1\times S^3$, which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial $S^3$-section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in $R^2$ gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters $\epsilon$ and $\eta<0$ and their relation $\epsilon\sim\eta^2$ characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree level potentials of these models in the Einstein frame. We also discuss the role of $R^2$-gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the non-dynamical (ghost free) nature of its scale factor and special properties of its cosmological garland type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields.

Star formation in the first galaxies – III. Formation, evolution, and characteristics of the first metal-enriched stellar cluster

We simulate the formation of a low metallicity (0.01 Zsun) stellar cluster in a dwarf galaxy at redshift z~14. Beginning with cosmological initial conditions, the simulation utilizes adaptive mesh refinement and sink particles to follow the collapse and evolution of gas past the opacity limit for fragmentation, thus resolving the formation of individual protostellar cores. A time- and location-dependent protostellar radiation field, which heats the gas by absorption on dust, is computed by integration of protostellar evolutionary tracks with the MESA code. The simulation also includes a robust non-equilibrium chemical network that self-consistently treats gas thermodynamics and dust-gas coupling. The system is evolved for 18 kyr after the first protostellar source has formed. In this time span, 30 sink particles representing protostellar cores form with a total mass of 81 Msun. Their masses range from ~0.1 Msun to 14.4 Msun with a median mass ~0.5-1 Msun. Massive protostars grow by competitive accretion while lower-mass protostars are stunted in growth by close encounters and many-body ejections. In the regime explored here, the characteristic mass scale is determined by the temperature floor set by the cosmic microwave background and by the onset of efficient dust-gas coupling. It seems unlikely that host galaxies of the first bursts of metal-enriched star formation will be detectable with the James Webb Space Telescope or other next-generation infrared observatories. Instead, the most promising access route to the dawn of cosmic star formation may lie in the scrutiny of metal-poor, ancient stellar populations in the Galactic neighborhood. The observable targets that correspond to the system simulated here are ultra-faint dwarf satellite galaxies such as Bootes II, Segue I and II, and Willman I.

Cosmological attractors and initial conditions for inflation

Inflationary $\alpha$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with built-in inflaton shift symmetry and by making a canonical choice of the goldstino Kahler potential. The refined models are stable with respect to all scalar fields at all $\alpha$, no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field $\varphi$, and an infinitely long dS valley of constant depth and width at large $\varphi$. Because of the infinite length of this shift-symmetric valley, the initial value of the inflaton field at the Planck density is expected to be extremely large. We show that the inflaton field $\varphi$ does not change much until all fields lose their energy and fall to the bottom of the dS valley at large $\varphi$. This provides natural initial conditions for inflation driven by the inflaton field slowly rolling along the dS valley towards the minimum of the potential at small $\varphi$. A detailed description of this process is given for $\alpha$-attractors in supergravity, but we believe that our general conclusions concerning naturalness of initial conditions for inflation are valid for a broad class of inflationary models with sufficiently flat potentials.

The first stars: formation under X-ray feedback

We investigate the impact of a cosmic X-ray background (CXB) on Population III stars forming in a minihalo at $z\simeq25$. Using the smoothed particle hydrodynamics code GADGET-2, we attain sufficient numerical resolution to follow gas collapsing into the centre of the minihalo from cosmological initial conditions up to densities of $10^{12}\,{\rm cm}^{-3}$, at which point we form sink particles. This allows us to study how the presence of a CXB affects the formation of H$_2$ and HD in the gas prior to becoming fully molecular. Using a suite of simulations for a range of possible CXB models, we follow each simulation for 5000\yr after the first sink particle forms. The CXB provides two competing effects, with X-rays both heating the gas and increasing the free electron fraction, allowing more H$_2$ to form. X-ray heating dominates below $n\sim1\,{\rm cm}^{-3}$, while the additional H$_2$ cooling becomes more important above $n\sim10^2\,{\rm cm}^{-3}$. The gas becomes optically thick to X-rays as it exits the quasi-hydrostatic `loitering phase,' such that the primary impact of the CXB is to cool the gas at intermediate densities, resulting in an earlier onset of baryonic collapse into the dark matter halo. At the highest densities, self-shielding results in similar thermodynamic behaviour across a wide range of CXB strengths. Consequently, we find that star formation is relatively insensitive to the presence of a CXB; both the number and the characteristic mass of the stars formed remains quite similar even as the strength of the CXB varies by several orders of magnitude.

Tensor modes in bigravity: Primordial to present

Massive bigravity, a theoretically consistent modification of general relativity with an additional dynamical rank two tensor, successfully describes the observed accelerated expansion of the Universe without a cosmological constant. Recent analyses of perturbations around a cosmological background have revealed power law instabilities in both scalar and tensor perturbations, motivating an analysis of the initial conditions, evolution, and cosmological observables to determine the viability of these theories. In this paper we focus on the tensor sector, and study a primordial stochastic gravitational wave background in massive bigravity. The phenomenology can differ from standard General Relativity due to non-trivial mixing between the two linearized tensor fluctuations in the theory, only one of which couples to matter. We study perturbations about two classes of cosmological solutions in bigravity, computing the tensor contribution to the temperature anisotropies in the Cosmic Microwave Background radiation and the present stochastic gravitational wave background. The result is strongly dependent on the choice of cosmological background and initial conditions. One class of background solution generically displaying tremendous growth in the amplitude of large-wavelength gravitational waves, while the other remains observationally indistinguishable from standard General Relativity for a wide variety of initial conditions. We analyze the initial conditions for tensor modes expected in an inflationary cosmology, finding again that there is a strong dependence on the assumed background. For one choice of background, the semi-classical theory is beyond the perturbative regime. For the other choice, inflation generically yields initial conditions that, when evolved, give rise to a stochastic background observationally indistinguishable from standard General Relativity.

The first Population II stars formed in externally enriched mini-haloes

We present a simulation of the formation of the earliest Population II stars, starting from cosmological initial conditions and ending when metals created in the first supernovae are incorporated into a collapsing gas-cloud. This occurs after a supernova blast-wave collides with a nearby mini-halo, inducing further turbulence that efficiently mixes metals into the dense gas in the center of the halo. The gas that first collapses has been enriched to a metallicity of Z ~ 2e-5 Zsun. Due to the extremely low metallicity, collapse proceeds similarly to metal-free gas until dust cooling becomes efficient at high densities, causing the cloud to fragment into a large number of low mass objects. This external enrichment mechanism provides a plausible origin for the most metal-poor stars observed, such as SMSS J031300.36-670839.3, that appear to have formed out of gas enriched by a single supernova. This mechanism operates on shorter timescales than the time for low-mass mini-halos (M < 5e5 Msun) to recover their gas after experiencing a supernova. As such, metal-enriched stars will likely form first via this channel if the conditions are right for it to occur. We identify a number of other externally enriched halos that may form stars in this manner. These halos have metallicities as high as 0.01 Zsun, suggesting that some members of the first generation of metal-enriched stars may be hiding in plain sight in current stellar surveys.

The origin of spin in galaxies: clues from simulations of atomic cooling haloes

In order to elucidate the origin of spin in both dark matter and baryons in galaxies, we have performed hydrodynamical simulations from cosmological initial conditions. We study atomic cooling haloes in the redshift range $100 > z > 9$ with masses of order $10^9{\rm M_{\odot}}$ at redshift $z=10$. We assume that the gas has primordial composition and that ${\rm H_2}$-cooling and prior star-formation in the haloes have been suppressed. We present a comprehensive analysis of the gas and dark matter properties of four halos with very low ($\lambda \approx 0.01$), low ($\lambda \approx 0.04$), high ($\lambda \approx 0.06$) and very high ($\lambda \approx 0.1$) spin parameter. Our main conclusion is that the spin orientation and magnitude is initially well described by tidal torque linear theory, but later on is determined by the merging and accretion history of each halo. We provide evidence that the topology of the merging region, i.e. the number of colliding filaments, gives an accurate prediction for the spin of dark matter and gas: halos at the center of knots will have low spin while those in the center of filaments will have high spin. The spin of a halo is given by $\lambda \approx 0.05 \times \left(\frac{7.6}{\rm number\,\,\, of \,\,\, filaments}\right)^{5.1}$.

Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models

We study the evolution of linear perturbations in a Lemaítre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations couple at first order. As shown by Clarkson et al. (2009) [1], the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to 25% for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.

Eternal inflation with arrival terminals

We analyze the cosmological role of terminal vacua in the string theory landscape, and point out that existing work on this topic makes very strong assumptions about the properties of the terminal vacua. We explore the implications of relaxing these assumptions (by including ``arrival'' as well as ``departure'' terminals) and demonstrate that the results in earlier work are highly sensitive to their assumption of no arrival terminals. We use our discussion to make some general points about tuning and initial conditions in cosmology.

The life and death of cosmic voids

We investigate the formation, growth, merger history, movement, and destruction of cosmic voids detected via the watershed transform code vide in a cosmological N-body dark matter Λ cold dark matter simulation. By adapting a method used to construct halo merger trees, we are able to trace individual voids back to their initial appearance and record the merging and evolution of their progenitors at high redshift. For the scales of void sizes captured in our simulation, we find that the void formation rate peaks at scale factor 0.3, which coincides with a growth in the void hierarchy and the emergence of dark energy. Voids of all sizes appear at all scale factors, though the median initial void size decreases with time. When voids become detectable they have nearly their present-day volumes. Almost all voids have relatively stable growth rates and suffer only infrequent minor mergers. Dissolution of a void via merging is very rare. Instead, most voids maintain their distinct identity as annexed subvoids of a larger parent. The smallest voids are collapsing at the present epoch, but void destruction ceases after scale factor 0.3. In addition, voids centres tend to move very little, less than 10−2 of their effective radii per ln a, over their lifetimes. Overall, most voids exhibit little radical dynamical evolution; their quiet lives make them pristine probes of cosmological initial conditions and the imprint of dark energy.

Introducing the Illustris project: the evolution of galaxy populations across cosmic time

We present an overview of galaxy evolution across cosmic time in the Illustris Simulation. Illustris is an N-body/hydrodynamical simulation that evolves 2*1820^3 resolution elements in a (106.5Mpc)^3 box from cosmological initial conditions down to z=0 using the AREPO moving-mesh code. The simulation uses a state-of-the-art set of physical models for galaxy formation that was tuned to reproduce the z=0 stellar mass function and the history of the cosmic star-formation rate density. We find that Illustris successfully reproduces a plethora of observations of galaxy populations at various redshifts, for which no tuning was performed, and provide predictions for future observations. In particular, we discuss (a) the buildup of galactic mass, showing stellar mass functions and the relations between stellar mass and halo mass from z=7 to z=0, (b) galaxy number density profiles around massive central galaxies out to z=4, (c) the gas and total baryon content of both galaxies and their halos for different redshifts, and as a function of mass and radius, and (d) the evolution of galaxy specific star-formation rates up to z=8. In addition, we (i) present a qualitative analysis of galaxy morphologies from z=5 to z=0, for the stellar as well as the gaseous components, and their appearance in HST mock observations, (ii) follow galaxies selected at z=2 to their z=0 descendants, and quantify their growth and merger histories, and (iii) track massive z=0 galaxies to high redshift and study their joint evolution in star-formation activity and compactness. We conclude with a discussion of several disagreements with observations, and lay out possible directions for future research.

The First Billion Years project: dark matter haloes going from contraction to expansion and back again

We study the effect of baryons on the inner dark matter profile of the first galaxies using the First Billion Years simulation between z=16-6 before secular evolution sets in. Using a large statistical sample from two simulations of the same volume and cosmological initial conditions, one with and one without baryons, we are able to directly compare haloes with their baryon-free counterparts, allowing a detailed study of the modifications to the dark matter density profile due to the presence of baryons during the first billion years of galaxy formation. For each of the ~ 5000 haloes in our sample we quantify the impact of the baryons using eta, defined as the ratio of dark matter mass enclosed in 100 pc in the baryonic run to its counterpart without baryons. During this epoch of rapid growth of galaxies, we find that many haloes of these first galaxies show an enhancement of dark matter in the halo centre compared to the baryon-free simulation, while many others show a deficit. We find that the mean value of eta is close to unity, but there is a large dispersion, with a standard deviation of 0.677. The enhancement is cyclical in time and tracks the star formation cycle of the galaxy; as gas falls to the centre and forms stars, the dark matter moves in as well. Supernova feedback then removes the gas, and the dark matter again responds to the changing potential. We study three physical models relating the motion of baryons to that of the dark matter: adiabatic contraction, dynamical friction, and rapid outflows. Abridged, see text for full abstract

Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations II: the effect of the transverse mode

We study the initial conditions for cosmological N-body simulationsfor precision cosmology. In general, Zel'dovich approximationhas been applied for the initial conditions of N-bodysimulations for a long time. These initial conditions provideincorrect higher-order growth. These error caused bysetting up the initial conditions by perturbation theory is calledtransients. We investigated the impact of transient on non-Gaussianityof density field by performing cosmological N-body simulationswith initial conditions based on first-, second-, and third-orderLagrangian perturbation theory in previous paper. In this paper,we evaluates the effect of the transverse mode in the third-orderLagrangian perturbation theory for several statistical quantitiessuch as power spectrum and non-Gaussianty.Then we clarified that the effect of the transverse mode inthe third-order Lagrangian perturbation theory is quite small.

THE FIRST STARS: A LOW-MASS FORMATION MODE

We perform numerical simulations of the growth of a Population III stellar system under photodissociating feedback. We start from cosmological initial conditions at z = 100, self-consistently following the formation of a minihalo at z = 15 and the subsequent collapse of its central gas to high densities. The simulations resolve scales as small as ~ 1 AU, corresponding to gas densities of 10^16 cm^-3. Using sink particles to represent the growing protostars, we evolve the stellar system for the next 5000 years. We find that this emerging stellar group accretes at an unusually low rate compared with minihalos which form at earlier times (z = 20 - 30), or with lower baryonic angular momentum. The stars in this unusual system will likely reach masses ranging from < 1 M_sun to 5 M_sun by the end of their main-sequence lifetimes, placing them in the mass range for which stars will undergo an asymptotic giant branch (AGB) phase. Based upon the simulation, we predict the rare existence of Population III stars that have survived to the present day and have been enriched by mass overflow from a previous AGB companion.

Formation of the first low-mass stars from cosmological initial conditions

Abstract We simulate the formation of a metal-poor (10−2 Z⊙) stellar cluster in one of the first galaxies to form in the early Universe, specifically a high-redshift atomic cooling halo (z ∼ 14). This is the first calculation that resolves the formation of individual metal-enriched stars in simulations starting from realistic cosmological initial conditions. We follow the evolution of a single dense clump among several in the parent halo. The clump forms a cluster of ∼40 stars and sub-stellar objects within 7000 yr and could continue forming stars ∼5 times longer. Protostellar dust heating has a negligible effect on the star formation efficiency, at least during the early evolutionary stages, but it moderately suppresses gaseous fragmentation and brown dwarf formation. We observe fragmentation in thin gaseous filaments and sustained accretion in larger, rotating structures as well as ejections by binary interactions. The stellar initial mass function above 0.1 M⊙, evaluated after ∼104 yr of fragmentation and accretion, seems in agreement with the recent measurement in ultrafaint dwarf spheroidal Galactic satellites of Geha et al.

Overcooled haloes at z ≥ 10: a route to form low-mass first stars

It has been shown by Shchekinov & Vasiliev2006 (SV06) that HD molecules can be an important cooling agent in high redshift z >10 haloes if they undergo mergers under specific conditions so suitable shocks are created. Here we build upon Prieto et al. (2012) who studied in detail the merger-generated shocks, and show that the conditions for HD cooling can be studied by combining these results with a suite of dark-matter only simulations. We have performed a number of dark matter only simulations from cosmological initial conditions inside boxes with sizes from 1 to 4 Mpc. We look for haloes with at least two progenitors of which at least one has mass M > M_cr (z), where M_cr (z) is the SV06 critical mass for HD over-cooling. We find that the fraction of over-cooled haloes with mass between M_cr (z) and 10^{0.2} M_cr (z), roughly below the atomic cooling limit, can be as high as ~ 0.6 at z ~ 10 depending on the merger mass ratio. This fraction decreases at higher redshift reaching a value ~0.2 at z ~ 15. For higher masses, i.e. above 10^{0.2} M_cr (z) up to 10^{0.6} M_cr (z), above the atomic cooling limit, this fraction rises to values ~ 0.8 until z ~ 12.5. As a consequence, a non negligible fraction of high redshift z > 10 mini-haloes can drop their gas temperature to the Cosmic Microwave Background temperature limit allowing the formation of low mass stars in primordial environments.

Relation Between Initial Cosmological Conditions and the Properties of Dark Matter Haloes

The core-cusp problem is one of the essential issues in modern cosmology. The Entropy Theory of haloes Evolution recently suggested by Lukash, Doroshkevich and Mikheeva is one of the possible solutions to this problem. This work compares some results of numerical simulation of Large-Scale Structure with the conclusions of the Entropy Theory in order to verify this theory. The numerical simulation was performed in a volume 100 Mpc/h in a side using ~ 17 million particles. Dark matter particles, which then form virialized haloes, were found in the initial perturbation field. This work investigates the distribution of these dark matter particles and measures the velocity dispersion profiles. It also traces evolution of haloes entropy profiles. On the whole, simulation results correspond to Entropy Theory of haloes evolution.