Einstein-de Sitter Cosmology Research Articles

Halo mass function in scale invariant models

ABSTRACTSheth–Tormen mass function has been widely used to quantify the abundance of dark matter haloes. It is a significant improvement over the Press–Schechter mass function as it uses ellipsoidal collapse in place of spherical collapse. Both of these mass functions can be written in a form that is universal, i.e. independent of cosmology and power spectrum when scaled in suitable variables. However, cosmological simulations have shown that this universality is approximate. In this paper, we investigate the power spectrum dependence of halo mass function through a suite of dark-matter-only N-body simulations of seven power-law models in an Einstein–de Sitter cosmology. This choice of cosmology and a power-law power spectrum ensures the self-similar evolution of dark matter distribution, allowing us to isolate the power spectrum dependence of mass function. We find that the mass function shows a clear non-universality. We present fits for the parameters of the Sheth–Tormen mass function for a range of power-law power spectrum indices. We find a mild evolution in the overall shape of the mass function with the epoch. Finally, we extend our result to LCDM cosmology. We show that the Sheth–Tormen mass function with parameter values derived from a matched power-law Einstein–de Sitter cosmology provides a better fit to the LCDM mass function than the standard Sheth–Tormen mass function. Our results indicate that an improved analytical theory is required to provide better fits to the mass function.

Local Scale Covariance and Its Radical Implications for Cosmology

Local scale covariance posits that no privileged length scales should appear in the fundamental equations of local, Minkowskian physics—why should nature have scale, but not position preferences?—yet, they clearly do. A resolution is proposed wherein scale covariance is promoted to the status of Poincaré covariance, and privileged scales emerge as a result of ‘scale clustering’, similarly to the way privileged positions emerge in a translation covariant theory. The implied ability of particles to ‘move in scale’ has recently been shown by the author to offer a possible elegant solution to the missing matter problem. For cosmology, the implications are: (a) a novel component of the cosmological redshift, due to scale-motion over cosmological times; (b) a radically different scenario for the early universe, during which the conditions for such scale clustering are absent. The former is quantitatively analyzed, resulting in a unique cosmological model, empirically coinciding with standard Einstein–de-Sitter cosmology, only in some non-physical limit. The latter implication is qualitatively discussed as part of a critique of the conceptual foundations of ΛCDM which ignores scale covariance altogether.

Time-sliced perturbation theory with primordial non-Gaussianity and effects of large bulk flows on inflationary oscillating features

We extend the formalism of time-sliced perturbation theory (TSPT) for cosmological large-scale structure to include non-Gaussian initial conditions. We show that in such a case the TSPT interaction vertices acquire new contributions whose time-dependence factorizes for the Einstein-de Sitter cosmology. The new formulation is free from spurious infrared (IR) enhancements and reveals a clear IR structure of non-Gaussian vertices. We use the new technique to study the evolution of oscillating features in primordial statistics and show that they are damped due to non-linear effects of large bulk flows. We derive the damping factors for the oscillating primordial power spectrum and bispectrum by means of a systematic IR resummation of relevant Feynman diagrams.

End of a dark age?

We argue that dark matter (DM)and dark energy phenomena associated with galactic rotation curves (RC’s), X-ray cluster mass profiles, and type Ia supernova data can be accounted for via small corrections to idealized general relativistic spacetime geometries due to disordered locality. Accordingly, we fit the HI nearby galaxy survey (THINGS) RC data rivaling modified Newtonian dynamics, Roentgen Satellite/Advanced Satellite for Cosmology and Astrophysics (ROSAT/ASCA) X-ray cluster mass profile data rivaling metric-skew-tensor gravity, and SCP Union2.1 SN Ia data rivaling [Formula: see text]CDM without nonbaryonic DM or a cosmological constant. In the case of DM, we geometrically modify proper mass interior to the Schwarzschild solution. In the case of dark energy, we modify proper distance in Einstein–de Sitter cosmology. Therefore, the phenomena of DM and dark energy may be chimeras created by an errant belief that spacetime is a differentiable manifold rather than a disordered graph.

The Jungle Universe: coupled cosmological models in a Lotka–Volterra framework

In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann–Lemaître universes is a special case of generalized Lotka–Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka–Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann–Lemaître cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserves the structure of the dynamical equations. Using the standard tools of Lotka–Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.

Evolution of isolated overdensities as a control on cosmological N-body simulations

Beyond convergence studies and comparison of different codes, there are essentially no controls on the accuracy in the non-linear regime of cosmological N body simulations, even in the dissipationless limit. We propose and explore here a simple test which has not been previously employed: when cosmological codes are used to simulate an isolated overdensity, they should reproduce, in physical coordinates, those obtained in open boundary conditions without expansion. In particular, the desired collisionless nature of the simulations can be probed by testing for stability in physical coordinates of virialized equilibria. We investigate and illustrate the test using a suite of simulations in an Einstein de Sitter cosmology from initial conditions which rapidly settle to virial equilibrium. We find that the criterion of stable clustering allows one to determine, for given particle number N in the "halo" and force smoothing, a maximum red-shift range over which the collisionless limit may be represented with desired accuracy. We also compare our results to the so-called Layzer Irvine test, showing that it provides a weaker, but very useful, tool to constrain the choice of numerical parameters. Finally we outline in some detail how these methods could be employed to test the choice of the numerical parameters used in a cosmological simulation.

EXPLAINING THE SUPERNOVA DATA WITHOUT ACCELERATING EXPANSION

The 2011 Nobel Prize in Physics was awarded "for the discovery of the accelerating expansion of the universe through observations of distant supernovae." However, it is not the case that the type Ia supernova data necessitates accelerating expansion. Since we do not have a successful theory of quantum gravity, we should not assume general relativity (GR) will survive unification intact, especially on cosmological scales where tests are scarce. We provide a simple example of how GR cosmology may be modified to produce a decelerating Einstein-de Sitter cosmology (EdS) that accounts for the Union2 Compilation data as well as the accelerating ΛCDM (EdS plus a cosmological constant).

Vorticity production and survival in viscous and magnetized cosmologies

We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to the diluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length bellow which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay-rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.

Modified Regge calculus as an explanation of dark energy

Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein–de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance DL is related to graphical proper distance Dp by the equation , where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through versus log z gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using Ho = 69.2 km s−1 Mpc, ΩM = 0.29 and ΩΛ = 0.71. The best fit EdS gives SSE = 2.68 using Ho = 60.9 km s−1 Mpc. The best-fit MORC gives SSE = 1.77 and Ho = 73.9 km s−1 Mpc using R = A−1 = 8.38 Gcy and m = 1.71 × 1052 kg, where R is the current graphical proper distance between nodes, A−1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating.

Universal merger histories of dark-matter haloes

We study merger histories of dark-matter haloes in a suite of N-body simulations that span different cosmological models. The simulated cases include the up-to-date WMAP5 cosmology and other test cases based on the Einstein-deSitter cosmology with different power spectra. We provide a robust fitting function for the conditional mass function (CMF) of progenitor haloes of a given halo. This fit is valid for the different cosmological models and for different halo masses and redshifts, and it is a significant improvement over earlier estimates. Based on this fit, we develop a simple and accurate technique for transforming the merger history of a given simulated halo into haloes of different mass, redshift and cosmology. Other statistics such as main-progenitor history and merger rates are accurately transformed as well. This method can serve as a useful tool for studying galaxy formation. It is less sensitive to the low accuracy of the fit at small time-steps, and it can thus replace the more elaborate task of construction Monte-Carlo realizations. As an alternative approach, we confirm the earlier finding by Neistein & Dekel that the main-progenitor follows a log-normal distribution. This property of merger trees allows us to better capture their behaviour as a function of time and descendant mass, but a broader suite of simulations is required for evaluating the dependence of the log-normal parameters on the cosmological model.

Power spectrum for the small-scale Universe

The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.

Phase-space density profiles in scale-free cosmologies

We use a set of high-resolution simulations of scale-free Einstein-de Sitter cosmologies to investigate the logarithmic slope of the phase-space density profile Q(r) = ρ(r)/σ 3 (r) of dark matter (DM) haloes. The initial conditions for the simulations are determined by a power-law power spectrum of the form P(k) ∝ k n . We compute the Q(r) profiles using the radial, tangential and full velocity dispersion, and the velocity anisotropy parameter, β(r). We express Q(r) as a single power-law Q(r) ∝ r α and derive a median slope a in each simulation and for each definition of Q. Our main findings are: (i) the various Q(r) profiles follow a power law to a good approximation. (ii) The slopes depend on the concentration parameter c of the DM haloes, where for c ≥ 10 the slopes steepen with rising concentration and for c ≤ 10 the trend flattens and even turns around. (iii) The asymptotic value of β as r → R vir increases with the value of c. (iv) In accordance with Zait, Hoffman & Shlosman, α rad becomes more negative as the asymptotic value of β at the virial radius increases. (iv) This introduces a weak dependence of the Q(r) slopes on the slope of the power spectrum.

Caustic ring model of the Milky Way halo

We present a proposal for the full phase-space distribution of the Milky Way halo. The model is axially and reflection symmetric and its time evolution is self-similar. It describes the halo as a set of discrete dark matter flows with stated densities and velocity vectors everywhere. We first discuss the general conditions under which the time evolution of a cold collisionless self-gravitating fluid is self-similar, and show that symmetry is not necessary for self-similarity. When spherical symmetry is imposed, the model is the same as described by Fillmore and Goldreich, and by Bertschinger, twenty-three years ago. The spherically symmetric model depends on one dimensionless parameter $ϵ$ and two dimensionful parameters. We set $ϵ=0.3$, a value consistent with the slope of the power spectrum of density perturbations on galactic scales. The dimensionful parameters are determined by the galactic rotation velocity ($220\text{ }\text{ }\mathrm{km}/\mathrm{s}$) at the position of the Sun and by the age of the Galaxy (13.7 Gyr). The properties of the outer caustics are derived in the spherically symmetric model. The structure of the inner halo depends on the angular momentum distribution of the dark matter particles. We assume that distribution to be axial and reflection symmetric, and dominated by net overall rotation. The inner caustics are rings whose radii are determined in terms of a single additional parameter ${j}_{\mathrm{max}}$. We summarize the observational evidence in support of the model. The evidence is consistent with ${j}_{\mathrm{max}}=0.18$ in Concordance cosmology, equivalent to ${j}_{\mathrm{max},\mathrm{old}}=0.26$ in Einstein-de Sitter cosmology. We give formulas to estimate the flow densities and velocity vectors anywhere in the Milky Way halo. The properties of the first 40 flows at the location of the Earth are listed.

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

Context. An important aim of standard relativistic cosmology is the empirical verification of its geometrical concept of homogeneity by considering various definitions of distance and astronomical observations occurring along the past light cone. Aims. We analyze the physical consequences of distinguishing between spatial homogeneity (SH), defined by the Cosmological Principle, and observational homogeneity (OH). We argue that OH is falsifiable by means of astronomical observations, whereas SH can be verified only indirectly. Methods. We simulate observational counts of cosmological sources, such as galaxies, by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes are derived using the various cosmological-distance definitions in the EdS cosmological model. The observational volumes and simulated counts are then used to derive differential densities. We present the behavior of these densities for increasing redshift values. Results. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. In addition, simulated counts with no OH features at low redshift begin to show OH characteristics at high redshift. The comoving distance appears to be the only distance definition for which both SH and OH are applicable simultaneously, even though with limitations. Conclusions. We demonstrate that observations indicative of a possible absence of OH do not necessarily falsify the standard Friedmannian cosmology, which implies that this cosmology does not always produce observable homogeneous densities. We conclude that using different cosmological distances in the characterization of the galaxy distribution can produce significant ambiguities in reaching conclusions about the large-scale galaxy distribution in the Universe.

Multiple inflation and the WMAP “glitches”. II. Data analysis and cosmological parameter extraction

Detailed analyses of the WMAP data indicate possible oscillatory features in the primordial curvature perturbation, which moreover appears to be suppressed beyond the present Hubble radius. Such deviations from the usual inflationary expectation of an approximately Harrison-Zeldovich spectrum are expected in the supergravity-based 'multiple inflation' model wherein phase transitions during inflation induce sudden changes in the mass of the inflaton, thus interrupting its slow-roll. In a previous paper we calculated the resulting curvature perturbation and showed how the oscillations arise. Here we perform a Markov Chain Monte Carlo fitting exercise using the 3-year WMAP data to determine how the fitted cosmological parameters vary when such a primordial spectrum is used as an input, rather than the usually assumed power-law spectrum. The 'concordance' LCDM model is still a good fit when there is just a 'step' in the spectrum. However if there is a 'bump' in the spectrum (due e.g. to two phase transitions in rapid succession), the precision CMB data can be well-fitted by a flat Einstein-de Sitter cosmology without dark energy. This however requires the Hubble constant to be h ~ 0.44 which is lower than the locally measured value. To fit the SDSS data on the power spectrum of galaxy clustering requires a ~10% component of hot dark matter, as would naturally be provided by 3 species of neutrinos of mass ~0.5 eV. This CHDM model cannot however fit the position of the baryon acoustic peak in the LRG redshift two-point correlation function. It may be possible to overcome these difficulties in an inhomogeneous Lemaitre-Tolman-Bondi cosmological model with a local void, which can potentially also account for the SN Ia Hubble diagram without invoking cosmic acceleration.

Cosmological distances and fractal statistics of galaxy distribution

This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density γ and the integral differential density of the dust distribution in the Einstein-de Sitter cosmology. The main results are as follows: (1) the choice of distance plays a crucial role in determining the scale where relativistic corrections must be taken into account, as both γ and are strongly affected by such a choice; (2) inappropriate distance choices may lead to failure to find evidence of a galaxy fractal structure when one calculates those quantities, even if such a structure does occur in the galaxy distribution; (3) the comoving distance and the distance given by Mattig's formula are unsuitable to probe for a possible fractal pattern as they render γ and constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100 Mpc () may only be found if those statistics are calculated with the luminosity or redshift distances, as they are the ones where γ and decrease at higher redshifts; (5) Célérier & Thieberger's ([CITE]) critique of Ribeiro's ([CITE]) earlier study are rendered impaired as their objections were based on misconceptions regarding relativistic distance definitions.

Cluster mergers, radio halos and hard X-ray tails: a statistical magneto-turbulent model

There is now firm evidence that the ICM consists of a mixture of hot plasma, magnetic fields and relativistic particles. The most important pieces of evidence for non-thermal phenomena in galaxy clusters come from the diffuse Mpc-scale synchrotron radio emission (radio halos), observed in a growing number of massive clusters (Feretti 2003), and from hard X-ray (HXR) excess emission (detected in a few cases), which can be explained in terms of IC scattering of relativistic electrons off the cosmic microwave background photons (Fusco-Femiano et al. 2003). There is now growing evidence that giant radio halos may be naturally accounted for by synchrotron emission from relativistic electrons reaccelerated by some kind of turbulence generated in the cluster volume during merger events (Brunetti 2003). With the aim of investigating the connection between thermal and non-thermal properties of the ICM, we have developed a statistical magneto-turbulent model which describes the evolution of the thermal and non-thermal emission from clusters. We calculate the energy and spectrum of the magne-!tosonic waves generated during cluster mergers, the acceleration and evolution of relativistic electrons and thus the resulting synchrotron and inverse Compton spectra. Here we give a brief description of the main results, while a more detailed discussion will be presented in a forthcoming paper (Cassano &amp; Brunetti, in preparation). Einstein-De Sitter cosmology, , is assumed.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The 2dF QSO Redshift Survey - XIII. A measurement of Λ from the quasi-stellar object power spectrum,PS(k∥,k⊥)

We report on measurements of the cosmological constant, A, and the redshift space distortion parameter β = Ω 0.6 m/b, based on an analysis of the quasi-stellar object (QSO) power spectrum parallel and perpendicular to the observer's line of sight, P S (k∥, k⊥), from the final catalogue of the Two-Degree Field (2dF) QSO Redshift Survey. We derive a joint Λ - β constraint from the geometric and redshift-space distortions in the power spectrum. By combining this result with a second constraint based on mass clustering evolution, we break this degeneracy and obtain strong constraints on both parameters. Assuming a flat (Ω m + Ω Λ = 1) cosmology and a A cosmology r(z) function to convert from redshift into comoving distance, we find best-fitting values of Ω Λ = 0.71 +0.09 -0.17 and β q (z ∼ 1.4) = 0.45 +0.09 -0.11. Assuming instead an Einstein-de Sitter cosmology r(z) we find that the best-fitting model obtained, with Ω Λ = 0.64 +0.11 -0.16 and β q (z ∼ 1.4) = 0.40 +0.09 -0.09, is consistent with the A r(z) results, and inconsistent with a Ω Λ = 0 flat cosmology at over 95 per cent confidence.

The CivMass Density of the Universe at Redshift 5

In order to search for metals in the Lyα forest at redshifts zabs > 4, we have obtained spectra of high signal-to-noise ratio and moderately high resolution of three QSOs at zem > 5.4 discovered by the Sloan Digital Sky Survey. These data allow us to probe to metal enrichment of the intergalactic medium at early times with higher sensitivity than previous studies. We find 16 C IV absorption systems with column densities log N(C ) = 12.50-13.98 over a total redshift path ΔX = 3.29. In the redshift interval z = 4.5-5.0, where our statistics are most reliable, we deduce a comoving mass density of C3+ ions Ω = (4.3 ± 2.5) × 10-8 (90% confidence limits) for absorption systems with log N(C ) ≥ 13.0 (for an Einstein-de Sitter cosmology with h = 0.65). This value of Ω is entirely consistent with those measured at z < 4; we confirm the earlier finding by Songaila that neither the column density distribution of C IV absorbers nor its integral show significant redshift evolution over a period of time that stretches from ~1.25 to ~4.5 Gyr after the big bang. This somewhat surprising conclusion may be an indication that the intergalactic medium was enriched in metals at z 5, perhaps by the sources responsible for its reionization. Alternatively, the C IV systems we see may be associated with outflows from massive star-forming galaxies at later times, while the truly intergalactic metals may reside in regions of the Lyα forest of lower density than those probed up to now.

Relativistic Cosmology Number Counts and the Luminosity Function

This paper aims to connect the theory of relativistic cosmology number counts with the astronomical data, practice, and theory behind the galaxy luminosity function (LF). We treat galaxies as the building blocks of the Universe, but ignore most aspects of their internal structures by considering them as point sources. However, we do consider general morphological types in order to use data from galaxy redshift surveys, where some kind of morphological classification is adopted. We start with a general relativistic treatment for a general spacetime, and then link the derived expressions with the LF definition adopted in observational cosmology. Then equations for differential number counts, the related relativistic density per source, and observed and total relativistic energy densities of the universe, and other related quantities are written in terms of the luminosity and selection functions. As an example of how these theoretical/observational relationships can be used, we apply them to test the LF parameters determined from the CNOC2 galaxy redshift survey, for consistency with the Einstein-de Sitter (EdS) cosmology, which they assume, for intermediate redshifts. We conclude that there is a general consistency for the tests we carried out, namely both the observed relativistic mass-energy density, and the observed relativistic mass-energy density per source, which is equivalent to differential number counts, in an EdS Universe. In addition, we find clear evidence of a large amount of hidden mass, as has been obvious from many earlier investigations. At the same time, we find that the CNOC2 LF give differential galaxy counts somewhat above the EdS predictions, indicating that this survey observes more galaxies at 0.1 < z < 0.4 than the model's predictions.