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).
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.
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.
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.
125568007
A Remark on the Existence of phi**4 in Four-Dimensions
123158581
The energy momentum spectrum and vacuum expectation values in quantum field theory, II
We prove that theP(ϕ)2 quantum field theory satisfies the spectral condition. The space time translationa=(x, t) is implemented by the unitary groupU(a)=exp(itH−ixP), and the joint spectrum of the energy operatorH and the momentum operatorP is contained in the forward cone. We also obtain bounds on certain vacuum expectation values of products of field operators. Our proofs involve an analysis of the limitV→∞ for approximate theories in a periodic box of volumeV. Assuming the existence of a uniform mass gap, we are able to establish all the Wightman axioms with the exception of the Lorentz invariance of the vacuum.
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.
118116787
Boson Quantum Field Models
Quantum fields, from a mathematical point of view, are highly singular. These fields are believed to describe the interactions of elementary particles. For the interaction of electrons with light (photons), the quantum field description is exact within the limits of experimental accuracy (5 significant figures). For these reasons, i.e. the mathematical difficulties and the importance to physics, the problem of formulating the mathematical foundations of quantum field theory has attracted the attention of both mathematicians and physicists over a period of several decades. On the side of the physicists, the most striking achievements were the calculation in the late 1940’s and early 1950’s of the Lamb shift and the anomalous magnetic moment of the electron together with the development of the renormalization method on which these calculations were based. Of the mathematicians, J. von Neumann was the first to realize that new mathematical theories would be required to formulate quantum field theory correctly and this realization was one of the motives for developing the theory of operator algebras.
16492814
CONSTRUCTIVE QUANTUM FIELD THEORY
The pioneering work of early non-relativistic quantum theory led to the understanding that quantum dynamics on Hilbert space is a comprehensive predictive framework for microscopic phenomena. From the Bohr atom, through the nonrelativistic quantum theory of Schrödinger and Heisenberg, and the relativistic Dirac equation for hydrogen, agreement between calculation and experiment improved rapidly over time. The incorporation of special relativity and field theory into quantum theory extended the scope of perturbative calculations, and these were tested through precision measurements of spectra and magnetic moments. Beginning in the 1940’s, experimental tests of the Lamb shift and the anomalous magnetic moment of the electron detected effects that one can ascribe to fluctuations in quantum electrodynamics. These effects deviated numerically from the predictions arising from equations that describe a fixed number of particles, so they were accurate tests of the quantum field hypothesis. Today these experiments have evolved to yield quantitative agreement with the most precise observations and calculations achieved in physics. For example, the anomalous magnetic moment of the electron is known theoretically and experimentally to amazing precision: (g − 2)/2 = 0.001159652200(±40). The success of this work, as well as the success of other less accurate, but compelling, predictions for weak and strong interactions, convince us to accept quantum field theory as the correct physical arena to describe particle physics down to the Planck scale. But the success of relativistic field theory calculations and of perturbative renormalization also led to a logical puzzle: is there any physically-relevant, relativistic quantum field theory that is also mathematically consistent? Put differently, can one give a mathematically complete example of any non-linear theory, relevant for the description of interacting particles, whose solutions incorporate relativistic covariance, positive energy, and causality? One must understand perturbative renormalization in order to resolve this problem, and have control over renormalization from a non-perturbative (or “exact”) point of view. In fact, one needs to overcome sophisticated problems, such as whether a field theory may appear correct on a perturbative level, while it may have no meaning at a non-perturbative level. Doubts about quantum electrodynamics or scalar meson theory were raised early by Dyson and Landau. They recur from the point of view of the renormalization group in the work of Kadanoff and Wilson, as well as in the analysis of “asymptotic