We use a statistical approach to determine the relationship between the stellar masses of galaxies and the masses of the dark matter halos in which they reside. We obtain a parameterized stellar-to-halo mass (SHM) relation by populating halos and subhalos in an N-body simulation with galaxies and requiring that the observed stellar mass function be reproduced. We find good agreement with constraints from galaxy-galaxy lensing and predictions of semi-analytic models. Using this mapping, and the positions of the halos and subhalos obtained from the simulation, we find that our model predictions for the galaxy two-point correlation function (CF) as a function of stellar mass are in excellent agreement with the observed clustering properties in the SDSS at z = 0. We show that the clustering data do not provide additional strong constraints on the SHM function and conclude that our model can therefore predict clustering as a function of stellar mass. We compute the conditional mass function, which yields the average number of galaxies with stellar masses in the range m ± dm/2 that reside in a halo of mass M. We study the redshift dependence of the SHM relation and show that, for low mass halos, the SHM ratio is lower at higher redshift. The derived SHM relation is used to predict the stellar mass dependent galaxy CF and bias at high redshift. Our model predicts that not only are massive galaxies more biased than low mass ones at all redshifts, but the bias increases more rapidly with increasing redshift for massive galaxies than for low mass ones. We present convenient fitting functions for the SHM relation as a function of redshift, the conditional mass function, and the bias as a function of stellar mass and redshift.

A series of high-resolution ΛCDM cosmological N-body simulations are used to study the properties of galaxy-size dark halos as a function of global environment. We analyse halos in three types of environment: "cluster" (cluster halos and their surroundings), "void" (large regions with density contrasts −0.85), and "field" (halos not contained within larger halos). We find that halos in clusters have a median spin parameter ∼ 1.3 times lower, a minor-to-major axial ratio ∼ 1.2 times lower (more spherical), and a less aligned internal angular momentum than halos in voids and the field. For masses 5 × 10 11 h −1 M ⊙ , halos in cluster regions are on average ∼ 30 − 40% more concentrated and have ∼ 2 times higher central densities than halos in voids. While for halos in cluster regions the concentration parameters decrease on average with mass with a slope of ∼ 0.1, for halos in voids these concentrations do not seem to change with mass. When comparing only parent halos from the samples, the differences are less pronounced but they are still significant. We obtain also the maximum circular velocity-and rms velocity-mass relations. These relations are shallower and more scattered for halos in clusters than in voids, and for a given circular velocity or rms velocity, the mass is smaller at z = 1 than at z = 0 for all environments. At z = 1, the differences in the halo properties with environment almost dissapear, suggesting this that the differences were stablished mainly after z ∼ 1. The halos in the cluster regions undergo more dramatic changes than those in the field or the voids. The differences in halo properties with environment are owing to (i) the dependence of halo formation time on global environment, and (ii) local effects as tidal stripping and the tumultuos histories that halos suffer in high-density regions.We calculate seminumerical models of disk galaxy evolution using halos with the concentrations and spin parameters found for the different environments. For a given disk mass, the galaxy disks have higher surface density, larger maximum circular velocity and secular bulge-to-disk ratio, lower gas fraction, and are redder as one goes from cluster to void environments. Although all these trends agree with observations, the latter tend to show more differences, suggesting this that physical ingredients not considered here as missalignment of angular momentum, halo triaxility, merging, ram pressure stripping, harassment, etc. play an important role for galaxy evolution, specially in high-density environments.

We show by means of a high-resolution N-body simulation how the mass assembly histories of galaxy-size cold dark matter (CDM) halos depend on environment. Halos in high density environments form earlier and a higher fraction of their mass is assembled in major mergers, compared to low density environments. The distribution of the present-day specific mass aggregation rate is strongly dependent on environment. While in low density environments only ∼ 20% of the halos are not accreting mass at the present epoch, this fraction rises to ∼ 80% at high densities. At z = 1 the median of the specific aggregation rate is ∼ 4 times larger than at z = 0 and almost independent on environment. All the dependences on environment found here are critically enhanced by local processes associated to subhalos because the fraction of subhalos increases as the environment gets denser. The distribution of the halo specific mass aggregation rate as well as its dependence on environment resemble the relations for the specific star formation rate distribution of galaxies. An analogue of the morphology-density relation is also present at the level of CDM halos, being driven by the halo major merging history. Nevertheless, baryonic processes are necessary in order to explain further details and the evolution of the star formation rate-, color-and morphology-environment relations.

We study the problem of the existence of a local quantum scalar field theory in a general affine metric space that in the semiclassical approximation would lead to the autoparallel motion of wave packets, thus providing a deviation of the spinless particle trajectory from the geodesics in the presence of torsion. The problem is shown to be equivalent to the inverse problem of the calculus of variations for the autoparallel motion with additional conditions that the action (if it exists) has to be invariant under time reparametrizations and general coordinate transformations, while depending analytically on the torsion tensor. The problem is proved to have no solution for a generic torsion in four-dimensional spacetime. A solution exists only if the contracted torsion tensor is a gradient of a scalar field. The corresponding field theory describes coupling of matter to the dilaton field.