A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope

We present a measurement of the angular power spectrum of the cosmic microwave background (CMB) using data from the South Pole Telescope (SPT). The data consist of 790 deg^2 of sky observed at 150 GHz during 2008 and 2009. Here we present the power spectrum over the multipole range 650 < ℓ < 3000, where it is dominated by primary CMB anisotropy. We combine this power spectrum with the power spectra from the seven-year Wilkinson Microwave Anisotropy Probe (WMAP) data release to constrain cosmological models. We find that the SPT and WMAP data are consistent with each other and, when combined, are well fit by a spatially flat, ΛCDM cosmological model. The SPT+WMAP constraint on the spectral index of scalar fluctuations is n_s = 0.9663 ± 0.0112. We detect, at ~5σ significance, the effect of gravitational lensing on the CMB power spectrum, and find its amplitude to be consistent with the ΛCDM cosmological model. We explore a number of extensions beyond the ΛCDM model. Each extension is tested independently, although there are degeneracies between some of the extension parameters. We constrain the tensor-to-scalar ratio to be r < 0.21 (95% CL) and constrain the running of the scalar spectral index to be dn_s /dln k = –0.024 ± 0.013. We strongly detect the effects of primordial helium and neutrinos on the CMB; a model without helium is rejected at 7.7σ, while a model without neutrinos is rejected at 7.5σ. The primordial helium abundance is measured to be Y_p = 0.296 ± 0.030, and the effective number of relativistic species is measured to be N_eff = 3.85 ± 0.62. The constraints on these models are strengthened when the CMB data are combined with measurements of the Hubble constant and the baryon acoustic oscillation feature. Notable improvements include ns = 0.9668 ± 0.0093, r < 0.17 (95% CL), and N_eff = 3.86 ± 0.42. The SPT+WMAP data show a mild preference for low power in the CMB damping tail, and while this preference may be accommodated by models that have a negative spectral running, a high primordial helium abundance, or a high effective number of relativistic species, such models are disfavored by the abundance of low-redshift galaxy clusters

A note on the field of decision analysis

This note provides a short overview of some history, context and concepts in the field of decision analysis. In particular, we describe the connection between normative, prescriptive and descriptive decision theory, and the connection between several different approaches to value and utility

How Massless Neutrinos Affect the Cosmic Microwave Background Damping Tail

We explore the physical origin and robustness of constraints on the energy density in relativistic species prior to and during recombination, often expressed as constraints on an effective number of neutrino species, Neff. Constraints from current data combination of Wilkinson Microwave Anisotropy Probe (WMAP) and South Pole Telescope (SPT) are almost entirely due to the impact of the neutrinos on the expansion rate, and how those changes to the expansion rate alter the ratio of the photon diffusion scale to the sound horizon scale at recombination. We demonstrate that very little of the constraining power comes from the early Integrated Sachs-Wolfe (ISW) effect, and also provide a first determination of the amplitude of the early ISW effect. Varying the fraction of baryonic mass in Helium, Yp, also changes the ratio of damping to sound-horizon scales. We discuss the physical effects that prevent the resulting near-degeneracy between Neff and Yp from being a complete one. Examining light element abundance measurements, we see no significant evidence for evolution of Neff and the baryon-to-photon ratio from the epoch of big bang nucleosynthesis to decoupling. Finally, we consider measurements of the distance-redshift relation at low to intermediate redshifts and their implications for the value of Neff.Comment: 11 pages. Replaced version extends our discussion of origin of constraints and updates for current data, submitted to PR

An assessment of prewhitening in estimating power spectra of atmospheric turbulence at long wavelengths

Synthetic time histories were generated and used to assess the effects of prewhitening on the long wavelength portion of power spectra of atmospheric turbulence. Prewhitening is not recommended when using the narrow spectral windows required for determining power spectral estimates below the 'knee' frequency, that is, at very long wavelengths

Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data

We present a measurement of the B-mode polarization power spectrum (the BB spectrum) from 100 deg^2 of sky observed with SPTpol, a polarization-sensitive receiver currently installed on the South Pole Telescope. The observations used in this work were taken during 2012 and early 2013 and include data in spectral bands centered at 95 and 150 GHz. We report the BB spectrum in five bins in multipole space, spanning the range 300 ≤ ℓ ≤ 2300, and for three spectral combinations: 95 GHz × 95 GHz, 95 GHz × 150 GHz, and 150 GHz × 150 GHz. We subtract small (<0.5σ in units of statistical uncertainty) biases from these spectra and account for the uncertainty in those biases. The resulting power spectra are inconsistent with zero power but consistent with predictions for the BB spectrum arising from the gravitational lensing of E-mode polarization. If we assume no other source of BB power besides lensed B modes, we determine a preference for lensed B modes of 4.9σ. After marginalizing over tensor power and foregrounds, namely, polarized emission from galactic dust and extragalactic sources, this significance is 4.3σ. Fitting for a single parameter, A_(lens), that multiplies the predicted lensed B-mode spectrum, and marginalizing over tensor power and foregrounds, we find A_(lens) = 1.08 ± 0.26, indicating that our measured spectra are consistent with the signal expected from gravitational lensing. The data presented here provide the best measurement to date of the B-mode power spectrum on these angular scales

Beginning of stability theory for Polish Spaces

We consider stability theory for Polish spaces and more generally for definable structures. We succeed to prove existence of indiscernibles under reasonable conditions

A cohort study of the associations between udder conformation, milk somatic cell count, and lamb weight in suckler ewes

A cohort study of 67 suckler ewes from 1 farm was carried out from January to May 2010 to investigate associations between udder conformation, udder half milk somatic cell count (SCC), and lamb weight. Ewes and lambs were observed at lambing. Ewe health and teat condition and lamb health and weight were recorded on 4 to 5 further occasions at 14-d intervals. At each observation, a milk sample was collected from each udder half for somatic cell counting. Two weeks after lambing, ewe udder conformation and teat placement were scored. Low lamb weight was associated with ewe SCC >400,000 cells/mL (−0.73kg), a new teat lesion 14 d previously (−0.91kg), suboptimal teat position (−1.38kg), rearing in a multiple litter (−1.45kg), presence of diarrhea at the examination (−1.19kg), and rearing by a 9-yr-old ewe compared with a 6-yr-old ewe (−2.36kg). High lamb weight was associated with increasing lamb age (0.21kg/d), increasing birth weight (1.65kg/kg at birth), and increasing number of days the ewe was given supplementary feed before lambing (0.06kg/d). High udder half SCC was associated with pendulous udders (9.6% increase in SCC/cm of drop) and greater total cross-sectional area of the teats (7.2% increase of SCC/cm2). Low SCC were associated with a heavier mean litter weight (6.7% decrease in SCC/kg). Linear, quadratic, and cubic terms for days in lactation were also significant. We conclude that poor udder and teat conformation are associated with high levels of intramammary infection, as indicated by increased SCC and that both physical attributes of the udder and SCC are linked to lamb growth, suggesting that selection of suckler ewes with better udder and teat conformation would reduce intramammary infection and increase lamb growth rate

On theories of random variables

We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type