Randomizations of models as metric structures

The notion of a randomization of a first order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure whose elements are random elements of the original first order structure. In this paper we treat randomizations as continuous structures in the sense of Ben Yaacov and Usvyatsov. In this setting, the earlier results show that the randomization of a complete first order theory is a complete theory in continuous logic that admits elimination of quantifiers and has a natural set of axioms. We show that the randomization operation preserves the properties of being omega-categorical, omega-stable, and stable

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

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

Model selection applied to reconstruction of the Primordial Power Spectrum

The preferred shape for the primordial spectrum of curvature perturbations is determined by performing a Bayesian model selection analysis of cosmological observations. We first reconstruct the spectrum modelled as piecewise linear in \log k between nodes in k-space whose amplitudes and positions are allowed to vary. The number of nodes together with their positions are chosen by the Bayesian evidence, so that we can both determine the complexity supported by the data and locate any features present in the spectrum. In addition to the node-based reconstruction, we consider a set of parameterised models for the primordial spectrum: the standard power-law parameterisation, the spectrum produced from the Lasenby & Doran (LD) model and a simple variant parameterisation. By comparing the Bayesian evidence for different classes of spectra, we find the power-law parameterisation is significantly disfavoured by current cosmological observations, which show a preference for the LD model.Comment: Minor changes to match version accepted by JCA

Computing the Primordial Power Spectra Directly

The tree order power spectra of primordial inflation depend upon the norm-squared of mode functions which oscillate for early times and then freeze in to constant values. We derive simple differential equations for the power spectra, that avoid the need to numerically simulate the physically irrelevant phases of the mode functions. We also derive asymptotic expansions which should be valid until a few e-foldings before first horizon crossing, thereby avoiding the need to evolve mode functions from the ultraviolet over long periods of inflation.Comment: 11 pages, uses LaTex2

CMB photons shedding light on dark matter

The annihilation or decay of Dark Matter (DM) particles could affect the thermal history of the universe and leave an observable signature in Cosmic Microwave Background (CMB) anisotropies. We update constraints on the annihilation rate of DM particles in the smooth cosmological background, using WMAP7 and recent small-scale CMB data. With a systematic analysis based on the Press-Schechter formalism, we also show that DM annihilation in halos at small redshift may explain entirely the reionization patterns observed in the CMB, under reasonable assumptions concerning the concentration and formation redshift of halos. We find that a mixed reionization model based on DM annihilation in halos as well as star formation at a redshift z~6.5 could simultaneously account for CMB observations and satisfy constraints inferred from the Gunn-Peterson effect. However, these models tend to reheat the inter-galactic medium (IGM) well above observational bounds: by including a realistic prior on the IGM temperature at low redshift, we find stronger cosmological bounds on the annihilation cross-section than with the CMB alone.Comment: 35 pages, 14 figures; version accepted in JCAP after minor revision

Measuring primordial gravitational waves from CMB B-modes in cosmologies with generalized expansion histories

We evaluate our capability to constrain the abundance of primordial tensor perturbations in cosmologies with generalized expansion histories in the epoch of cosmic acceleration. Forthcoming satellite and sub-orbital experiments probing polarization in the CMB are expected to measure the B-mode power in CMB polarization, coming from PGWs on the degree scale, as well as gravitational lensing on arcmin scales; the latter is the main competitor for the measurement of PGWs, and is directly affected by the underlying expansion history, determined by the presence of a DE component. In particular, we consider early DE possible scenarios, in which the expansion history is substantially modified at the epoch in which the CMB lensing is most relevant. We show that the introduction of a parametrized DE may induce a variation as large as 30% in the ratio of the power of lensing and PGWs on the degree scale. We find that adopting the nominal specifications of upcoming satellite measurements the constraining power on PGWs is weakened by the inclusion of the extra degrees of freedom, resulting in a reduction of about 10% of the upper limits on r in fiducial models with no GWs, as well as a comparable increase in the error bars in models with non-zero r. Moreover, we find that the inclusion of sub-orbital CMB experiments, capable of mapping the B-mode power up to the angular scales affected by lensing, can restore the forecasted performances with a cosmological constant. Finally, we show how the combination of CMB data with Type Ia SNe, BAO and Hubble constant allows to constrain simultaneously r and the DE quantities in the parametrization we consider, consisting of present abundance and first redshift derivative of the energy density. We compare this study with results obtained using the forecasted lensing potential measurement precision from CMB satellite observations, finding consistent results.Comment: 17 pages, 9 figures, accepted for publication by JCAP. Modified version after the referee's comment

Leptin and IGF-I as Metabolic Indicators of Reproductive Performance

Last updated: 6/12/200