Flat CDM Models Research Articles

Quasars as high‐redshift standard candles

AbstractIn the past few years, we built a Hubble diagram of quasars up to redshift , based on the nonlinear relation between quasars' x‐ray and UV luminosities. Such a Hubble diagram shows a deviation from the standard flat CDM model at . Given the important consequences of this result, it is fundamental to rule out any systematic effect in the selection of the sample and/or in the flux measurements, and to investigate possible redshift dependences of the relation, that would invalidate the use of quasars as standard candles. Here we review all the observational results supporting our method: the match of the Hubble diagram of quasars with that of supernovae in the common redshift range, the constant slope of the relation at all redshifts, the redshift non‐evolution of the spectral properties of our sources both in the x‐rays and in the UV. An independent test of our results requires the observation of other standard candles at high redshift. In particular, we expect that future observations of supernovas at will confirm the deviation from the concordance model found with the Hubble diagram of quasars.

The observational constraints on the flat phi CDM models

Most dark energy models have the varLambda CDM as their limit, and if future observations constrain our universe to be close to varLambda CDM Bayesian arguments about the evidence and the fine-tuning will have to be employed to discriminate between the models. Assuming a baseline varLambda CDM model we investigate a number of quintessence and phantom dark energy models, and we study how they would perform when compared to observational data, such as the expansion rate, the angular distance, and the growth rate measurements, from the upcoming Dark Energy Spectroscopic Instrument (DESI) survey. We sample posterior likelihood surfaces of these dark energy models with Monte Carlo Markov Chains while using central values consistent with the Planck varLambda CDM universe and covariance matrices estimated with Fisher information matrix techniques. We find that for this setup the Bayes factor provides a substantial evidence in favor of the varLambda CDM model over most of the alternatives. We also investigated how well the CPL parametrization approximates various scalar field dark energy models, and identified the location for each dark energy model in the CPL parameter space.

Dark-energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5

<i>Aims. <i/>We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark-energy equation-of-state parameter <i>w<i/>. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters.<i>Methods. <i/>We implemented an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant <i>w<i/>. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-redshift galaxies.<i>Results. <i/>Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae alone; the parameter uncertainties are underestimated by 10%. The weak-lensing field-to-field variance between 1 deg<sup>2<sup/>-MegaCam pointings is 5-15% higher than predicted from <i>N<i/>-body simulations. We find no bias in the lensing signal at high redshift, within the framework of a simple model, and marginalising over cosmological parameters. Assuming a systematic underestimation of the lensing signal, the normalisation increases by up to 8%. Combining all three probes we obtain at 68% confidence ( at 95%), including systematic errors. Our results are therefore consistent with the cosmological constant <i>Λ<i/>. Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15<i>σ<i/>.

The X‐Ray Concentration–Virial Mass Relation

We present the concentration (c)-virial mass (M) relation of 39 galaxy systems ranging in mass from individual early-type galaxies up to the most massive galaxy clusters, (0.06-20) × 1014 M☉. We selected for analysis the most relaxed systems possessing the highest quality data currently available in the Chandra and XMM-Newton public data archives. A power-law model fitted to the X-ray c-M relation requires at high significance (6.6 σ) that c decreases with increasing M, which is a general feature of CDM models. The median and scatter of the c-M relation produced by the flat, concordance ΛCDM model (Ωm = 0.3, σ8 = 0.9) agrees with the X-ray data, provided that the sample is comprised of the most relaxed, early-forming systems, which is consistent with our selection criteria. When allowing only σ8 to vary in the concordance model, the c-M relation requires 0.76 99% confidence) both open CDM models and flat CDM models with Ωm ≈ 1. This result provides novel evidence for a flat, low-Ωm universe with dark energy using observations only in the local (z 1) universe. Possible systematic errors in the X-ray mass measurements of a magnitude ≈10% suggested by CDM simulations do not change our conclusions.

How many parameters in the cosmological models with dark energy?

In cosmology many dramatically different scenarios in the past (big bang versus bounce) and in the future (de Sitter versus big rip) are compatible with the present day observations. This difficulties are called the degeneracy problem. We use the Akaike (AIC) and Bayesian (BIC) information criteria of model selection to avoid this degeneracy and to determine the model with such a set of parameters which gives the most preferred fit to the data. We consider seven representative scenarios, namely: the ΛCDM, CDM model with topological defect, phantom CDM model, bouncing ΛCDM model, bouncing phantom CDM model, brane ΛCDM model and model with the dynamical equation of state parameter linearized around the present epoch. Applying the information criteria to the currently available SNIa data we show that AIC indicates the flat phantom model while BIC indicates both flat phantom CDM and flat ΛCDM models. Finally we conclude that number of essential parameters chosen by dark energy models which are compared with SNIa data is two.

Arc statistics in cosmological models with dark energy

We investigate how the probability of the formation of giant arcs in galaxy clusters is expected to change in cos- mological models dominated by dark energy with an equation of state p = wρc 2 compared to cosmological-constant or open models. To do so, we use a simple analytic model for arc cross sections based on the Navarro-Frenk-White density profile which we demonstrate reproduces essential features of numerically determined arc cross sections. Since analytic lens models are known to be inadequate for accurate absolute quantifications of arc probabilities, we use them only for studying changes rel- ative to cosmological-constant models. Our main results are (1) the order of magnitude difference between the arc probabilities in low density, spatially flat and open CDM models found numerically is reproduced by our analytic model, and (2) dark-energy cosmologies with w> −1 increase the arc optical depth by at most a factor of two and are thus unlikely to reconcile arc statistics with spatially flat cosmological models with low matter density.

Toward a Precise Measurement of Matter Clustering: Lyα Forest Data at Redshifts 2–4

We measure the filling factor, correlation function, and power spectrum of transmitted flux in a large sample of Lya forest spectra, comprised of 30 Keck HIRES spectra and 23 Keck LRIS spectra. We infer the linear matter power spectrum P(k) from the flux power spectrum P_F(k), using an improved version of the method of Croft et al. (1998) that accounts for the influence of z-space distortions, non- linearity, and thermal broadening on P_F(k). The evolution of the shape and amplitude of P(k) over the range z= 2-4 is consistent with gravitational instability, implying that non-gravitational fluctuations do not make a large contribution. Our fiducial measurement of P(k) comes from data with <z> = 2.72. It has amplitude Delta^2(k_p)=0.74^0.20_-0.16 at wavenumber k_p=0.03 (km/s)^-1 and is well described by a power-law of index -2.43 +/- 0.06 or by a CDM-like power spectrum with shape parameter Gamma'=1.3^+0.7_-0.5*10^-3 (km/s) at z=2.72. For Omega_m=0.4, Omega_Lam=0.6, the best-fit Gamma =0.16 (h^-1mpc)^-1, in good agreement with the 2dF Galaxy Redshift Survey, and the best-fit sigma_8=0.82 (Gamma/0.15)^-0.44. Matching the observed cluster mass function and our Delta^2(k_p) in spatially flat models requires Omega_m=0.38^+0.10_-0.08 + 2.2 (Gamma-0.15). Matching Delta^2(k_p) in COBE-normalized, flat CDM models with no tensor fluctuations requires Omega_m = (0.29 +/-0.04) n^-2.89 h_65^-1.9. The Lya forest complements other probes of P(k) by constraining a regime of redshift and lengthscale not accessible by other means, and the consistency of these inferred parameters with independent estimates provides further support for inflation, cold dark matter, and vacuum energy (abridged).

The host haloes of Lyman-break galaxies and submillimetre sources

We use the observed sizes and star formation rates of Lyman-break galaxies (LBGs) to understand their properties expected in the hierarchical scenario of galaxy formation. The observed size distribution constrains the masses (or circular velocities) of the host haloes of LBGs from below, because small haloes can only host galaxies with small sizes. The observed star formation distribution constrains the masses from above, because the number density of massive haloes in duty cycle is too low to host all the observed galaxies. Assuming a flat CDM model with a cosmological constant (Omega (Lambda) = 0.7), we find that consistency with observations requires the circular velocities of LBG host haloes to be in the range 100-300 km s(-1). The star formation in these haloes is efficient; a large fraction of all the gas in them can form stars on a time-scale of about 10-20 per cent of the Hubble time at redshift of 3. The predicted comoving correlation length of these objects is similar to3 h(-1) Mpc, and the predicted velocity dispersion of their stellar contents is typically 70 km s(-1).

Breaking Degeneracy of Dark Matter Models by the Scale‐Scale Correlations of Galaxies

Recently, scale-scale correlations have been detected in the distributions of quasars' Lyα absorption lines and the maps of cosmic temperature fluctuations. This paper investigates the scale-scale correlations in galaxy distributions. Using samples of mass field given by N-body simulation, we first show that the scale-scale correlation of two-dimensional and three-dimensional mass distributions at present day are capable of breaking the degeneracy between the SCDM (standard cold dark matter model) and OCDM (open CDM model) or LCDM (flat CDM model) and even show the difference between the OCDM and LCDM. Using biased galaxy samples produced in an appropriate bias model, we show that the scale-scale correlation of galaxy distribution at zero redshift is still a powerful tool to break the degeneracy in the parameter space, including both cosmological and biasing parameters. We analyze the scale-scale correlations of the APM bright galaxy catalog and compare it with the mock catalog in the SCDM, OCDM, and LCDM models. We find that all the spectra of local and nonlocal scale-scale correlations predicted by the OCDM model are in excellent agreement with those of the APM-BGC sample, while the SCDM and LCDM mock catalog appear to have somewhat weaker scale-scale correlations than the observation.

Abundances and Correlations of Structures beyond Galaxy Clusters

We investigated the structures on scales beyond the typical clusters of galaxies. These structures are crucial to understanding the cosmic gravitational clustering in the previrialized stage, or quasi-linear regime. Based on the multiresolution analysis of the discrete wavelet transformation, we obtained statistically available ensembles of rcl clusters, i.e., the structures on scale rcl, in the range of 1 ≤ rcl ≤ 24 h-1 Mpc for both N-body simulation and the IRAS 1.2 Jy galaxy survey samples. When the mass-to-light ratio (M/L) on scales larger than that of the clusters asymptotically reaches a constant, we found that the abundances and correlations of these IRAS rcl clusters were basically consistent with the predictions of the flat low-density CDM model (LCDM) and the open CDM model (OCDM), except that the model-predicted abundance of rcl = 24 h-1 Mpc clusters seems to be higher than that predicted by the IRAS data. The standard CDM (SCDM) gives too much power and provides correlations that are too weak on all the scales. For a given rcl, the amplitude of the two-point correlation function of rcl clusters increases with their richness. However, for a given richness (defined by the mean separation of neighboring objects), the clustering strengths of both the simulation and observation samples decline with rcl when rcl is larger than 3-4 h-1 Mpc. Therefore, the "universal" increase of the correlation amplitude with the scale of objects from galaxies, groups, to poor, rich clusters is broken down for structures of rcl > 3-4 h-1 Mpc. Superclusters should not be members of the "universal" increase family.

The cluster distribution as a test of dark matter models - IV. Topology and geometry

We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 h−1 Mpc, and compare them with available data on real clusters. The simulations we use are generated by the Zel’dovich approximation, using the same methods as we have used in the first three papers in this series. We consider the following models to see if there are measurable differences in the topology and geometry of the superclustering they produce: (i) the standard cold dark matter model (SCDM); (ii) a CDM model with Ω0 = 0.2 (OCDM); (iii) a CDM model with a ‘tilted’ power spectrum having n = 0.7 (TCDM); (iv) a CDM model with a very low Hubble constant, h = 0.3 (LOWH); (v) a model with mixed CDM and HDM (CHDM); (vi) a flat low-density CDM model with Ω0 = 0.2 and a non-zero cosmological Λ term (ΛCDM). We analyse these models using a variety of statistical tests based on the analysis of: (i) the Euler–Poincare characteristic; (ii) percolation properties; (iii) the minimal spanning tree construction. Taking all these tests together we find that the best-fitting model is ΛCDM and, indeed, the others do not appear to be consistent with the data. Our results demonstrate that despite their biased and extremely sparse sampling of the cosmological density field, it is possible to use clusters to probe subtle statistical diagnostics of models, which go far beyond the low-order correlation functions usually applied to study superclustering.

Likely Values of the Cosmological Constant

In theories in which the cosmological constant Lambda takes a variety of values in different ``subuniverses,'' the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it. This probability is proportional to the fraction of matter which is destined to condense out of the background into mass concentrations large enough to form observers. We calculate this ``collapsed fraction'' by a simple, pressure-free, spherically symmetric, nonlinear model for the growth of density fluctuations in a flat universe with arbitrary value of the cosmological constant, applied in a statistical way to the observed spectrum of density fluctuations at recombination. From this, the probability distribution for the vacuum energy density rho_V=Lambda/8pi G for Gaussian random density fluctuations is derived analytically. It is shown that the results depend on only one quantity, sigma^3 RHO, where sigma^2 and RHO are the variance and mean value of the fluctuating matter density field at recombination, respectively. To calculate sigma, we adopt the flat CDM model with nonzero cosmological constant and fix the amplitude and shape of the primordial power spectrum in accordance with data on cosmic microwave background anisotropy from the COBE satellite DMR experiment. A comparison of the results of this calculation of the likely values of rho_V with present observational bounds on the cosmological constant indicates that the small, positive value of rho_V (up to 3 times greater than the present cosmic mass density) suggested recently by several lines of evidence is a reasonably likely value to observe, even if all values of rho_V are equally likely a priori.

The cosmological constant and the clusters of galaxies

The dependence of the formation redshift of clusters of galaxies on the cosmological constant is discussed on the basis of recent measurements of gravitational masses and radii from X-ray astronomy techniques. For a flat CDM model with several different values of the cosmological constant, the cluster number density as a function of the redshift is calculated. Comparing the calculated number density at z − 0 with the observed value limits the spectrum parameter Γ to the range 0.15–0.32. We also show that if Γ and/or Ω Λ were larger, many more clusters of galaxies would have been formed at high redshifts.

Large-scale structure in COBE-normalized cold dark matter cosmogonies

We study the clustering of the mass distribution in COBE-normalized open and flat CDM models using large N-body simulations. With an age of the universe of 14 Gyr (12 Gyr) for the flat (open) models and a baryon density fixed by nucleosynthesis constraints, the observed abundance of rich galaxy clusters leads to tight constraints on the density parameter; 0.25<Omega_0<0.4 (0.4<Omega_0<0.5) for flat (open) models. The upper limits on Omega_0 can be relaxed if one lowers the H_0 and increases the age of the universe, but h<0.25 is required to allow Omega_0=1. The constraints also change if one allows tilted primordial power spectra. An acceptable Omega_0=1 model with h=0.5 can be constructed, with a tilt of n=0.8. We compare the evolved mass correlation functions of the most promising models with those of APM galaxies. The flat models have steep correlation functions at small scales and require galaxies to be antibiased on scales r<8 Mpc/h. The open models require little or no antibias on small scales and a positive bias on large scales. The lack of a positive bias on small scales is difficult to reconcile with the virial analysis of galaxy clusters which, if Omega_0>0.2, implies that galaxies are overabundant in clusters relative to the field. The tilted Omega_0=1 model, on the other hand, does require that galaxies be positively biased on all scales. We also compute the topology of isodensity contours in these models, obtaining theoretical predictions that are less sensitive to galaxy bias.

Cosmology using cluster internal velocity dispersions

We compare the cumulative distribution of internal velocity dispersions of galaxy clusters, N(>συ), for a large observational sample to those obtained from a set of N-body simulations that we run for seven COBE-normalized cosmological scenarios. They are: the standard CDM (SCDM) and a tilted (n = 0.85) CDM (TCDM) model, a cold + hot DM (CHDM) model with Ων = 0.25, two low-density flat CDM (ΛCDM) models with Ω0 = 0.3 and 0.5, two open CDM (OCDM) models with Ω0 = 0.4 and 0.6. The Hubble constant is chosen so that t0 ⋍ 13 Gyrs in all the models, while Ωb = 0.02 h2 is assumed for the baryon fraction. Clusters identified in the simulations are observed in projection so as to reproduce the main observational biases of the real data set. Clusters in the simulations are analysed by applying the same algorithm for interlopers removal and velocity dispersion estimate as for the reference observational sample. We find that συ for individual model clusters can be largely affected by observational biases, especially for συ ≲ 600 km s−1. The resulting effect of N(>συ) is rather model dependent: models in which clusters had less time to virialize show larger discrepancies between intrinsic (3D) and projected distribution of velocity dispersions. From the comparison with real clusters we find that both SCDM and TCDM largely overproduce clusters. We verified for TCDM that agreement with the observational N(>συ) requires σ8 ⋍ 0.5. As for the CHDM model, it marginally overproduces clusters and requires a somewhat larger σ8 value than a purely CDM model in order to produce the same cluster abundance. The ΛCDM model with Ω0 = 0.3 agrees with data, while the open model with Ω0 = 0.4 and 0.6 underproduces and marginally overproduces clusters, respectively.

The cluster distribution as a test of dark matter models - I. Clustering properties

We present simulations of the cluster distribution in several dark matter models, using an optimized version of the truncated Zel'dovich approximation (TZA). We compare them with N-body cluster simulations and find that the TZA provides a very accurate description of the cluster distribution as long as fluctuations on the cluster mass scale are in the mildly non-linear regime. The simulated dark matter models are: Standard CDM (SCDM), Tilted CDM (TCDM) with n=0.7, Cold+Hot DM (CHDM) with 30% of hot component, low Hubble constant (h=0.3) CDM (LOWH) and a spatially flat low-density CDM model with \Omega_0=0.2. We compare the simulations with a redshift sample of Abell/ACO clusters, using the integral of the 2-point correlation function and the probability density function. We find that the best models at reproducing the data are CHDM and LCDM. All the other models are ruled out. The reduced skewness S_3 is fairly constant with S_3=1.9, independent of the DM model and consistent with observational data. The abundances of clusters predicted using the Press--Schechter theory provide strong constraints: only the CHDM, LOWH and LCDM models appear to produce the correct number-density of clusters.

The observed properties of high-redshift cluster galaxies

We use the semi-analytic models of galaxy formation developed by Kauffmann, White \& Guiderdoni to generate predictions for the observed properties of cluster and group galaxies at redshifts between 0 and 0.6. We examine four sets of cosmological initial conditions: low-density CDM models with and without cosmological constant, a flat CDM model and a mixed dark matter model. These models were selected because they span a wide range in cluster formation epoch. The semi-analytic models that we employ are able to follow both the evolution of the dark matter component of clusters and the formation and evolution of the stellar populations of the cluster galaxies. We are thus able to generate model predictions that can be compared directly with the observational data. In the low-density CDM models, clusters form at high red- shift and accrete very little mass at recent times. Our models predict that essentially no evolution in the observed properties of clusters will have occurred by a redshift of 0.6, in direct contradiction with the data. In contrast, in the MDM model, both galaxies and clusters form extremely late. This model predicts evolution which appears to be too extreme to be in agreement with the observations. The flat CDM model, which is intermediate in structure formation epoch, is most successful. This model is able to account for the evolution of the blue fraction of rich clusters with redshift, the relationship between blue fraction and cluster richness at different epochs, and the changes in the distribution of the morphologies of cluster galaxies by a redshift of 0.4.

Cold + hot dark matter cosmology with m( nu micro)

Cold + hot dark matter (CHDM) =1 cosmological models require a total neutrino mass 5 eV. Because recent data support the oscillation explanation of the cosmic ray deficit, which requires that m()m(), this suggests that m()m()2.4 eV. The linear calculations and N-body simulation reported here indicate that an =1 CHDM model with two 2.4 eV neutrinos (designated C2DM) agrees remarkably well with all available observations, but only if the Hubble parameter h0.5. We also show that even one 2.4 eV neutrino raises serious difficulties for low- flat CDM models. © 1995 The American Physical Society.

Abundance of moderate-redshift clusters in the cold plus hot dark matter model

view Abstract Citations (61) References (37) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Abundance of Moderate-Redshift Clusters in the Cold Plus Hot Dark Matter Model Jing, Yi-Peng ; Fang, Li-Zhi Abstract Using a particle-particle/particle-mesh simulation which accurately treats the density evolution of two components of dark matter, we study the evolution of clusters in the cold plus hot dark matter (CHDM) model. The mass function, the velocity dispersion function, and the temperature function of clusters are calculated for four different epochs of z <= 0.5. We also use the simulation data to test the Press-Schechter expression of the halo abundance as a function of the velocity dispersion σnu_. The model predictions are in good agreement with the observational data of local cluster abundances (z = 0). We also tentatively compare the model with the Gunn and his collaborators' observation of rich clusters at z ~ 0.8 and with the X-ray luminous clusters at z ~ 0.5 of the Einstein Extended Medium Sensitivity Survey. The important feature of the model is the rapid formation of clusters in the near past: the abundances of clusters of σnu_ => 700 km s^- 1^ and of σnu_ >= 1200 km s^-1^ at z = 0.5 are only 1/4 and 1/10, respectively, of the present values (z = 0). Ongoing ROSAT and AXAF surveys of distant clusters will provide sensitive tests to the model. The abundance of clusters at z~0.5 would also be a good discriminator between the CHDM model and a low-density flat CDM model, both of which show very similar clustering properties at z = 0. Publication: The Astrophysical Journal Pub Date: September 1994 DOI: 10.1086/174582 arXiv: arXiv:astro-ph/9403012 Bibcode: 1994ApJ...432..438J Keywords: Abundance; Astronomical Models; Dark Matter; Galactic Clusters; Galactic Evolution; Galactic Halos; Many Body Problem; Cosmology; Quadrupoles; Red Shift; Universe; Astrophysics; COSMOLOGY: DARK MATTER; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; COSMOLOGY: THEORY; GALAXIES: CLUSTERING; GALAXIES: EVOLUTION; Astrophysics E-Print: 21 pages + 6 figures (uuencoded version of the PS files), Steward Preprints No. 1184 full text sources arXiv | ADS |