15450342
THE ANGULAR THREE-POINT CORRELATION FUNCTION IN THE QUASI-LINEAR REGIME
We calculate the normalized angular three-point correlation function (3PCF), q, as well as the normalized angular skewness, s{sub 3}, assuming the small-angle approximation, for a biased mass distribution in flat and open cold dark matter (CDM) models with Gaussian initial conditions. The leading-order perturbative results incorporate the explicit dependence on the cosmological parameters, the shape of the CDM transfer function, the linear evolution of the power spectrum, the form of the assumed redshift distribution function, and linear and nonlinear biasing, which may be evolving. Results are presented for different redshift distributions, including that appropriate for the APM Galaxy Survey, as well as for a survey with a mean redshift of z{approx_equal}1 (such as the VLA FIRST Survey). Qualitatively, many of the results found for s{sub 3} and q are similar to those obtained in a related treatment of the spatial skewness and 3PCF, such as a leading-order correction to the standard result for s{sub 3} in the case of nonlinear bias (as defined for unsmoothed density fields), and the sensitivity of the configuration dependence of q to both cosmological and biasing models. We show that since angular correlation functions (CFs) are sensitive to clustering over a range of redshifts, themore » various evolutionary dependences included in our predictions imply that measurements of q in a deep survey might better discriminate between models with different histories, such as evolving versus nonevolving bias, that can have similar spatial CFs at low redshift. Our calculations employ a derived equation, valid for open, closed, and flat models, to obtain the angular bispectrum from the spatial bispectrum in the small-angle approximation. (c) (c) 2000. The American Astronomical Society.« less
119383399
Detection of Anisotropy in the Cosmic Microwave Background at Horizon and Sub-Horizon Scales with the BOOMERanG Experiment
BOOMERanG has recently resolved with high signal to noise sub-horizon structures on the last scattering surface at z=1000. We shortly review the technical advances which made this possible, and we focus on the current results for maps and power spectra, with special attention to the determination of the total mass-energy density in the Universe
15684873
H0 and Odds on Cosmology
Recent observations by the Hubble Space Telescope of Cepheids in the Virgo cluster imply a Hubble constant H0 = 80 ± 17 km s−1 Mpc−1; other recent observations find 70 H0 90 km s−1 Mpc−1, with several large excursions in either direction. We attempt to clarify some issues of interpretation of these results for determining the global cosmological parameters Ω and Λ. In this paper, we use these results as a case study in the formalism of Bayesian model comparison, allowing a rigorous comparison of the different cosmological possibilities. We concentrate our analysis on three recent determinations of the Hubble constant, but the results are generic so long as they prefer H0 t0 1, which would seem to require Λ > 0 within the context of Friedmann-Robertson-Walker cosmologies. With our more rigorous methods, the data do indeed suggest a universe with a nonzero cosmological constant but vanishing curvature: Ω + Λ = 1.
119408227
CMB likelihood functions for beginners and experts
Although the broad outlines of the appropriate pipeline for cosmological likelihood analysis with CMB data has been known for several years, only recently have we had to contend with the full, large-scale, computationally challenging problem involving both highly-correlated noise and extremely large datasets (N>1000). In this talk we concentrate on the beginning and end of this process. First, we discuss estimating the noise covariance from the data itself in a rigorous and unbiased way; this is essentially an iterated minimum-variance mapmaking approach. We also discuss the unbiased determination of cosmological parameters from estimates of the power spectrum or experimental bandpowers.
119068104
A Bayesian analysis of the 27 highest energy cosmic rays detected by the Pierre Auger Observatory
It is possible that ultrahigh energy cosmic rays (UHECRs) are generated by active galactic nuclei (AGNs), but there is currently no conclusive evidence for this hypothesis. Several reports of correlations between the arrival directions of UHECRs and the positions of nearby AGNs have been made, the strongest detection coming from a sample of 27 UHECRs detected by the Pierre Auger Observatory (PAO). However, the PAO results were based on a statistical methodology that not only ignored some relevant information (most obviously the UHECR arrival energies, but also some of the information in the arrival directions), but also involved some problematic fine-tuning of the correlation parameters. Here we present a fully Bayesian analysis of the PAO data (collected before 2007 September), which makes use of more of the available information, and find that a fraction FAGN= 0.15+0.10−0.07 of the UHECRs originate from known AGNs in the Veron-Cetty and Veron (VCV) catalogue. The hypothesis that all the UHECRs come from VCV AGNs is ruled out, although there remains a small possibility that the PAO–AGN correlation is coincidental (FAGN= 0.15 is 200 times as probable as FAGN= 0.00).
15621530
Constraining large–scale structure theories with the cosmic background radiation
The case is strong that cosmic microwave background (CMB) and large scale structure (LSS) observations can be combined to determine the theory of structure formation and the cosmological parameters that define it. We review: the relevant (10+) parameters associated with the inflation model of fluctuation generation and the matter content of the universe; the relation between LSS and primary and secondary CMB anisotropy probes as a function of wavenumber; how COBE constraints on energy injection rule out explosions as a dominant source of LSS; and how current anisotropy band–powers in multipole–space, at levels ca. 10−5)2, strongly support the gravitational instability theory and suggest the universe could not have reionized too early. We use Bayesian analysis methods to determine what current CMB and CMB+LSS data imply for inflation–based Gaussian fluctuations in tilted &Lgr;CDM, &Lgr;hCDM and oCDM model sequences with cosmological age 11 – 15 Gyr, consisting of mixtures of baryons, cold ‘c’ (and possibly hot ‘h’) dark matter, vacuum energy &Lgr;, and curvature energy ‘o’ in open cosmologies. For example, we find the slope of the initial spectrum is within about 5% of the (preferred) scale–invariant form when just the CMB data are used, and for &Lgr;CDM when LSS data are combined with CMB; with both, a non–zero value of Ω&Lgr; is strongly preferred (ca. ⅔ for a 13 Gyr sequence, similar to the value from SNIa). The oCDM sequence prefers Ωtot < 1, but is overall much less likely than the flat Ω&Lgr; ≠ 0 sequence with CMB+LSS. We also review the rosy forecasts of angular power spectra and parameter estimates from future balloon and satellite experiments when foreground and systematic effects are ignored to show where cosmic parameter determination can go with CMB information alone.
117682886
Quantum field theory : a selection of papers in memorian Kurt Symanzik
To the Memory of Kurt Symanzik.- Monte Carlo Simulations for Quantum Field Theories Involving Fermions.- SU(2) Lattice Gauge Theory: Standard Action Versus Symanzik's Tree-Improved Action.- On-shell Improved Lattice Gauge Theories.- On the Modular Structure of Local Algebras of Observables.- The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory.- Intersection Properties of Simple Random Walks: A Renormalization Group Approach.- Self-Avoiding Walk in 5 or More Dimensions.- Indecomposable Representations with Invariant Inner Product A Theory of the Gupta-Bleuler Triplet.- Classical Models of Confinement II.- The Energy-Momentum Spectrum in Local Field Theories with Broken Lorentz-Symmetry.- Large Deviations for Stationary Gaussian Processes.- Reduction in the Number of Coupling Parameters.- Conformal Gauges and Renormalized Equations of Motion in Massless Quantum Electrodynamics.- Longitudinal Jet Cross Sections in Order ?s2.- Convergent Perturbation Expansions for Euclidean Quantum Field Theory.- Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory.
123980035
MODEL ESTIMATES AND RESULTS.
49335927
Index of a family of Dirac operators on loop space
We use methods of constructive field theory to generalize index theory to an infinite-dimensional setting. We study a family of Dirac operatorsQ on loop space. These operators arise in the context of supersymmetric nonlinear quantum field models with HamiltoniansH=Q2. In these modelsQ is self-adjoint and Fredholm. A natural grading operator Γ exists such that ΓQ+QΓ=0. We studyQ+=P−QP+, whereP±=1/2 (1±Γ) are the orthogonal projections onto the eigenspaces of Γ. We calculate the indexi(Q+) for Wess-Zumino models defined by a superpotentialV(ω). HereV is a polynomial of degreen≧2. We establish thati(Q+)=n−1=degδV. In particular, the field theory models have unbroken supersymmetry, and (forn≧3) they have degenerate vacua. We believe that this is the first index theorem for a Dirac operator that couples infinitely many degrees of freedom.
15299742
Complex Classical Fields: A Framework for Reflection Positivity
We explore a framework for complex classical fields, appropriate for describing quantum field theories. Our fields are linear transformations on a Hilbert space, so they are more general than random variables for a probability measure. Our method generalizes Osterwalder and Schrader’s construction of Euclidean fields. We allow complex-valued classical fields in the case of quantum field theories that describe neutral particles.From an analytic point-of-view, the key to using our method is reflection positivity. We investigate conditions on the Fourier representation of the fields to ensure that reflection positivity holds. We also show how reflection positivity is preserved by various spacetime compactifications of $${\mathbb{R}^{d}}$$Rd in different coordinate directions.
123457713
SUPERSYMMETRIC QUANTUM FIELDS AND INFINITE DIMENSIONAL ANALYSIS
Supersymmetric quantum fields are interesting from the point of view both of physics and of mathematics. Their interest for physics (see, e g. [35]) stems primarily from the fact that they may provide a natural framework for a unified theory of elementary interactions. In particular, recent developments in superstring theory [15] suggest that such a theory has the potential to unify gravitational forces with the strong, weak and electromagnetic forces.