18067206
Using the Comoving Maximum of the Galaxy Power Spectrum to Measure Cosmological Curvature
The large-scale maximum at k~0.05 identified in the power-spectrum of galaxy fluctuations provides a co-moving scale for measuring cosmological curvature. In shallow 3D surveys the peak is broad, but appears to be well resolved in 1D, at ~130 Mpc (k=0.048), comprising evenly spaced peaks and troughs. Surprisingly similar behaviour is evident at z=3 in the distribution of Lyman-break galaxies, for which we find a 5 sigma excess of pairs separated by Delta z=0.22pm0.02, equivalent to 85Mpc for Omega=1, increasing to 170 Mpc for Omega=0, with a number density contrast of 30% averaged over 5 independent fields. The combination, 3.2\Omega_m -\Omega_{\Lambda}=0.7, matches the local scale of 130 Mpc, i.e. Omega=0.2\pm0.1 or Omega_{m}=0.4\pm0.1 for the matter-dominated and flat models respectively, with an uncertainty given by the width of the excess correlation. The consistency here of the flat model with SNIa based claims is encouraging, but overshadowed by the high degree of coherence observed in 1D compared with conventional Gaussian models of structure formation. The appearance of this scale at high redshift and its local prominence in the distribution of Abell clusters lends support to claims that the high-z `spikes' represent young clusters. Finally we show that a spike in the primordial power spectrum of delta\rho/\rho=0.3 at k=0.05 has little effect on the CMB, except to exaggerate the first Doppler peak in flat matter-dominated models, consistent with recent observations. \\effect on the CMB, except to exaggerate the first Doppler peak in flat matter-dominated models, consistent with recent observations.
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.
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.
17460509
Simultaneous Estimation of Noise and Signal in Cosmic Microwave Background Experiments
To correctly analyse data sets from current microwave detection technology, one is forced to estimate the sky signal and experimental noise simultaneously. Given a time-ordered data set we propose a formalism and method for estimating the signal and associated errors without prior knowledge of the noise power spectrum. We derive the method using a Bayesian formalism and relate it to the standard methods; in particular we show how this leads to a change in the estimate of the noise covariance matrix of the sky signal. We study the convergence and accuracy of the method on two mock observational strategies and discuss its application to a currently-favoured calibration procedure.
119468667
Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries
We calculate the expected nHz-μHz gravitational wave (GW) spectrum from coalescing massive black hole (MBH) binaries resulting from mergers of their host galaxies. We consider detection of this spectrum by precision pulsar timing and a future pulsar timing array. The spectrum depends on the merger rate of massive galaxies, the demographics of MBHs at low and high redshift, and the dynamics of MBH binaries. We apply recent theoretical and observational work on all of these fronts. The spectrum has a characteristic strain hc(f) ~ 10-15(f/yr-1)-2/3, just below the detection limit from recent analysis of precision pulsar timing measurements. However, the amplitude of the spectrum is still very uncertain owing to approximations in the theoretical formulation of the model, to our lack of knowledge of the merger rate and MBH population at high redshift, and to the dynamical problem of removing enough angular momentum from the MBH binary to reach a GW-dominated regime.
122687802
Imaging the early universe with the BOOMERanG Experiment
The BOOMERanG experiment has recently detected temperature fluctuations the Cosmic Microwave Background (CMB), the otherwise isotropic radiation coming from the early Universe. These anisotropies have a low contrast (about 30 ppm) and feature a peculiar angular power spectrum at angles corresponding to sub-horizon scales at recombination. In the current cosmological model, these structures result from acoustic oscillations in the primeval plasma. In the framework of the Hot Big Bang theory with the inflationary hypothesis, the statistical properties of the image of the CMB allow us to measure most of the cosmological parameters.
122683434
Convergence of an iterative neural network learning algorithm for linearly dependent patterns
The authors show that a local iterative learning algorithm of Diederich and Opper (1987) converges for any set of patterns, including linearly dependent sets, and that the resulting coupling constants for a given set of patterns are the same as those given by the pseudoinverse rule for any maximal linearly independent subset of the given set. Thus, the matrix of couplings produced by the algorithm is the desired projection matrix onto the subspace spanned by the training set.
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.
15199369
Quantum Yang-Mills theory
Since the early part of the twentieth century, it has been understood that the description of nature at the subatomic scale requires quantum mechanics. In quantum mechanics, the position and velocity of a particle are noncommuting operators acting on a Hilbert space, and classical notions such as “the trajectory of a particle” do not apply. But quantum mechanics of particles is not the whole story. In nineteenth and early twentieth century physics, many aspects of nature were described in terms of fields—the electric and magnetic fields that enter in Maxwell’s equations, and the gravitational field governed by Einstein’s equations. Since fields interact with particles, it became clear by the late 1920’s that an internally coherent account of nature must incorporate quantum concepts for fields as well as for particles. After doing this, quantities such as the components of the electric field at different points in space-time become non-commuting operators. When one attempts to construct a Hilbert space on which these operators act, one finds many surprises. The distinction between fields and particles breaks down, since the Hilbert space of a quantum field is constructed in terms of particle-like excitations. Conventional particles, such as electrons, are reinterpreted as states of the quantized field. In the process, one finds the prediction of “antimatter;” for every particle, there must be a corresponding antiparticle, with the same mass and opposite electric charge. Soon after P. A. M. Dirac predicted this on the basis of quantum field theory, the “positron” or oppositely charged antiparticle of the electron was discovered in cosmic rays. The most important Quantum Field Theories (QFT’s) for describing elementary particle physics are gauge theories. The classical example of a gauge theory is Maxwell’s theory of electromagnetism. For electromagnetism the gauge symmetry group is the abelian group U(1). If A denotes the U(1) gauge connection, locally a one-form on space-time, then the curvature or electromagnetic field tensor is the two-form F = dA, and Maxwell’s equations in the absence of charges and currents read 0 = dF = d ∗ F . Here ∗ denotes the Hodge duality operator; indeed Hodge introduced his celebrated theory of harmonic forms as a generalization of the solutions to Maxwell’s equations. Maxwell’s equations describe large-scale electric and magnetic fields and also—as Maxwell discovered—the propagation of light waves, at a characteristic velocity, the speed of light.
124867759
The Particle Structure of the Weakly Coupled P(φ)2 Model and Other Applications of High Temperature Expansions: Part I. Physics of Quantum Field Models
55400839
On Super-KMS Functionals and Entire Cyclic Cohomology*
We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder - associated by Kastler to a super-KMS functional - satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.