Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive halos. We present analytical results on the eight shear three-point correlation functions constructed using combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E-mode from the B-mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster halos from lensing surveys. Shear correlations on small scales arise from the lensing matter within halos of mass M > 10^13 solar masses. Thus the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10% accuracy on profile parameters is achievable with surveys like the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties.Comment: 30 pages, 21 figures. Corrected typos in equations (23) and (28). Matches version for publication in MNRA

Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering

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 photon-baryon 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 sigma(N_nu) = 0.05 to 0.09, depending on the constraints on the helium abundance.Comment: 38 pages, 7 figures. Version accepted for publication in PR

Constraining the dark energy dynamics with the cosmic microwave background bispectrum

We consider the influence of the dark energy dynamics at the onset of cosmic acceleration on the Cosmic Microwave Background (CMB) bispectrum, through the weak lensing effect induced by structure formation. We study the line of sight behavior of the contribution to the bispectrum signal at a given angular multipole $l$: we show that it is non-zero in a narrow interval centered at a redshift $z$ satisfying the relation $l/r(z)\simeq k_{NL}(z)$, where the wavenumber corresponds to the scale entering the non-linear phase, and $r$ is the cosmological comoving distance. The relevant redshift interval is in the range 0.1\lsim z\lsim 2 for multipoles 1000\gsim\ell\gsim 100; the signal amplitude, reflecting the perturbation dynamics, is a function of the cosmological expansion rate at those epochs, probing the dark energy equation of state redshift dependence independently on its present value. We provide a worked example by considering tracking inverse power law and SUGRA Quintessence scenarios, having sensibly different redshift dynamics and respecting all the present observational constraints. For scenarios having the same present equation of state, we find that the effect described above induces a projection feature which makes the bispectra shifted by several tens of multipoles, about 10 times more than the corresponding effect on the ordinary CMB angular power spectrum.Comment: 15 pages, 7 figures, matching version accepted by Physical Review D, one figure improve

The First Magnetic Fields

We review current ideas on the origin of galactic and extragalactic magnetic fields. We begin by summarizing observations of magnetic fields at cosmological redshifts and on cosmological scales. These observations translate into constraints on the strength and scale magnetic fields must have during the early stages of galaxy formation in order to seed the galactic dynamo. We examine mechanisms for the generation of magnetic fields that operate prior during inflation and during subsequent phase transitions such as electroweak symmetry breaking and the quark-hadron phase transition. The implications of strong primordial magnetic fields for the reionization epoch as well as the first generation of stars is discussed in detail. The exotic, early-Universe mechanisms are contrasted with astrophysical processes that generate fields after recombination. For example, a Biermann-type battery can operate in a proto-galaxy during the early stages of structure formation. Moreover, magnetic fields in either an early generation of stars or active galactic nuclei can be dispersed into the intergalactic medium.Comment: Accepted for publication in Space Science Reviews. Pdf can be also downloaded from http://canopus.cnu.ac.kr/ryu/cosmic-mag1.pd

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Keeping It Real: Revisiting a Real-Space Approach to Running Ensembles of Cosmological N-body Simulations

In setting up initial conditions for ensembles of cosmological N-body simulations there are, fundamentally, two choices: either maximizing the correspondence of the initial density field to the assumed fourier-space clustering or, instead, matching to real-space statistics and allowing the DC mode (i.e. overdensity) to vary from box to box as it would in the real universe. As a stringent test of both approaches, I perform ensembles of simulations using power law and a "powerlaw times a bump" model inspired by baryon acoustic oscillations (BAO), exploiting the self-similarity of these initial conditions to quantify the accuracy of the matter-matter two-point correlation results. The real-space method, which was originally proposed by Pen 1997 and implemented by Sirko 2005, performed well in producing the expected self-similar behavior and corroborated the non-linear evolution of the BAO feature observed in conventional simulations, even in the strongly-clustered regime (sigma8 >= 1). In revisiting the real-space method championed by Sirko 2005, it was also noticed that this earlier study overlooked an important integral constraint correction to the correlation function in results from the conventional approach that can be important in LambdaCDM simulations with Lbox == Lbox / 10. Rectifying this shows that the fourier space and real space methods are about equally accurate and efficient for modeling the evolution and growth of the correlation function, contrary to previous claims. An appendix provides a useful independent-of-epoch analytic formula for estimating the importance of the integral constraint bias on correlation function measurements in LambdaCDM simulations.Comment: 28 pages, 7 figures, substantial improvements throughou

Cosmological constraints from galaxy clustering

In this manuscript I review the mathematics and physics that underpins recent work using the clustering of galaxies to derive cosmological model constraints. I start by describing the basic concepts, and gradually move on to some of the complexities involved in analysing galaxy redshift surveys, focusing on the 2dF Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky survey (SDSS). Difficulties within such an analysis, particularly dealing with redshift space distortions and galaxy bias are highlighted. I then describe current observations of the CMB fluctuation power spectrum, and consider the importance of measurements of the clustering of galaxies in light of recent experiments. Finally, I provide an example joint analysis of the latest CMB and large-scale structure data, leading to a set of parameter constraints.Comment: 30 pages, 13 figures. Lecture given at Third Aegean Summer School, The invisible universe: Dark matter and Dark energ

Primordial Nucleosynthesis for the New Cosmology: Determining Uncertainties and Examining Concordance

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) have a long history together in the standard cosmology. The general concordance between the predicted and observed light element abundances provides a direct probe of the universal baryon density. Recent CMB anisotropy measurements, particularly the observations performed by the WMAP satellite, examine this concordance by independently measuring the cosmic baryon density. Key to this test of concordance is a quantitative understanding of the uncertainties in the BBN light element abundance predictions. These uncertainties are dominated by systematic errors in nuclear cross sections. We critically analyze the cross section data, producing representations that describe this data and its uncertainties, taking into account the correlations among data, and explicitly treating the systematic errors between data sets. Using these updated nuclear inputs, we compute the new BBN abundance predictions, and quantitatively examine their concordance with observations. Depending on what deuterium observations are adopted, one gets the following constraints on the baryon density: OmegaBh^2=0.0229\pm0.0013 or OmegaBh^2 = 0.0216^{+0.0020}_{-0.0021} at 68% confidence, fixing N_{\nu,eff}=3.0. Concerns over systematics in helium and lithium observations limit the confidence constraints based on this data provide. With new nuclear cross section data, light element abundance observations and the ever increasing resolution of the CMB anisotropy, tighter constraints can be placed on nuclear and particle astrophysics. ABRIDGEDComment: 54 pages, 20 figures, 5 tables v2: reflects PRD version minor changes to text and reference

Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS

On very large scales, density fluctuations in the Universe are small, suggesting a perturbative model for large-scale clustering of galaxies (or other dark matter tracers), in which the galaxy density is written as a Taylor series in the local mass density, delta, with the unknown coefficients in the series treated as free "bias" parameters. We extend this model to include dependence of the galaxy density on the local values of nabla_i nabla_j phi and nabla_i v_j, where phi is the potential and v is the peculiar velocity. We show that only two new free parameters are needed to model the power spectrum and bispectrum up to 4th order in the initial density perturbations, once symmetry considerations and equivalences between possible terms are accounted for. One of the new parameters is a bias multiplying s_ij s_ji, where s_ij=[nabla_i nabla_j \nabla^-2 - 1/3 delta^K_ij] delta. The other multiplies s_ij t_ji, where t_ij=[nabla_i nabla_j nabla^-2 - 1/3 delta^K_ij](theta-delta), with theta=-(a H dlnD/dlna)^-1 nabla_i v_i. (There are other, observationally equivalent, ways to write the two terms, e.g., using theta-delta instead of s_ij s_ji.) We show how short-range (non-gravitational) non-locality can be included through a controlled series of higher derivative terms, starting with R^2 nabla^2 delta, where R is the scale of non-locality (this term will be a small correction as long as k^2 R^2 is small, where k is the observed wavenumber). We suggest that there will be much more information in future huge redshift surveys in the range of scales where beyond-linear perturbation theory is both necessary and sufficient than in the fully linear regime.Comment: 24 pg., 5 fi