117901039
Multiple Peaks in the Angular Power Spectrum of the Cosmic Microwave Background: Significance and Consequences for Cosmology
Multiple Peaks in the Angular Power Spectrum of the Cosmic Microwave Background: Signiﬁcance and Consequences for Cosmology arXiv:astro-ph/0105296 v1 17 May 2001 P. de Bernardis 1 , P.A.R. Ade 2 , J.J. Bock 3 , J.R. Bond 4 , J. Borrill 5 , A. Boscaleri 6 , K. Coble 7 , C.R. Contaldi 4 , B.P. Crill 8 , G. De Troia 1 , P. Farese 7 , K. Ganga 9 , M. Giacometti 1 , E. Hivon 9 , V.V. Hristov 8 , A. Iacoangeli 1 , A.H. Jaﬀe 10 , W.C. Jones 8 , A.E. Lange 8 , L. Martinis 11 , S. Masi 1 , P. Mason 8 , P.D. Mauskopf 12 , A. Melchiorri 13 , T. Montroy 7 , C.B. Netterﬁeld 14 , E. Pascale 6 , F. Piacentini 1 , D. Pogosyan 4 , G. Polenta 1 , F. Pongetti 15 , S. Prunet 4 , G. Romeo 15 , J.E. Ruhl 7 , F. Scaramuzzi 11 Dipartimento di Fisica, Universita’ La Sapienza, Roma, Italy Queen Mary and Westﬁeld College, London, UK Jet Propulsion Laboratory, Pasadena, CA, USA Canadian Institute for Theoretical Astrophysics, University of Toronto, Canada National Energy Research Scientiﬁc Computing Center, LBNL, Berkeley, CA, USA IROE-CNR, Firenze, Italy Dept. of Physics, Univ. of California, Santa Barbara, CA, USA California Institute of Technology, Pasadena, CA, USA IPAC, California Institute of Technology, Pasadena, CA, USA Department of Astronomy, Space Sciences Lab and Center for Particle Astrophysics, University of CA, Berkeley, CA 94720 USA ENEA, Frascati, Italy Dept. of Physics and Astronomy, Cardiﬀ University, Cardiﬀ CF24 3YB, Wales, UK Nuclear and Astrophysics Laboratory, University of Oxford, Keble Road, Oxford, OX 3RH, UK Depts. of Physics and Astronomy, University of Toronto, Canada Istituto Nazionale di Geoﬁsica, Roma, Italy ABSTRACT Three peaks and two dips have been detected in the power spectrum of the cosmic microwave background from the BOOMERANG experiment, at ∼ 210, 540, 840 and ∼ 420, 750, respec- tively. Using model-independent analyses, we ﬁnd that all ﬁve features are statistically signiﬁcant and we measure their location and amplitude. These are consistent with the adiabatic inﬂation- ary model. We also calculate the mean and variance of the peak and dip locations and amplitudes in a large 7-dimensional parameter space of such models, which gives good agreement with the model-independent estimates, and forecast where the next few peaks and dips should be found if the basic paradigm is correct. We test the robustness of our results by comparing Bayesian marginalization techniques on this space with likelihood maximization techniques applied to a sec- ond 7-dimensional cosmological parameter space, using an independent computational pipeline, and ﬁnd excellent agreement: Ω tot = 1.02 +0.06 vs. 1.04±0.05, Ω b h 2 = 0.022 −0.003 vs. 0.019 +0.005 , and n s = 0.96 −0.09 vs. 0.90±0.08. The deviation in primordial spectral index n s is a consequence of the strong correlation with the optical depth. Subject headings: Cosmic Microwave Background Anisotropy, Cosmology
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.
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.
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.
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.
44838446
Renormalization of the Higgs model: Minimizers, propagators and the stability of mean field theory
We study the effective actionsS(k) obtained byk iterations of a renormalization transformation of the U(1) Higgs model ind=2 or 3 spacetime dimensions. We identify a quadratic approximationSQ(k) toS(k) which we call mean field theory, and which will serve as the starting point for a convergent expansion of the Green's functions, uniformly in the lattice spacing. Here we show how the approximationsSQ(k) arise and how to handle gauge fixing, necessary for the analysis of the continuum limit. We also establish stability bounds onSQ(k), uniformly ink. This is an essential step toward proving the existence of a gap in the mass spectrum and exponential decay of gauge invariant correlations.
119588441
Response to comments on ``Theoretical Mathematics''
The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].
119453045
Quantum Physics: A Functional Integral Point of View
This book is addressed to one problem and to three audiences. The problem is the mathematical structure of modem physics: statistical physics, quantum mechanics, and quantum fields. The unity of mathemati cal structure for problems of diverse origin in physics should be no surprise. For classical physics it is provided, for example, by a common mathematical formalism based on the wave equation and Laplace's equation. The unity transcends mathematical structure and encompasses basic phenomena as well. Thus particle physicists, nuclear physicists, and con densed matter physicists have considered similar scientific problems from complementary points of view. The mathematical structure presented here can be described in various terms: partial differential equations in an infinite number of independent variables, linear operators on infinite dimensional spaces, or probability theory and analysis over function spaces. This mathematical structure of quantization is a generalization of the theory of partial differential equa tions, very much as the latter generalizes the theory of ordinary differential equations. Our central theme is the quantization of a nonlinear partial differential equation and the physics of systems with an infinite number of degrees of freedom. Mathematicians, theoretical physicists, and specialists in mathematical physics are the three audiences to which the book is addressed. Each of the three parts is written with a different scientific perspective."
117975725
Particles and bound states and progress toward unitarity and scaling