14182141
The effect of the detector response time on bolometric cosmic microwave background anisotropy experiments
We analyze the effects of the detector response time on bolometric measurements of the anisotropy of the cosmic microwave background (CMB). We quantify the effect in terms of a single dimensionless parameter $L$ defined as the ratio between the time the beam sweeps its own size and the bolometer response time. As $L$ decreases below $\sim 2.5$ the point source response of the experiment becomes elongated. We introduce a window function matrix based on the timestream data to assess the effects of the elongated beam. We find that the values of the window function matrix elements decrease slowly as a function $L$. Our analysis and results apply to other cases of beam asymmetry. For the High Frequency Instrument on board the Planck Surveyor satellite we show that for a broad range of $L$ the ability of the experiment to extract the cosmological parameters is not degraded. Our analysis enhances the flexibility in tuning the design parameters of CMB anisotropy experiments.
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.
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.
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.
119956317
Self-adjointness of the Yukawa2 Hamiltonian
Abstract We prove that the Hamiltonian H ( g ) for the Yukawa 2 interaction with a spatial cutoff is self-adjoint. We define H ( g ) as the limit of operators H ( g , κ ) with an ultraviolet cutoff. The ultraviolet cutoff makes the mass renormalization constant δm 2 ( g , κ ) and the vacuum self-energy E ( g , κ ) finite, but these constants both diverge logarithmically as κ → ∞. We choose the renormalization constants required by perturbation theory. As κ → ∞, the resolvents of the self-adjoint operators H ( g , κ ) converge in norm to the resolvent of the self-adjoint operator H ( g ). In addition H ( g ) has a vacuum vector.
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
121286855
Meron Pairs and Quark Confinement
We discuss the consequences of our classical meron-pair model on the quark-confinement phase transition in an SU(2) Yang-Mills quantum field theory.
117116150
Exact Renormalization Group for Gauge Theories
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe — quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored.
121225135
Asymptotically commuting families of operators
We study families of symmetric operators (Qn) with domains given by the range of self-adjoint contraction semigroups (e−tHn). Assuming the asymptotic commutativity, limn[Qn, e−tHn]=0, and certain other estimates, we establish the existence and properties of a limiting self-adjoint operatorQ=limnQn. We apply these results to the study of an elementary supersymmetry algebra.