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The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theorys ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.
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We present a method to measure the small-scale matter power spectrum using high-resolution measurements of the gravitational lensing of the Cosmic Microwave Background (CMB). To determine whether small-scale structure today is suppressed on scales below 10 kiloparsecs (corresponding to M < 10^9 M_sun), one needs to probe CMB-lensing modes out to L ~ 35,000, requiring a CMB experiment with about 20 arcsecond resolution or better. We show that a CMB survey covering 4,000 square degrees of sky, with an instrumental sensitivity of 0.5 uK-arcmin at 18 arcsecond resolution, could distinguish between cold dark matter and an alternative, such as 1 keV warm dark matter or 10^(-22) eV fuzzy dark matter with about 4-sigma significance. A survey of the same resolution with 0.1 uK-arcmin noise could distinguish between cold dark matter and these alternatives at better than 20-sigma significance; such high-significance measurements may also allow one to distinguish between a suppression of power due to either baryonic effects or the particle nature of dark matter, since each impacts the shape of the lensing power spectrum differently. CMB temperature maps yield higher signal-to-noise than polarization maps in this small-scale regime; thus, systematic effects, such as from extragalactic astrophysical foregrounds, need to be carefully considered. However, these systematic concerns can likely be mitigated with known techniques. Next-generation CMB lensing may thus provide a robust and powerful method of measuring the small-scale matter power spectrum.
In this paper we show how effects from small scales enter the angular-redshift power spectrum $C_ell(z,z)$. In particular, we show that spectroscopic surveys with high redshift resolution are affected by small scales already on large angular scales, i.e. at low multipoles. Therefore, when considering the angular power spectrum with spectroscopic redshift resolution, it is important to account for non-linearities relevant on small scales even at low multipoles. This may also motivate the use of the correlation function instead of the angular power spectrum. These effects, which are very relevant for bin auto-correlations, but not so important for cross-correlations, are quantified in detail.
We argue that the global signal of neutral hydrogen 21cm line can be a powerful probe of primordial power spectrum on small scales. Since the amplitude of small scale primordial fluctuations is important to determine the early structure formation and the timing when the sources of Lyman ${alpha}$ photons are produced, they in turn affect the neutral hydrogen 21cm line signal. We show that the information of the position of the absorption trough can severely constrain the small scale amplitude of primordial fluctuations once astrophysical parameters relevant to the 21cm line signal are fixed. We also discuss how the uncertainties of astrophysical parameters affect the constraints.
The dark matter enclosed in a density perturbation with a large initial amplitude (delta-rho/rho > 1e-3) collapses shortly after recombination and forms an ultracompact minihalo (UCMH). Their high central densities make UCMHs especially suitable for detection via astrometric microlensing: as the UCMH moves, it changes the apparent position of background stars. A UCMH with a mass larger than a few solar masses can produce a distinctive astrometric microlensing signal that is detectable by the space astrometry mission Gaia. If Gaia does not detect gravitational lensing by any UCMHs, then it establishes an upper limit on their abundance and constrains the amplitude of the primordial power spectrum for k~2700 Mpc^{-1}. These constraints complement the upper bound on the amplitude of the primordial power spectrum derived from limits on gamma-ray emission from UCMHs because the astrometric microlensing signal produced by an UCMH is maximized if the dark-matter annihilation rate is too low to affect the UCMHs density profile. If dark matter annihilation within UCMHs is not detectable, a search for UCMHs by Gaia could constrain the amplitude of the primordial power spectrum to be less than 1e-5; this bound is three orders of magnitude stronger than the bound derived from the absence of primordial black holes.
In the cold dark matter (CDM) picture of structure formation, galaxy mass distributions are predicted to have a considerable amount of structure on small scales. Strong gravitational lensing has proven to be a useful tool for studying this small-scale structure. Much of the attention has been given to detecting individual dark matter subhalos through lens modeling, but recent work has suggested that the full population of subhalos could be probed using a power spectrum analysis. In this paper we quantify the power spectrum of small-scale structure in simulated galaxies, with the goal of understanding theoretical predictions and setting the stage for using measurements of the power spectrum to test dark matter models. We use a sample of simulated galaxies generated from the texttt{Galacticus} semi-analytic model to determine the power spectrum distribution first in the CDM paradigm and then in a warm dark matter scenario. We find that a measurement of the slope and amplitude of the power spectrum on galaxy strong lensing scales ($ksim 1$ kpc$^{-1}$) could be used to distinguish between CDM and alternate dark matter models, especially if the most massive subhalos can be directly detected via gravitational imaging.
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