We present a detailed analytical study of ultra-relativistic neutrinos in cosmological perturbation theory and of the observable signatures of inhomogeneities in the cosmic neutrino background. We note that a modification of perturbation variables that removes all the time derivatives of scalar gravitational potentials from the dynamical equations simplifies their solution notably. The used perturbations of particle number per coordinate, not proper, volume are generally constant on superhorizon scales. In real space an analytical analysis can be extended beyond fluids to neutrinos.The faster cosmological expansion due to the neutrino background changes the acoustic and damping angular scales of the cosmic microwave background (CMB). But we find that equivalent changes can be produced by varying other standard parameters, including the primordial helium abundance. The low-l integrated Sachs-Wolfe effect is also not sensitive to neutrinos. However, the gravity of neutrino perturbations suppresses the CMB acoustic peaks for the multipoles with l 200 while it enhances the amplitude of matter fluctuations on these scales. In addition, the perturbations of relativistic neutrinos generate a unique phase shift of the CMB acoustic oscillations that for adiabatic initial conditions cannot be caused by any other standard physics. The origin of the shift is traced to neutrino free-streaming velocity exceeding the sound speed of the photonbaryon plasma. We find that from a high resolution, low noise instrument such as CMBPOL the effective number of light neutrino species can be determined with an accuracy of σ(Nν ) ≃ 0.05 to 0.09, depending on the constraints on the helium abundance.
We study the formation of dark matter halos in the concordance ΛCDM model over a wide range of redshifts, from z = 20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 h −1 Mpc), we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (10 7 -10 13.5 h −1 M ⊙ ). Historically, there has been considerable variation in the high redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high-redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshifts, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near z = 0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed et al. may exist at low redshifts. Overall, our results are consistent with a "universal" form for the mass function at high redshifts.
We suggest a method of constructing gauge invariant quark and gluon distributions that describe an abstract QCD observable and apply this method to analyze angular momentum of a hadron. In addition to the known quark and gluon polarized structure functions, we obtain gauge invariant distributions for quark and gluon orbital angular momenta, and consider some basic properties of these distributions and their moments.
We show that the linear dynamics of cosmological perturbations can be described by coupled wave equations, allowing their efficient numerical and, in certain limits, analytical integration directly in position space. The linear evolution of any perturbation can then be analyzed with the Green's function method. Prior to hydrogen recombination, assuming tight coupling between photons and baryons, neglecting neutrino perturbations, and taking isentropic (adiabatic) initial conditions, the obtained Green's functions for all metric, density, and velocity perturbations vanish beyond the acoustic horizon. A localized primordial cosmological perturbation expands as an acoustic wave of photon-baryon density perturbation with narrow spikes at its acoustic wavefronts. These spikes provide one of the main contributions to the cosmic microwave background radiation anisotropy on all experimentally accessible scales. The gravitational interaction between cold dark matter and baryons causes a dip in the observed temperature of the radiation at the center of the initial perturbation. We first model the radiation by a perfect fluid and then extend our analysis to account for finite photon mean free path. The resulting diffusive corrections smear the sharp features in the photon and baryon density Green's functions over the scale of Silk damping.
We suggest that the cosmic microwave background (CMB) temperature correlation function C(θ) as a function of angle provides a direct connection between experimental data and the fundamental cosmological quantities. The evolution of inhomogeneities in the prerecombination universe is studied using their Green's functions in position space. We find that a primordial adiabatic point perturbation propagates as a sharp-edged spherical acoustic wave. Density singularities at its wavefronts create a feature in the CMB correlation function distinguished by a dip at θ ≈ 1.2• . Characteristics of the feature are sensitive to the values of cosmological parameters, in particular to the total and the baryon densities.The cosmic microwave background (CMB) radiation provides the best probe today of the early universe and a number of fundamental astrophysical constants [1][2][3][4][5][6][7]. Dynamical evolution of primordial perturbations manifests itself in the form of "acoustic peaks" in the CMB temperature angular power spectrum C l . After over a decade of studies, the physical content of the peaks has become qualitatively understood [8][9][10][11]. Nevertheless, one has to rely on standard numerical codes [12,13] to establish a quantitative connection between the CMB anisotropy pattern and cosmological parameters. This connection is particularly important now that highprecision CMB measurements have become reality.In this letter we show that previously unnoticed interesting phenomena are unraveled by considering the radiation-matter dynamics in position rather than Fourier space.Traditional CMB anisotropy analyses begin with the Fourier expansion of spatial inhomogeneities and studying time evolution of individual Fourier modes [16][17][18]. The position space approach, while offering a formally equivalent description, differs in its physical interpretation, associated calculational methods, and its implications for data analysis. As we show here, a new side of CMB physics is revealed in position space. One goal of our work is a deeper physical understanding of both the CMB power spectrum C l and the angular correlation function C(θ). We demonstrate that acoustic evolution of perturbations before recombination, as viewed in position space, produces sharp features in C(θ). These signatures not only provide a simple interpretation of the acoustic peaks, but they may also enable fast and accurate extraction of cosmological parameters directly from C(θ).As a simplified model for the essential physical processes, we consider the evolution of potential and density perturbations in gravitationally interacting photonbaryon and cold dark matter fluids. We use the conformal Newtonian gauge [18,19] to describe gravity and assume adiabatic (isentropic) primordial fluctuations as preferred by the present data [14,15] and the simplest inflationary models. The photons are assumed to be tightly coupled to electrons and baryons by Thomson scattering until recombination at redshift z rec ∼ 1100. Neutrinos are treated like photons. The disre...
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