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.
118090873
Cosmological parameters from the first results of Boomerang
The anisotropy of the cosmic microwave background radiation contains information about the contents and history of the universe. We report new limits on cosmological parameters derived from the angular power spectrum measured in the first Antarctic flight of the Boomerang experiment. Within the framework of models with adiabatic perturbations, and using only weakly restrictive prior probabilities on the age of the universe and the Hubble expansion parameter h, we find that the curvature is consistent with flat and that the primordial fluctuation spectrum is consistent with scale invariant, in agreement with the basic inflation paradigm. We find that the data prefer a baryon density Ωbh2 above, though similar to, the estimates from light element abundances and big bang nucleosynthesis. When combined with large scale structure observations, the Boomerang data provide clear detections of both dark matter and dark energy contributions to the total energy density Ωtot, independent of data from high-redshift supernovae.
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
2973336
RADICAL COMPRESSION OF COSMIC MICROWAVE BACKGROUND DATA
Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with 104 pixels. We present a method for approximating the likelihood that takes power spectrum constraints, e.g., "band-powers," as inputs. We identify a bias which results if one approximates the probability distribution of the band-power errors as Gaussian—as is the usual practice. This bias can be eliminated by using specific approximations to the non-Gaussian form for the distribution specified by three parameters (the maximum likelihood or mode, curvature or variance, and a third quantity). We advocate the calculation of this third quantity by experimenters, to be presented along with the maximum-likelihood band-power and variance. We use this non-Gaussian form to estimate the power spectrum of the CMB in 11 bands from multipole moment l = 2 (the quadrupole) to l = 3000 from all published band-power data. We investigate the robustness of our power spectrum estimate to changes in these approximations as well as to selective editing of the data.
119280456
Planck 2013 results. III. LFI systematic uncertainties
We present the current accounting of systematic effect uncertainties for the Low Frequency Instrument (LFI) that are relevant to the 2015 release of the Planck cosmological results, showing the robustness and consistency of our data set, especially for polarization analysis. We use two complementary approaches: (i) simulations based on measured data and physical models of the known systematic effects; and (ii) analysis of difference maps containing the same sky signal (“null-maps”). The LFI temperature data are limited by instrumental noise. At large angular scales the systematic effects are below the cosmic microwave background (CMB) temperature power spectrum by several orders of magnitude. In polarization the systematic uncertainties are dominated by calibration uncertainties and compete with the CMB E-modes in the multipole range 10–20. Based on our model of all known systematic effects, we show that these effects introduce a slight bias of around 0.2σ on the reionization optical depth derived from the 70GHz EE spectrum using the 30 and 353GHz channels as foreground templates. At 30GHz the systematic effects are smaller than the Galactic foreground at all scales in temperature and polarization, which allows us to consider this channel as a reliable template of synchrotron emission. We assess the residual uncertainties due to LFI effects on CMB maps and power spectra after component separation and show that these effects are smaller than the CMB amplitude at all scales. We also assess the impact on non-Gaussianity studies and find it to be negligible. Some residuals still appear in null maps from particular sky survey pairs, particularly at 30 GHz, suggesting possible straylight contamination due to an imperfect knowledge of the beam far sidelobes.
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.
123457713
SUPERSYMMETRIC QUANTUM FIELDS AND INFINITE DIMENSIONAL ANALYSIS
Supersymmetric quantum fields are interesting from the point of view both of physics and of mathematics. Their interest for physics (see, e g. [35]) stems primarily from the fact that they may provide a natural framework for a unified theory of elementary interactions. In particular, recent developments in superstring theory [15] suggest that such a theory has the potential to unify gravitational forces with the strong, weak and electromagnetic forces.
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.
122859727
Charges, vortices and confinement
Abstract We study the confinement phase transition. We point out the relation between the decay rates of the Wilson loop integral, Osterwalder and Seiler's n -ality restriction, and Polyakov and 't Hooft's analysis of the center of the gauge group. Vortices and merons are analyzed as possible mechanisms to produce disorder in the center. We show how to realize the 't Hooft commutation relations, and we estimate the critical coupling for vortices to be in approximate agreement with the critical coupling determined by Callan, Dashen and Gross from the analysis of instantons.
13103184
An Exchange Identity for Non-linear Fields
We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.
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.