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.
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.
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.
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
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.
16492814
CONSTRUCTIVE QUANTUM FIELD THEORY
The pioneering work of early non-relativistic quantum theory led to the understanding that quantum dynamics on Hilbert space is a comprehensive predictive framework for microscopic phenomena. From the Bohr atom, through the nonrelativistic quantum theory of Schrödinger and Heisenberg, and the relativistic Dirac equation for hydrogen, agreement between calculation and experiment improved rapidly over time. The incorporation of special relativity and field theory into quantum theory extended the scope of perturbative calculations, and these were tested through precision measurements of spectra and magnetic moments. Beginning in the 1940’s, experimental tests of the Lamb shift and the anomalous magnetic moment of the electron detected effects that one can ascribe to fluctuations in quantum electrodynamics. These effects deviated numerically from the predictions arising from equations that describe a fixed number of particles, so they were accurate tests of the quantum field hypothesis. Today these experiments have evolved to yield quantitative agreement with the most precise observations and calculations achieved in physics. For example, the anomalous magnetic moment of the electron is known theoretically and experimentally to amazing precision: (g − 2)/2 = 0.001159652200(±40). The success of this work, as well as the success of other less accurate, but compelling, predictions for weak and strong interactions, convince us to accept quantum field theory as the correct physical arena to describe particle physics down to the Planck scale. But the success of relativistic field theory calculations and of perturbative renormalization also led to a logical puzzle: is there any physically-relevant, relativistic quantum field theory that is also mathematically consistent? Put differently, can one give a mathematically complete example of any non-linear theory, relevant for the description of interacting particles, whose solutions incorporate relativistic covariance, positive energy, and causality? One must understand perturbative renormalization in order to resolve this problem, and have control over renormalization from a non-perturbative (or “exact”) point of view. In fact, one needs to overcome sophisticated problems, such as whether a field theory may appear correct on a perturbative level, while it may have no meaning at a non-perturbative level. Doubts about quantum electrodynamics or scalar meson theory were raised early by Dyson and Landau. They recur from the point of view of the renormalization group in the work of Kadanoff and Wilson, as well as in the analysis of “asymptotic
120285803
Effective action and cluster properties of the abelian Higgs model
We continue our program to establish the Higgs mechanism and mass gap for the abelian Higgs model in two and three dimensions. We develop a multiscale cluster expansion for the high frequency modes of the theory, within a framework of iterated renormalization group transformations. The expansions yield decoupling properties needed for a proof of exponential decay of correlations. The result of this analysis is a gauge invariant unit lattice theory with a deep Higgs potential of the shape required to exhibit the Higgs mechanism.
119621087
Quantum Harmonic Analysis and Geometric Invariants
We develop two topics in parallel and show their inter-relation. The first centers on the notion of a fractional-differentiable structure on a commutative or a non-commutative space. We call this studyquantum harmonic analysis. The second concerns homotopy invariants for these spaces and is an aspect of non-commutative geometry. We study an algebra A, which will be a Banach algebra with unit, represented as an algebra of operators on a Hilbert space H. In order to obtain a geometric interpretation of A, we define a derivative on elements of A. We do this in a Hilbert space context, takingdaas a commutatorda=[Q, a]. HereQis a basic self-adjoint operator with discrete spectrum, increasing sufficiently rapidly that exp(−βQ)2has a trace wheneverβ>0. We can define fractional differentiability of orderμ, with 0 0. We concentrate on subalgebras A of Jβ, αwhich have certain additional covariance properties under a group Z2×G acting on H by a unitary representationγ×U(g). In addition, the derivativeQis assumed to be G-invariant. The geometric interpretation flows from the assumption that elements of A possess an arbitrarily small fractional derivative. We study homotopy invariants of A in terms of equivariant, entire cyclic cohomology. In fact, the existence of a fractional derivative on A allows the construction of the cochainτJLO, which plays the role of the integral of differential forms. We give a simple expression for a homotopy invariant ZQ(a; g), determined by pairingτJLO, with a G-invariant elementa∈A, such thatais a square root of the identity. This invariant is ZQ(a; g)=(1/π) ∫∞−∞ e−t2Tr(γU(g) ae−Q2+it da) dt. This representation of the pairing is reminiscent of the heat-kernel representation for an index. In fact this quantity is an invariant, in the following sense. We isolate a simple condition on a familyQ(λ) of differentiations that yields a continuously-differentiable familyτJLO(λ) of cochains. Since ZQ(a; g) need not be an integer, continuity ofτJLO(λ) inλis insufficient to prove the constancy of the pairing. However the existence of the derivative leads to the existence of the homotopy. As τ, a vanishes forτa coboundary, and asdτJLO(λ)/dλis a coboundary, our condition onQ(λ) ensures that ZQ(λ)(a; g) is independent ofλ. Hence it is a homotopy invariant. The theory of ZQ(a; g) reduces to the study of the Radon transform of sequences of certain functions. The fractional differentiability properties of elements of A translate into properties of the asymptotics of the sequences of Radon transforms. The condition thatτJLOfit into the framework of entire cyclic cohomology translates to the existence of some fractional derivative for functions in the algebra under study, and in particular the assumptionα+β<1. Thus the study of fractionally- differentiable structures dove-tails naturally with the theory of homotopy invariants. In our study of quantum harmonic analysis, we introduce spaces T(−β, α) of operator-valued distributions. These spaces are bounded, linear operators between Sobolev spaces. The elements of the interpolation spaces, the Banach algebras Jβ, αhave derivativesdawhich belong to the spaces T(−β, α). For a certain range ofβandα, we extend the theory of the Radon transform from products of regularized, bounded operators to products of regularized, operator-valued distributions. We sometimes wish to evaluate such an invariant at the endpoint of an interval such asλ∈(0, 1], where ZQ(λ)(a; g) becomes singular asλ→0. We discuss in brief a procedure to regularize the endpoint, and a method to recover ZQ(λ)(a; g) fully from certain partial information at the endpoint. Finally, we generalize this approach to cover the case whenQcan be split into the sum of “independent” partsQ1+Q2, such that (Q1+Q2)2=(Q1)2+(Q2)2. Here we assume thatQ1and (Q2)2are G-invariant, but not necessarilyQ2. With further assumptions ona, the most important being that (Q1)2−(Q2)2commutes witha, we obtain a modified formula for an invariant, namely Z{Qj}(a; g)=(1/π) ∫∞−∞ e−t2Tr(γU(g) ae−(Q21+Q22)/2+itd1a) dt.
115879784
Functional Integral Methods in Quantum Field Theory
We give a special form of the Osterwalder-Schrader axioms in terms of conditions on a functional integral S{f} = ∫eiϕ(f)dμ. This yields a simple, self-contained construction of a Hamiltonian H, a relativistic, local boson quantum field Φ, and a Feynman-Kac formula to study perturbations H + Φ of H.
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.