The Correlation Function of Clusters of Galaxies and the Amplitude of Mass Fluctuations in the Universe

We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus if the shape of the initial fluctuation spectrum is known, its amplitude $\sigma_8$ can be estimated directly from the correlation length of a cluster sample in a way which is independent of the value of $\Omega_0$. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity $\sigma_8\Omega_0^{0.6}$. Thus cluster data should allow both $\sigma_8$ and $\Omega_0$ to be determined observationally. We explore these questions using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length $r_0$ in excess of 20\mpch for Abell clusters would require $\sigma_8>1$, while r_0<15\mpch would require $\sigma_8<0.5$. With conventional estimates of the relevant mass threshold these imply \Omega_0\la 0.3 and \Omega_0\ga 1 respectively.Comment: Latex, 25 pages (including 8 PS figures). The PS-file of the paper is also available via anonymous ftp at: ftp://ibm-3.mpa-garching.mpg.de/pub/jing/xicc.ps . Submitted to MNRAS. In the replaced version, a typo in Eq.(1a) is fixe

Establishing the relationship between galaxies and dark matter

We use two methods to establish the relationship between galaxies and dark matter halos. One is based the conditional luminosity function model, which links galaxies and dark matter halos by matching the number density and clustering properties of galaxies with those of dark matter halos in the current CDM model. The second is based on galaxy systems identified from large redshift surveys of galaxies. The galaxy - dark halo relationships established by these two methods match well, and can provide important constraints on how galaxies form and evolve in the univers

Halo Shapes, Dynamics and Environment

In the hierarchical structure formation model cosmic halos are supposed to form by accretion of smaller units along anisotropic direction, defined by large-scale filamentary structures. After the epoch of primary mass aggregation (which depend on the cosmological model), violent relaxation processes will tend to alter the halo phase-space configuration producing quasi-spherical halos with a relatively smooth density profiles. Here we attempt to investigate the relation between halos shapes, their environment and their dynamical state. To this end we have run a large ($L=500 h^{-1}$ Mpc, $N_{p}=512^3$ particles) N-body simulation of a flat low-density cold dark matter model with a matter density $\Omega_{\rm m}=1-\Omega_{\Lambda}=0.3$, Hubble constant $H_{\circ}=70$ km s$^{-1}$ Mpc$^{-1}$ and a normalization parameter of $\sigma_{8}=0.9$. The particle mass is $m_{\rm p}\ge 7.7\times 10^{10} h^{-1} M_{\odot}$ comparable to the mass of one single galaxy. The halos are defined using a friends-of-friend algorithm with a linking length given by $l=0.17\bar{\nu}$ where $\bar{\nu}$ is the mean density. This linking length corresponds to an overdensity $\rho/\rho_{\rm mean}\simeq 200$ at the present epoch ($z=0$) and the total number of halos with more than 130 particles ($M>3 \times 10^{13} h^{-1} M_{\odot}$) is 57524.Comment: To be published in "Groups Of Galaxies In The Nearby Universe", held in Chile, December 2005, edited by I.Saviane, V.Ivanov and J.Borissova. Springer-Verlag series "ESO Astrophysics Symposia

Dynamical Dark Energy simulations: high accuracy Power Spectra at high redshift

Accurate predictions on non--linear power spectra, at various redshift z, will be a basic tool to interpret cosmological data from next generation mass probes, so obtaining key information on Dark Energy nature. This calls for high precision simulations, covering the whole functional space of w(z) state equations and taking also into account the admitted ranges of other cosmological parameters; surely a difficult task. A procedure was however suggested, able to match the spectra at z=0, up to k~3, hMpc^{-1}, in cosmologies with an (almost) arbitrary w(z), by making recourse to the results of N-body simulations with w = const. In this paper we extend such procedure to high redshift and test our approach through a series of N-body gravitational simulations of various models, including a model closely fitting WMAP5 and complementary data. Our approach detects w= const. models, whose spectra meet the requirement within 1% at z=0 and perform even better at higher redshift, where they are close to a permil precision. Available Halofit expressions, extended to (constant) w \neq -1 are unfortunately unsuitable to fit the spectra of the physical models considered here. Their extension to cover the desired range should be however feasible, and this will enable us to match spectra from any DE state equation.Comment: method definitely improved in semplicity and efficacy,accepted for publication on JCA

Correlated Hybrid Fluctuations from Inflation with Thermal Dissipation

We investigate the primordial scalar perturbations in the thermal dissipative inflation where the radiation component (thermal bath) persists and the density fluctuations are thermally originated. The perturbation generated in this model is hybrid, i.e. it consists of both adiabatic and isocurvature components. We calculate the fractional power ratio ($S$) and the correlation coefficient ($\cos\Delta$) between the adiabatic and the isocurvature perturbations at the commencing of the radiation regime. Since the adiabatic/isocurvature decomposition of hybrid perturbations generally is gauge-dependent at super-horizon scales when there is substantial energy exchange between the inflaton and the thermal bath, we carefully perform a proper decomposition of the perturbations. We find that the adiabatic and the isocurvature perturbations are correlated, even though the fluctuations of the radiation component is considered uncorrelated with that of the inflaton. We also show that both $S$ and $\cos \Delta$ depend mainly on the ratio between the dissipation coefficient $\Gamma$ and the Hubble parameter $H$ during inflation. The correlation is positive ($\cos\Delta > 0$) for strong dissipation cases where $\Gamma/H >0.2$, and is negative for weak dissipation instances where $\Gamma/H <0.2$. Moreover, $S$ and $\cos \Delta$ in this model are not independent of each other. The predicted relation between $S$ and $\cos\Delta$ is consistent with the WMAP observation. Other testable predictions are also discussed.Comment: 18 pages using revtex4, accepted for publication in PR

Effects of dark sectors' mutual interaction on the growth of structures

We present a general formalism to study the growth of dark matter perturbations when dark energy perturbations and interactions between dark sectors are present. We show that dynamical stability of the growth of structure depends on the type of coupling between dark sectors. By taking the appropriate coupling to ensure the stable growth of structure, we observe that the effect of the dark sectors' interaction overwhelms that of dark energy perturbation on the growth function of dark matter perturbation. Due to the influence of the interaction, the growth index can differ from the value without interaction by an amount within the observational sensibility, which provides a possibility to disclose the interaction between dark sectors through future observations on the growth of large structure.Comment: 15 pages, 4 figures, revised version, to appear in JCA

Testing the interaction of dark energy to dark matter through the analysis of virial relaxation of clusters Abell Clusters A586 and A1689 using realistic density profiles

Interaction between dark energy and dark matter is probed through deviation from the virial equilibrium for two relaxed clusters: A586 and A1689. The evaluation of the virial equilibrium is performed using realistic density profiles. The virial ratios found for the more realistic density profiles are consistent with the absence of interaction.Comment: 16pp 1 fig; accepted by GeR

The phase-space structure of a dark-matter halo: Implications for dark-matter direct detection experiments

We study the phase-space structure of a dark-matter halo formed in a high resolution simulation of a Lambda CDM cosmology. Our goal is to quantify how much substructure is left over from the inhomogeneous growth of the halo, and how it may affect the signal in experiments aimed at detecting the dark matter particles directly. If we focus on the equivalent of ``Solar vicinity'', we find that the dark-matter is smoothly distributed in space. The probability of detecting particles bound within dense lumps of individual mass less than 10^7 M_\sun h^{-1} is small, less than 10^{-2}. The velocity ellipsoid in the Solar neighbourhood deviates only slightly from a multivariate Gaussian, and can be thought of as a superposition of thousands of kinematically cold streams. The motions of the most energetic particles are, however, strongly clumped and highly anisotropic. We conclude that experiments may safely assume a smooth multivariate Gaussian distribution to represent the kinematics of dark-matter particles in the Solar neighbourhood. Experiments sensitive to the direction of motion of the incident particles could exploit the expected anisotropy to learn about the recent merging history of our Galaxy.Comment: 13 pages, 13 figures, Phys. Rev. D in press. Postscript version with high resolution figures available from http://www.mpa-garching.mpg.de/~ahelmi/research/lcdm_dm.html; some changes in the text; constraints on the effect of bound dark-matter lumps revised; remaining conclusions unchange

Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information

By use of the two measures presented recently, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and the reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relations between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed

An analytical model for the non-linear redshift-space power spectrum

We use N-body simulations to test the predictions of the redshift distortion in the power spectrum given by the halo model in which the clustering of dark matter particles is considered as a result both of the clustering of dark halos in space and of the distribution of dark matter particles in individual dark halo. The predicted redshift distortion depends sensitively on several model parameters in a way different from the real-space power spectrum. An accurate model of the redshift distortion can be constructed if the following properties of the halo population are modelled accurately: the mass function of dark halos, the velocity dispersion among dark halos, and the non-linear nature of halo bias on small scales. The model can be readily applied to interpreting the clustering properties and velocity dispersion of different populations of galaxies once a cluster-weighted bias (or equivalently an halo occupation number model) is specified for the galaxies. Some non-trivial bias features observed from redshift surveys of optical galaxies and of IRAS galaxies relative to the standard low-density cold dark matter model can be easily explained in the cluster weighted bias model. The halo model further indicates that a linear bias can be a good approximation only on for k <= 0.1 hMpc^{-1}.Comment: 10 pages, 10 figures, accepted for publication in MNRA