Abstract:
Although the currently favored cold dark matter plus cosmological constant model for structure formation assumes an n=1 scale-invariant initial power spectrum, most inflation models produce at least mild deviations from n=1. Because the lever arm from the CMB normalization to galaxy scales is long, even a small ``tilt'' can have important implications for galactic observations. Here we calculate the COBE-normalized power spectra for several well-motivated models of inflation and compute implications for the substructure content and central densities of galaxy halos. Using an analytic model, normalized against N-body simulations, we show that while halos in the standard (n=1) model are overdense by a factor of ~6 compared to observations, several of our example inflation+LCDM models predict halo densities well within the range of observations, which prefer models with n ~ 0.85. We go on to use a semi-analytic model (also normalized against N-body simulations) to follow the merger histories of galaxy-sized halos and track the orbital decay, disruption, and evolution of the merging substructure. Models with n ~0.85 predict a factor of ~3 fewer subhalos at a fixed circular velocity than the standard $n = 1$ case. Although this level of reduction does not resolve the ``dwarf satellite problem'', it does imply that the level of feedback required to match the observed number of dwarfs is sensitive to the initial power spectrum. Finally, the fraction of galaxy-halo mass that is bound up in substructure is consistent with limits imposed by multiply imaged quasars for all models considered: f_sub > 0.01 even for an effective tilt of n ~0.8.We conclude that, at their current level, lensing constraints of this kind do not provide strong limits on the primordial power spectrum.

Abstract:
Dark matter annihilation in Galactic substructure produces diffuse gamma-ray emission of remarkably constant intensity across the sky, and in general this signal dominates over the smooth halo signal at angles greater than a few tens of degrees from the Galactic Center. The large-scale isotropy of the emission from substructure suggests that it may be difficult to extract this Galactic dark matter signal from the extragalactic gamma-ray background. I show that dark matter substructure induces characteristic small-scale anisotropies in the diffuse emission which may provide a robust means of distinguishing this component. I discuss predictions for the angular power spectrum of the diffuse emission from various extragalactic source classes as well as from Galactic dark matter, and show that the energy dependence of the angular power spectrum of the total measured emission could be used to confidently identify a gamma-ray signal from Galactic dark matter.

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 develop the formalism to include substructure in the halo model of clustering. Real halos are not likely to be perfectly smooth, but have substructure which has so far been neglected in the halo model -- our formalism allows one to estimate the effects of this substructure on measures of clustering. We derive expressions for the two-point correlation function, the power-spectrum, the cross-correlation between galaxies and mass, as well as higher order correlation functions. Simple forms of the formulae are obtained for the limit in which the size of the subclumps and mass fraction in them is small. Inclusion of substructure allows for a more accurate analysis of the statistical effects of gravitational lensing. It can also bring the halo model predictions into better agreement with the small-scale structure seen in recent high resolution simulations of hierarchical clustering.

Abstract:
We explore the connection between halo concentration and the dark matter power spectrum using the halo model. We fit halo model parameters to non-linear power spectra over a large range of cosmological models. We find that the non-linear evolution of the power spectrum generically prefers the concentration at non-linear mass scale to decrease with the effective slope of the linear power spectrum, in agreement with the direct analysis of the halo structure in different cosmological models. Using these analyses, we compute the predictions for non-linear power spectrum beyond the current resolution of N-body simulations. We find that the halo model predictions are generically below the analytical non-linear models, suggesting that the latter may overestimate the amount of power on small scales.

Abstract:
We revisit an analytical model to describe the halo-matter cross-power spectrum and the halo auto-power spectrum in the weakly nonlinear regime, by combining the perturbation theory (PT) for matter clustering, the local bias model, and the halo bias. Nonlinearities in the power spectra arise from the nonlinear clustering of matter as well as the nonlinear relation between the matter and halo density fields. By using the "renormalization" approach, we express the nonlinear power spectra by a sum of the two contributions: the nonlinear matter power spectrum with the effective linear bias parameter, and the higher-order PT spectra having the halo bias parameters as the coefficients. The halo auto-power spectrum includes the residual shot noise contamination that needs to be treated as additional free parameter. The term(s) of the higher-order PT spectra and the residual shot noise cause a scale-dependent bias function relative to the nonlinear matter power spectrum in the weakly nonlinear regime. We show that the model predictions are in good agreement with the spectra measured from a suit of high-resolution $N$-body simulations up to $k\simeq 0.2 h$/Mpc at $z=0.35$, for different halo mass bins.

Abstract:
The thermal and expansion history of the Universe before big bang nucleosynthesis is unknown. We investigate the evolution of cosmological perturbations through the transition from an early matter era to radiation domination. We treat reheating as the perturbative decay of an oscillating scalar field into relativistic plasma and cold dark matter. After reheating, we find that subhorizon perturbations in the decay-produced dark matter density are significantly enhanced, while subhorizon radiation perturbations are instead suppressed. If dark matter originates in the radiation bath after reheating, this suppression may be the primary cutoff in the matter power spectrum. Conversely, for dark matter produced nonthermally from scalar decay, enhanced perturbations can drive structure formation during the cosmic dark ages and dramatically increase the abundance of compact substructures. For low reheat temperatures, we find that as much as 50% of all dark matter is in microhalos with M > 0.1 Earth masses at z=100, compared to a fraction of 1e-10 in the standard case. In this scenario, ultradense substructures may constitute a large fraction of dark matter in galaxies today.

Abstract:
In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies. Typically, only the most massive subhalos in the strong lensing region may be detected this way. In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually. In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing. We develop the mathematical framework of power spectrum estimation, and test our method on mock observations. We use our results to determine the types of observations required to measure the substructure power spectrum with high significance. We predict that deep observations ($\sim10$ hours on a single target) with current facilities can measure this power spectrum at the $3\sigma$ level, with no apparent degeneracy with unknown clumpiness in the background source structure or fluctuations from detector noise. Upcoming ALMA measurements of strong lenses are capable of placing strong constraints on the abundance of dark matter subhalos and the underlying particle nature of dark matter.

Abstract:
Recently there has been a lot of attention focussed on a virialized halo-based approach to understanding the properties of the matter and galaxy power spectrum. We show that this model allows a natural treatment of the large and small scale redshift space distortions, which we develop here, which extends the pedagogical value of the approach.

Abstract:
High-resolution N-body simulations are used to examine the power spectrum dependence of the concentration of galaxy-sized dark matter halos. It is found that dark halo concentrations depend on the amplitude of mass fluctuations as well as on the ratio of power between small and virial mass scales. This finding is consistent with the original results of Navarro, Frenk & White (NFW), and allows their model to be extended to include power spectra substantially different from Cold Dark Matter (CDM). In particular, the single-parameter model presented here fits the concentration dependence on halo mass for truncated power spectra, such as those expected in the warm dark matter scenario, and predicts a stronger redshift dependence for the concentration of CDM halos than proposed by NFW. The latter conclusion confirms recent suggestions by Bullock et al., although this new modeling differs from theirs in detail. These findings imply that observational limits on the concentration, such as those provided by estimates of the dark matter content within individual galaxies, may be used to constrain the amplitude of mass fluctuations on galactic and subgalactic scales. The constraints on $\Lambda$CDM models posed by the dark mass within the solar circle in the Milky Way and by the zero-point of the Tully-Fisher relation are revisited, with the result that neither dataset is clearly incompatible with the `concordance' ($\Omega_0=0.3$, $\Lambda_0=0.7$, $\sigma_8=0.9$) $\Lambda$CDM cosmogony. This conclusion differs from that reached recently by Navarro & Steinmetz, a disagreement that can be traced to inconsistencies in the normalization of the $\Lambda$CDM power spectrum used in that work.