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.
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.
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.
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.
35704824
The particle search in a quantum field model
The goal of quantum field theory is a description of elementary particles. When successful, this description should be both a mathematical theory and a law of nature. In our approach, we emphasize the construction of specific field theory models. The first motive for this emphasis is the mathematical consistency of quantum field theory. In addition, we follow closely the formal ideas of physics in order to provide a more solid foundation for the main task of quantum field theory: the study of elementary particles. It is clear by now that the first motive has been attained in two spacetime dimensions. In two space-time dimensions, quantum fields with nonlinear interactions have been constructed [1], [2]. For the polynomial boson (^(0)2) interactions with small coupling constant, all the Wightman axioms have been verified [5]. We announce two new results. The first is an estimate which is a major technical step toward establishing the above results in three space-time dimensions. The second result concerns the physical interpretation of our two dimensional models (the second motive of our study). In ( )2 models with a small coupling constant, we establish the existence of particles and we verify the Haag-Ruelle axioms for scattering. Thus we conclude that the ^((/>)2 model has the qualitative structure required for the description of (many particle) scattering experiments. In our first result we consider the $3 interaction: a $ 4 coupling in the interaction Hamiltonian for boson fields in three space-time dimensions. We introduce a space cut-off g e CQ(R), 0 ^ 0 ^ 1, in the interaction Hamiltonian density, and we let the resulting total Hamiltonian (with infinite counterterms from second and third order perturbation theory) be denoted H(g). Let A(g) denote the set of points within distance 1 of supp g.
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.
49336522
Ground state structure in supersymmetric quantum mechanics
We present a rigorous analysis of the vacuum structure of two models of supersymmetric quantum mechanics. They are the quantum mechanics versions of the two-dimensional N = 1 and N = 2 Wess-Zumino quantum field models. We find that the N = 2 quantum mechanics has degenerate vacua. The space of vacuum states is bosonic, and its dimension is determined by the topological properties of the superpotential. ( 1987 Academic Press. Inc. 1. SUPERSYMMETRY In this paper we address the ground state structure of supersymmetric quantum theory models. We study the simplest class of such models, anharmonic oscillators, in order to illustrate the phenomena which are qualitatively different from the usual ones.
115879784
Functional Integral Methods in Quantum Field Theory
We give a special form of the Osterwalder-Schrader axioms in terms of conditions on a functional integral S{f} = ∫eiϕ(f)dμ. This yields a simple, self-contained construction of a Hamiltonian H, a relativistic, local boson quantum field Φ, and a Feynman-Kac formula to study perturbations H + Φ of H.