1392831
Nonlinear Effects in the Amplitude of Cosmological Density Fluctuations
The amplitude of cosmological density fluctuations, sigma_8, has been studied and estimated by analysing many cosmological observations. The values of the estimates vary considerably between the various probes. However, different estimators probe the value of sigma_8 in different cosmological scales and do not take into account the nonlinear evolution of the parameter at late times. We show that estimates of the amplitude of cosmological density fluctuations derived from cosmic flows are systematically higher than those inferred at early epochs from the CMB because of nonlinear evolution at later times. We discuss the past and future evolution of linear and nonlinear perturbations, derive corrections to the value of sigma_8 and compare amplitudes after accounting for these differences.
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.
15450342
THE ANGULAR THREE-POINT CORRELATION FUNCTION IN THE QUASI-LINEAR REGIME
We calculate the normalized angular three-point correlation function (3PCF), q, as well as the normalized angular skewness, s{sub 3}, assuming the small-angle approximation, for a biased mass distribution in flat and open cold dark matter (CDM) models with Gaussian initial conditions. The leading-order perturbative results incorporate the explicit dependence on the cosmological parameters, the shape of the CDM transfer function, the linear evolution of the power spectrum, the form of the assumed redshift distribution function, and linear and nonlinear biasing, which may be evolving. Results are presented for different redshift distributions, including that appropriate for the APM Galaxy Survey, as well as for a survey with a mean redshift of z{approx_equal}1 (such as the VLA FIRST Survey). Qualitatively, many of the results found for s{sub 3} and q are similar to those obtained in a related treatment of the spatial skewness and 3PCF, such as a leading-order correction to the standard result for s{sub 3} in the case of nonlinear bias (as defined for unsmoothed density fields), and the sensitivity of the configuration dependence of q to both cosmological and biasing models. We show that since angular correlation functions (CFs) are sensitive to clustering over a range of redshifts, themore » various evolutionary dependences included in our predictions imply that measurements of q in a deep survey might better discriminate between models with different histories, such as evolving versus nonevolving bias, that can have similar spatial CFs at low redshift. Our calculations employ a derived equation, valid for open, closed, and flat models, to obtain the angular bispectrum from the spatial bispectrum in the small-angle approximation. (c) (c) 2000. The American Astronomical Society.« less
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.
123628830
The holonomy expansion: Invariants and approximate supersymmetry
Abstract In this paper we give a new expansion, based on cyclicity of the trace, to study regularity properties of twisted expectations 〈 X ( s )〉=Tr H ( γU ( θ )  X ( s )). Here X ( s )= X 0 e − s 0 Q 2 X 1 e − s 1 Q 2 … X k e − s k Q 2 is a product of operators X j , regularized by heat kernels e − s j Q 2 with s j >0. The twist groups γ ∈ Z 2 and U ( θ )∈ U (1) are commuting symmetries of Q 2 . The name “holonomy expansion” arises from picturing 〈 X ( s )〉 as a circular graph, with vertices in the graph representing the operators X j , in the order that they appear in the product, and the linesegment following X j representing the heat kernel e − s j Q 2 . The trace functional is cyclic, so the graph is circular. We generate our expansion by “transporting” a vertex X k around the circle, ending in its original position. We choose an X k that transforms under a one-dimensional representation of Z 2 × U (1). For θ in the complement of the discrete set ϒ sing (where the group Z 2 × U (1) acts trivially on X k ) we obtain an identity between the original expectation and some new expectations. We study an example from supersymmetric quantum mechanics, with a Dirac operator Q ( λ ) depending on a parameter λ and with a U (1) group of symmetries U ( θ ). We apply our expansion to invariants Z ( λ ;  θ )= Z ( Q ( λ );  θ ) suggested by non-commutative geometry. These invariants are sums of expectations of the form above. We investigate this example as a first step toward developing an expansion to evaluate related invariants arising in supersymmetric quantum field theory. We establish differentiability of Z ( λ ; ,  θ ) in λ for λ ∈(0, 1] and show Z ( λ ;  θ ) is independent of λ . We wish to evaluate Z ( λ ;  θ ) at the endpoint λ =0, but Z (0;  θ ) is ill-defined. We regularize the endpoint, while preserving the U ( θ )-symmetry, by replacing Q ( λ ) 2 with H ( e ,  λ )= Q ( λ ) 2 + e 2  | z | 2 . The regularized function Z ( e ,  λ ;  θ ) depends on all three variables e , λ , θ ; for fixed θ , it is differentiable in the unit ( e ,  λ ) square, except at the origin. Using the holonomy expansion, we prove for fixed θ ∉ ϒ sing that Z ( e ,  λ ;  θ ) is also jointly continuous in ( e ,  λ ), at the origin. As a consequence, if θ ∉ ϒ sing , then we can interchange limits and Z ( λ ;  θ )=lim e →0 Z ( e , 0;  θ ). We observe that the joint continuity of Z ( e ,  λ ;  θ ) in ( e ,  λ ) is not uniform in θ , and Z ( e ,  λ ;  θ ) is not jointly continuous for θ ∈ ϒ sing . But the limiting function Z ( λ ;  θ ) is continuous in θ ; so the e -limit also determines Z ( λ ;  θ ) for all θ , including for θ ∈ ϒ sing . We use these facts to calculate Z ( λ ;  θ ). Our regularization destroys supersymmetry, but the holonomy expansion gives quantitative bounds on the error terms.
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.
124739574
Critical point dominance in quantum field models
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.
58901623
Representations of the Heisenberg algebra on a Riemann surface
We formulate reflection positivity for meromorphic functions and for 1-forms on a Riemann surface. This construction yields representations of the Heisenberg algebra on a Riemann surface.