14214545
Predicting and analyzing topological correlations in the CMB
The Cosmic Microwave Background (CMB) power spectrum derived from the first year WMAP data demonstrates an intriguing lack of power at large scales that cannot be accounted for within the framework of the standard cosmological model. We explore the possibility that this anomaly could be explained by waiving the implicit assumption of a simply connected topology, rather than modifying the physics of the standard model. In particular, we assume that the Universe is slightly closed and its spatial section can be described by one of the simplest spherical multi‐connected manifolds (the quaternionic, the octahedral, the truncated cube and the Poincare space). We discuss the implications for the CMB in each case.
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.
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.
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.
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.
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.
124739574
Critical point dominance in quantum field models
6478419
“Theoretical mathematics”: toward a cultural synthesis of mathematics and theoretical physics
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and destructive consequences. Serious caution is required, and the issue should be considered before, rather than after, obvious damage occurs. With the hazards carefully in mind, we propose a framework that should allow a healthy and positive role for speculation
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.
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].
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.