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

Hypernatural Numbers as Ultrafilters

In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers

Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data

We present measurements of the $E$-mode polarization angular auto-power spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) of the cosmic microwave background (CMB) using 150 GHz data from three seasons of SPTpol observations. We report the power spectra over the spherical harmonic multipole range $50 < \ell \leq 8000$, and detect nine acoustic peaks in the $EE$ spectrum with high signal-to-noise ratio. These measurements are the most sensitive to date of the $EE$ and $TE$ power spectra at $\ell > 1050$ and $\ell > 1475$, respectively. The observations cover 500 deg$^2$, a fivefold increase in area compared to previous SPTpol analyses, which increases our sensitivity to the photon diffusion damping tail of the CMB power spectra enabling tighter constraints on \LCDM model extensions. After masking all sources with unpolarized flux $>50$ mJy we place a 95% confidence upper limit on residual polarized point-source power of $D_\ell = \ell(\ell+1)C_\ell/2\pi <0.107\,\mu{\rm K}^2$ at $\ell=3000$, suggesting that the $EE$ damping tail dominates foregrounds to at least $\ell = 4050$ with modest source masking. We find that the SPTpol dataset is in mild tension with the $\Lambda CDM$ model ($2.1\,\sigma$), and different data splits prefer parameter values that differ at the $\sim 1\,\sigma$ level. When fitting SPTpol data at $\ell < 1000$ we find cosmological parameter constraints consistent with those for $Planck$ temperature. Including SPTpol data at $\ell > 1000$ results in a preference for a higher value of the expansion rate (H_0 = 71.3 \pm 2.1\,\mbox{km}\,s^{-1}\mbox{Mpc}^{-1} ) and a lower value for present-day density fluctuations ($\sigma_8 = 0.77 \pm 0.02$).Comment: Updated to match version accepted to ApJ. 34 pages, 17 figures, 6 table

Performance and on-sky optical characterization of the SPTpol instrument

In January 2012, the 10m South Pole Telescope (SPT) was equipped with a polarization-sensitive camera, SPTpol, in order to measure the polarization anisotropy of the cosmic microwave background (CMB). Measurements of the polarization of the CMB at small angular scales (~several arcminutes) can detect the gravitational lensing of the CMB by large scale structure and constrain the sum of the neutrino masses. At large angular scales (~few degrees) CMB measurements can constrain the energy scale of Inflation. SPTpol is a two-color mm-wave camera that consists of 180 polarimeters at 90 GHz and 588 polarimeters at 150 GHz, with each polarimeter consisting of a dual transition edge sensor (TES) bolometers. The full complement of 150 GHz detectors consists of 7 arrays of 84 ortho-mode transducers (OMTs) that are stripline coupled to two TES detectors per OMT, developed by the TRUCE collaboration and fabricated at NIST. Each 90 GHz pixel consists of two antenna-coupled absorbers coupled to two TES detectors, developed with Argonne National Labs. The 1536 total detectors are read out with digital frequency-domain multiplexing (DfMUX). The SPTpol deployment represents the first on-sky tests of both of these detector technologies, and is one of the first deployed instruments using DfMUX readout technology. We present the details of the design, commissioning, deployment, on-sky optical characterization and detector performance of the complete SPTpol focal plane.Comment: 15 pages, 6 figures. Conference: SPIE Astronomical Telescopes and Instrumentation 201

Detection of B-mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope

Gravitational lensing of the cosmic microwave background generates a curl pattern in the observed polarization. This "B-mode" signal provides a measure of the projected mass distribution over the entire observable Universe and also acts as a contaminant for the measurement of primordial gravity-wave signals. In this Letter we present the first detection of gravitational lensing B modes, using first-season data from the polarization-sensitive receiver on the South Pole Telescope (SPTpol). We construct a template for the lensing B-mode signal by combining E-mode polarization measured by SPTpol with estimates of the lensing potential from a Herschel-SPIRE map of the cosmic infrared background. We compare this template to the B modes measured directly by SPTpol, finding a non-zero correlation at 7.7 sigma significance. The correlation has an amplitude and scale-dependence consistent with theoretical expectations, is robust with respect to analysis choices, and constitutes the first measurement of a powerful cosmological observable.Comment: Two additional null tests, matches version published in PR

A Measurement of the Cosmic Microwave Background Gravitational Lensing Potential from 100 Square Degrees of SPTpol Data

We present a measurement of the cosmic microwave background (CMB) gravitational lensing potential using data from the first two seasons of observations with SPTpol, the polarization-sensitive receiver currently installed on the South Pole Telescope (SPT). The observations used in this work cover 100 deg$^2$ of sky with arcminute resolution at 150 GHz. Using a quadratic estimator, we make maps of the CMB lensing potential from combinations of CMB temperature and polarization maps. We combine these lensing potential maps to form a minimum-variance (MV) map. The lensing potential is measured with a signal-to-noise ratio of greater than one for angular multipoles between $100< L <250$. This is the highest signal-to-noise mass map made from the CMB to date and will be powerful in cross-correlation with other tracers of large-scale structure. We calculate the power spectrum of the lensing potential for each estimator, and we report the value of the MV power spectrum between $100< L <2000$ as our primary result. We constrain the ratio of the spectrum to a fiducial $\Lambda$CDM model to be $A_{\rm MV}=0.92 \pm 0.14 {\rm\, (Stat.)} \pm 0.08 {\rm\, (Sys.)}$. Restricting ourselves to polarized data only, we find $A_{\rm POL}=0.92 \pm 0.24 {\rm\, (Stat.)} \pm 0.11 {\rm\, (Sys.)}$. This measurement rejects the hypothesis of no lensing at $5.9 \sigma$ using polarization data alone, and at $14 \sigma$ using both temperature and polarization data.Comment: 16 pages, 8 figure

Mass Calibration and Cosmological Analysis of the SPT-SZ Galaxy Cluster Sample Using Velocity Dispersion σv\sigma_v and X-ray YXY_\textrm{X} Measurements

We present a velocity dispersion-based mass calibration of the South Pole Telescope Sunyaev-Zel'dovich effect survey (SPT-SZ) galaxy cluster sample. Using a homogeneously selected sample of 100 cluster candidates from 720 deg2 of the survey along with 63 velocity dispersion ($\sigma_v$) and 16 X-ray Yx measurements of sample clusters, we simultaneously calibrate the mass-observable relation and constrain cosmological parameters. The calibrations using $\sigma_v$ and Yx are consistent at the $0.6\sigma$ level, with the $\sigma_v$ calibration preferring ~16% higher masses. We use the full cluster dataset to measure $\sigma_8(\Omega_ m/0.27)^{0.3}=0.809\pm0.036$. The SPT cluster abundance is lower than preferred by either the WMAP9 or Planck+WMAP9 polarization (WP) data, but assuming the sum of the neutrino masses is $\sum m_\nu=0.06$ eV, we find the datasets to be consistent at the 1.0$\sigma$ level for WMAP9 and 1.5$\sigma$ for Planck+WP. Allowing for larger $\sum m_\nu$ further reconciles the results. When we combine the cluster and Planck+WP datasets with BAO and SNIa, the preferred cluster masses are $1.9\sigma$ higher than the Yx calibration and $0.8\sigma$ higher than the $\sigma_v$ calibration. Given the scale of these shifts (~44% and ~23% in mass, respectively), we execute a goodness of fit test; it reveals no tension, indicating that the best-fit model provides an adequate description of the data. Using the multi-probe dataset, we measure $\Omega_ m=0.299\pm0.009$ and $\sigma_8=0.829\pm0.011$. Within a $\nu$CDM model we find $\sum m_\nu = 0.148\pm0.081$ eV. We present a consistency test of the cosmic growth rate. Allowing both the growth index $\gamma$ and the dark energy equation of state parameter $w$ to vary, we find $\gamma=0.73\pm0.28$ and $w=-1.007\pm0.065$, demonstrating that the expansion and the growth histories are consistent with a LCDM model ($\gamma=0.55; \,w=-1$).Comment: Accepted by ApJ (v2 is accepted version); 17 pages, 6 figure

South Pole Telescope Software Systems: Control, Monitoring, and Data Acquisition

We present the software system used to control and operate the South Pole Telescope. The South Pole Telescope is a 10-meter millimeter-wavelength telescope designed to measure anisotropies in the cosmic microwave background (CMB) at arcminute angular resolution. In the austral summer of 2011/12, the SPT was equipped with a new polarization-sensitive camera, which consists of 1536 transition-edge sensor bolometers. The bolometers are read out using 36 independent digital frequency multiplexing (\dfmux) readout boards, each with its own embedded processors. These autonomous boards control and read out data from the focal plane with on-board software and firmware. An overall control software system running on a separate control computer controls the \dfmux boards, the cryostat and all other aspects of telescope operation. This control software collects and monitors data in real-time, and stores the data to disk for transfer to the United States for analysis

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 $\mathrm{deg}^2$ 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 $300 \le \ell \le 2300$, and for three spectral combinations: 95 GHz $\times$ 95 GHz, 95 GHz $\times$ 150 GHz, and 150 GHz $\times$ 150 GHz. We subtract small ($< 0.5 \sigma$ 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 $4.9 \sigma$. After marginalizing over tensor power and foregrounds, namely polarized emission from galactic dust and extragalactic sources, this significance is $4.3 \sigma$. Fitting for a single parameter, $A_\mathrm{lens}$, that multiplies the predicted lensed $B$-mode spectrum, and marginalizing over tensor power and foregrounds, we find $A_\mathrm{lens} = 1.08 \pm 0.26$, 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.Comment: 21 pages, 4 figure