Abstract:
In two previous papers (Salvador-Sol\'e 2012a,b), it was shown that: i) the typical structural and kinematic properties of haloes in (bottom-up) hierarchical cosmologies endowed with random Gaussian density perturbations of dissipationless collisionless dark matter emerge naturally from the typical properties of peaks in the primordial density field and ii) halo statistics are well described by the peak formalism. In the present paper, we use these results to model halo substructure. Specifically, making use of the peak formalism and the fact that accreting haloes evolve from the inside-out, we derive the subhalo mass abundance and number density profile per infinitesimal mass for subhaloes of different masses, as a function of the subhalo maximum circular velocity or mass, before and after the tidal truncation of subhaloes by the host potential well. The subhalo properties obtained by assuming that subhaloes are mainly made of diffuse particles are in very good agreement with those found in current high-resolution N-body simulations. We also predict the subhalo properties in the opposite extreme case, likely better suited for the real universe in CDM cosmologies, that haloes are made of subhaloes within subhaloes at all scales.

Abstract:
We consider a self-gravitating ideal fermion gas at nonzero temperature as a model for the Galactic halo. The Galactic halo of mass ~ 2 x 10^12 Msol enclosed within a radius of ~ 200 kpc implies the existence of a supermassive compact dark object at the Galactic center that is in hydrostatic and thermal equilibrium with the halo. The central object has a maximal mass of ~ 2.3 x 10^6 Msol within a minimal radius of ~ 18 mpc for fermin masses ~ 15 keV.

Abstract:
In a recent paper, Salvador-Sol\'e et al. (2012) have derived the typical inner structure of dark matter haloes from that of peaks in the initial random Gaussian density field, determined by the power-spectrum of density perturbations characterising the hierarchical cosmology under consideration. In the present paper, we extend this formalism to the typical kinematics and triaxial shape of haloes. Specifically, we establish the link between such halo properties and the power-spectrum of density perturbations through the typical shape of peaks. The trends of the predicted typical halo shape, pseudo phase-space density and anisotropy profiles are in good agreement with the results of numerical simulations. Our model sheds light on the origin of the power-law-like pseudo phase-space density profile for virialised haloes.

Abstract:
We derive the density profile for collisionless dissipationless dark matter haloes in hierarchical cosmologies making use of the Secondary Infall (SI) model. The novelties are: i) we deal with triaxial virialised objects; ii) their seeds in the linear regime are peaks endowed with {\it unconvolved} spherically averaged density profiles according to the peak formalism; iii) the initial peculiar velocities are taken into account; and iv) accreting haloes are assumed to develop from the inside out, keeping the instantaneous inner system unaltered. The validity of this latter assumption is accurately checked by comparing analytical predictions on such a growth with the results of numerical simulation. We show that the spherically averaged density profile of virialised objects can be inferred with no need to specify their shape. The {\it typical} spherically averaged halo density profile is inferred, down to arbitrarily small radii, from the power-spectrum of density perturbations. The predicted profile in the $\Lambda$CDM cosmology is approximately described by an Einasto profile, meaning that it does not have a cusp but rather a core, where the inner slope slowly converges to zero. Down to one hundredth the total radius, the profile has the right NFW and Einasto forms, being close to the latter down to a radius of about four orders of magnitude less. The inner consistency of the model implies that the density profiles of haloes harbour no information on their past aggregation history. This would explain why major mergers do not alter the typical density profile of virialised objects formed by SI and do not invalidate the peak formalism based on such a formation.

Abstract:
Using high--resolution N--body simulations, we test two theoretical models, based either on spherical or on ellipsoidal collapse model, for the higher--order moments of the dark matter halo distribution in CDM models. We find that a theoretical model based on spherical collapse describes accurately the simulated counts--in--cells moments for haloes of several mass ranges. It appears that the model using ellipsoidal collapse instead of spherical collapse in defining dark haloes is unable to improve the models for the higher--order moments of halo distribution, for haloes much smaller than $M^*$ (the mass scale on which the fluctuation of the density field has a rms about 1). Both models are particularly accurate for the descendants of haloes selected at high redshift, and so are quite useful in interpreting the high--order moments of galaxies. As an application we use the theoretical model to predict the higher--order moments of the Lyman break galaxies observed at $z\approx 3$ and their descendants at lower redshifts.

Abstract:
Accurate knowledge of the non-linear dark-matter power spectrum is important for understanding the large-scale structure of the Universe, the statistics of dark-matter haloes and their evolution, and cosmological gravitational lensing. We analytically model the dark-matter power spectrum and its cross-power spectrum with dark-matter haloes. Our model extends the halo-model formalism, including realistic substructure population within individual dark-matter haloes and the scatter of the concentration parameter at fixed halo mass. We consider three prescriptions for the mass-concentration relation and two for the substructure distribution in dark-matter haloes. We show that this extension of the halo model mainly increases the predicted power on the small scales, and is crucial for proper modeling the cosmological weak-lensing signal due to low-mass haloes. Our extended formalism shows how the halo model approach can be improved in accuracy as one increases the number of ingredients that are calibrated from n-body simulations.

Abstract:
We investigate the transition from regular to chaotic motion in a composite galaxy model with a disk-halo, a massive dense nucleus and a dark halo component. We obtain relationships connecting the critical value of the mass of the nucleus or the critical value of the angular momentum, with the mass of the dark halo, where the transition from regular motion to chaos occurs. We also present 3D diagrams connecting the mass of nucleus the energy and the percentage of stars that can show chaotic motion. The fraction of the chaotic orbits observed in the phase plane, as a function of the mass of the dark halo is also computed. We use a semi-numerical method, that is a combination of theoretical and numerical procedure. The theoretical results obtained using the version 8.0 of the Mathematica package, while all the numerical calculations were made using a Bulirsch-Stoer FORTRAN routine in double precision. The results can be obtained in semi-numerical or numerical form and give good description for the connection of the physical quantities entering the model and the transition between regular and chaotic motion. We observe that the mass of the dark halo, the mass of the dense nucleus and the L_z component of the angular momentum, are important physical quantities, as they are linked to the regular or chaotic character of orbits in disk galaxies described by the model. Our numerical experiments suggest, that the amount of the dark matter plays an important role in disk galaxies represented by the model, as the mass of the halo affects, not only the regular or chaotic nature of motion but it is also connected with the existence of the different families of regular orbits. Comparison of the present results with earlier work is also presented.

Abstract:
We study the impact of theoretical uncertainty in the dark matter halo mass function and halo bias on dark energy constraints from imminent galaxy cluster surveys. We find that for an optical cluster survey like the Dark Energy Survey, the accuracy required on the predicted halo mass function to make it an insignificant source of error on dark energy parameters is ~ 1%. The analogous requirement on the predicted halo bias is less stringent (~ 5%), particularly if the observable-mass distribution can be well constrained by other means. These requirements depend upon survey area but are relatively insensitive to survey depth. The most stringent requirements are likely to come from a survey over a significant fraction of the sky that aims to observe clusters down to relatively low mass, Mth ~ 10^13.7 Msun/h; for such a survey, the mass function and halo bias must be predicted to accuracies of ~ 0.5% and ~ 1%, respectively. These accuracies represent a limit on the practical need to calibrate ever more accurate halo mass and bias functions. We find that improving predictions for the mass function in the low-redshift and low-mass regimes is the most effective way to improve dark energy constraints.

Abstract:
We present a modification of the standard halo model with the goal of providing an improved description of galaxy clustering. Recent surveys, like the Sloan Digital Sky Survey (SDSS) and the Anglo-Australian Two-degree survey (2dF), have shown that there seems to be a correlation between the clustering of galaxies and their properties such as metallicity and star formation rate, which are believed to be environment-dependent. This environmental dependence is not included in the standard halo model where the host halo mass is the only variable specifying galaxy properties. In our approach, the halo properties i.e., the concentration, and the Halo Occupation Distribution --HOD-- prescription, will not only depend on the halo mass (like in the standard halo model) but also on the halo environment. We examine how different environmental dependence of halo concentration and HOD prescription affect the correlation function. We see that at the level of dark matter, the concentration of haloes affects moderately the dark matter correlation function only at small scales. However the galaxy correlation function is extremely sensitive to the HOD details, even when only the HOD of a small fraction of haloes is modified.

Abstract:
We review different dark energy cosmologies. In particular, we present the $\Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the $\Lambda$CDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the $\Lambda$CDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes $F(R)$ gravity as well as $F(R)$ Ho\v{r}ava-Lifshitz gravity and the teleparallel $f(T)$ gravity. The cosmology of such models representing the $\Lambda$CDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.