16153057
Minimal microwave anisotrophy from perturbations induced at late times
Aside from primordial gravitational instability of the cosmological fluid, various mechanisms have been proposed to generate large-scale structure at relatively late times, including, e.g., 'late-time' cosmological phase transitions. In these scenarios, it is envisioned that the universe is nearly homogeneous at the times of last scattering and that perturbations grow rapidly sometimes after the primordial plasma recombines. On this basis, it was suggested that large inhomogeneities could be generated while leaving relatively little imprint on the cosmic microwave background (MBR) anisotropy. In this paper, we calculate the minimal anisotropies possible in any 'late-time' scenario for structure formation, given the level of inhomogeneity observed at present. Since the growth of the inhomogeneity involves time-varying gravitational fields, these scenarios inevitably generate significant MBR anisotropy via the Sachs-Wolfe effect. Moreover, we show that the large-angle MBR anisotropy produced by the rapid post-recombination growth of inhomogeneity is generally greater than that produced by the same inhomogeneity growth via gravitational instability. In 'realistic' scenarios one can decrease the anisotropy compared to models with primordial adiabatic fluctuations, but only on very small angular scales. The value of any particular measure of the anisotropy can be made small in late-time models, but only by making the time-dependence of the gravitational field sufficiently 'pathological'.
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.
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.
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.
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.
118116787
Boson Quantum Field Models
Quantum fields, from a mathematical point of view, are highly singular. These fields are believed to describe the interactions of elementary particles. For the interaction of electrons with light (photons), the quantum field description is exact within the limits of experimental accuracy (5 significant figures). For these reasons, i.e. the mathematical difficulties and the importance to physics, the problem of formulating the mathematical foundations of quantum field theory has attracted the attention of both mathematicians and physicists over a period of several decades. On the side of the physicists, the most striking achievements were the calculation in the late 1940’s and early 1950’s of the Lamb shift and the anomalous magnetic moment of the electron together with the development of the renormalization method on which these calculations were based. Of the mathematicians, J. von Neumann was the first to realize that new mathematical theories would be required to formulate quantum field theory correctly and this realization was one of the motives for developing the theory of operator algebras.
121716582
A priori estimates forN=2 Wess-Zumino models on a cylinder
We establish bounds uniform in the ultraviolet cutoff (i.e., in the number of degrees of freedom) for a family of two-dimensional Wess-Zumino models. These estimates are useful in proving existence of the models, as well as in investigating their properties. For example, we require these estimates for the analysis of the supercharge and of the Hamiltonian. These are the fundamental a priori estimates for elliptic regularity in infinite dimensions.
118881742
Constructive Field Theory, Phase II
It now appears possible to study a realm of problems in CFT which, two years ago, appeared an order of magnitude too difficult to tackle. The finishing touches have just been put on the first paper of this sort1, and in this talk I will describe some of the basic ideas; these ideas are simple, although the details of the paper are complicated. The main question that I will discuss today has been around as long as field theory: Namely how does an interacting field model react to perturbations by an external source? Such perturbations of \(\textup{P}\left (\phi \right )_{2}\), or in fact any reasonable local perturbations of the \(\textup{P}\left (\phi \right )_{2}\) model, have been shown to be regular by James Glimm and myself1. As a consequence, (i) further properties of the original model have been established1, (ii) some new breakthroughs are being made2 and (iii) these methods appear promising for use in the study of more singular models than \(\textup{P}\left (\phi \right )_{2}\).
121389988
Whither Axiomatic Field Theory
120735488
A priori quantum field equations
We study the fields cp and $ in a class of finite quantum field models on the cylindrical space-time S’ x Iw. We show that cp and II, satisfy a system of local, nonlinear partial differential equations. These are just the equations of evolution for the critical points of the corresponding action functional. c 1989 Academic Press, Inc.