2895797
Large-scale power in the CMB and new physics: An analysis using Bayesian model comparison
One of the most tantalizing results from the Wilkinson Microwave Anisotropy Probe ~WMAP! experiment is the suggestion that the power at large scales is anomalously low when compared to the prediction of the ‘‘standard’’ L cold dark matter ~CDM! model. The same anomaly, although with somewhat larger uncertainty, was also previously noted in the COBE data. In this work we discuss possible alternate models that give better fits on large scales and apply a model-comparison technique to select amongst them. We find that models with a cutoff in the power spectrum at large scales are indeed preferred by data, but only by a factor of 3.6, at most, in the likelihood ratio, corresponding to about ‘‘1.6 s’’ if interpreted in the traditional manner. Using the same technique, we have also examined the possibility of a systematic error in the measurement or prediction of the large-scale power. Ignoring other evidence that the large-scale modes are properly measured and predicted, we find this possibility somewhat more likely, with roughly a 2.75s evidence.
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.
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.
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.
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.
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.
118881742
Constructive Field Theory, Phase II
It now appears possible to study a realm of problems in CFT which, two years ago, appeared an order of magnitude too difficult to tackle. The finishing touches have just been put on the first paper of this sort1, and in this talk I will describe some of the basic ideas; these ideas are simple, although the details of the paper are complicated. The main question that I will discuss today has been around as long as field theory: Namely how does an interacting field model react to perturbations by an external source? Such perturbations of \(\textup{P}\left (\phi \right )_{2}\), or in fact any reasonable local perturbations of the \(\textup{P}\left (\phi \right )_{2}\) model, have been shown to be regular by James Glimm and myself1. As a consequence, (i) further properties of the original model have been established1, (ii) some new breakthroughs are being made2 and (iii) these methods appear promising for use in the study of more singular models than \(\textup{P}\left (\phi \right )_{2}\).
121044390
Infinite Renormalization of the Hamiltonian Is Necessary
We show that the unrenormalized Hamiltonian in quantum field theory is unbounded from below whenever lowest‐order perturbation theory indicates that this is true. We conclude that perturbation theory is an accurate guide to the divergence of the vacuum energy in quantum field theory.
14089951
The Elliptic Genus and Hidden Symmetry
Abstract: We study the elliptic genus (a partition function) in certain interacting, twist quantum field theories. Without twists, these theories have N=2 supersymmetry. The twists provide a regularization, and also partially break the supersymmetry. In spite of the regularization, one can establish a homotopy of the elliptic genus in a coupling parameter. Our construction relies on a priori estimates and other methods from constructive quantum field theory; this mathematical underpinning allows us to justify evaluating the elliptic genus at one endpoint of the homotopy. We obtain a version of Witten's proposed formula for the elliptic genus in terms of classical theta functions. As a consequence, the elliptic genus has a hidden SL(2, ℤ) symmetry characteristic of conformal theory, even though the underlying theory is not conformal.
121627004
The resummation of one particle lines
We propose a partial resummation for a weak coupling cluster expansion. The resummation gives one particle lines with in/out field propagators. We give a Bethe-Salpeter equation in which one particle subtractions are defined using physical one particle states. By these methods, we show thatP(φ)2 quantum fields in the weak coupling region have only isolated bound state spectrum below the 2m threshold. HereP is not restricted to be even.