The Imprint of Gravitational Waves on the Cosmic Microwave Background

Long-wavelength gravitational waves can induce significant temperature anisotropy in the cosmic microwave background. Distinguishing this from anisotropy induced by energy density fluctuations is critical for testing inflationary cosmology and theories of large-scale structure formation. We describe full radiative transport calculations of the two contributions and show that they differ dramatically at angular scales below a few degrees. We show how anisotropy experiments probing large- and small-angular scales can combine to distinguish the imprint due to gravitational waves.Comment: 11 pages, Penn Preprint-UPR-

Fast, exact CMB power spectrum estimation for a certain class of observational strategies

We describe a class of observational strategies for probing the anisotropies in the cosmic microwave background (CMB) where the instrument scans on rings which can be combined into an n-torus, the {\em ring torus}. This class has the remarkable property that it allows exact maximum likelihood power spectrum estimation in of order $N^2$ operations (if the size of the data set is $N$) under circumstances which would previously have made this analysis intractable: correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes, non-uniform distribution of integration time on the sky and partial sky coverage. This ease of computation gives us an important theoretical tool for understanding the impact of instrumental effects on CMB observables and hence for the design and analysis of the CMB observations of the future. There are members of this class which closely approximate the MAP and Planck satellite missions. We present a numerical example where we apply our ring torus methods to a simulated data set from a CMB mission covering a 20 degree patch on the sky to compute the maximum likelihood estimate of the power spectrum $C_\ell$ with unprecedented efficiency.Comment: RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1 and additional materials are at http://feynman.princeton.edu/~bwandelt/RT

Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology

As the era of high precision cosmology approaches, the empirically determined power spectrum of the microwave background anisotropy, $C_l$, will provide a crucial test for cosmological theories. We present a unified semi-analytic framework for the study of the statistical properties of the $C_l$ coefficients computed from the results of balloon, ground based, and satellite experiments. An illustrative application shows that commonly used approximations {\it bias} the estimation of the baryon parameter $\Omega_b$ at the 1% level even for a satellite capturing as much as $\sim 70$% of the sky.Comment: 4 pages, 3 figures. Also available at http://www.tac.dk/~wandelt/downloads.htm

Can inflationary models of cosmic perturbations evade the secondary oscillation test?

We consider the consequences of an observed Cosmic Microwave Background (CMB) temperature anisotropy spectrum containing no secondary oscillations. While such a spectrum is generally considered to be a robust signature of active structure formation, we show that such a spectrum {\em can} be produced by (very unusual) inflationary models or other passive evolution models. However, we show that for all these passive models the characteristic oscillations would show up in other observable spectra. Our work shows that when CMB polarization and matter power spectra are taken into account secondary oscillations are indeed a signature of even these very exotic passive models. We construct a measure of the observability of secondary oscillations in a given experiment, and show that even with foregrounds both the MAP and \pk satellites should be able to distinguish between models with and without oscillations. Thus we conclude that inflationary and other passive models can {\em not} evade the secondary oscillation test.Comment: Final version accepted for publication in PRD. Minor improvements have been made to the discussion and new data has been included. The conclusions are unchagne

CMBfit: Rapid WMAP likelihood calculations with normal parameters

We present a method for ultra-fast confrontation of the WMAP cosmic microwave background observations with theoretical models, implemented as a publicly available software package called CMBfit, useful for anyone wishing to measure cosmological parameters by combining WMAP with other observations. The method takes advantage of the underlying physics by transforming into a set of parameters where the WMAP likelihood surface is accurately fit by the exponential of a quartic or sextic polynomial. Building on previous physics based approximations by Hu et.al., Kosowsky et.al. and Chu et.al., it combines their speed with precision cosmology grade accuracy. A Fortran code for computing the WMAP likelihood for a given set of parameters is provided, pre-calibrated against CMBfast, accurate to Delta lnL ~ 0.05 over the entire 2sigma region of the parameter space for 6 parameter ``vanilla'' Lambda CDM models. We also provide 7-parameter fits including spatial curvature, gravitational waves and a running spectral index.Comment: 14 pages, 8 figures, References added, accepted for publication in Phys.Rev.D., a Fortran code can be downloaded from http://space.mit.edu/home/tegmark/cmbfit

Accelerated learning at masters’ level: problem based learning of diagnostic reasoning skills by physician associate students

Physician Associates (PA) complete a two year postgraduate course, and are expected to graduate with diagnostic skills equivalent to those of newly qualified doctors who have completed a five year course. BSMS has utilised Problem Based Learning (PBL) in an attempt to accelerate the acquisition of these skills by PAs. Weekly PBL sessions were conducted during year 1 of the PA course, focusing on the ‘top 20’ core conditions within the curriculum. Alongside this, students had weekly clinical exposure in General practice. In order to assess the impact of this strategy the ‘Diagnostic Thinking Inventory‘ (DTI) developed by Bordage et al. (1990) was conducted three times across year 1 and the results compared to standardised data for medical students and doctors. This found that PA students had a significantly higher baseline score in terms of flexibility of thinking (equivalent to newly qualified doctors engaged in foundation training) and structure of memory (equivalent to third year medical students). Results showed a statistically significant improvement in structure of memory across year 1: achieving an improvement in score which took over four years to achieve in medical students. This appears to suggest that PBL can facilitate increased assimilation of diagnostic reasoning skills within postgraduate learners. Keywords: Physician Associate, Diagnostic Reasoning, Problem Based Learning, Postgraduate

Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge

It is shown that the fluctuation in the temperature of the cosmic microwave background in any direction may be evaluated as an integral involving scalar and dipole form factors, which incorporate all relevant information about acoustic oscillations before the time of last scattering. A companion paper gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of these form factors. Explicit expressions are given here for the form factors in a simplified hydrodynamic model for the evolution of perturbations.Comment: 35 pages, no figures. Improved treatment of damping, including both Landau and Silk damping; inclusion of late-time effects; several references added; minor changes and corrections made. Accepted for publication in Phys. Rev. D1

Standard Model Neutrinos as Warm Dark Matter

Standard Model neutrinos are not usually considered plausible dark matter candidates because the usual treatment of their decoupling in the early universe implies that their mass must be sufficiently small to make them ``hot'' dark matter. In this paper we show that decoupling of Standard Model neutrinos in low reheat models may result in neutrino densities very much less than usually assumed, and thus their mass may be in the keV range. Standard Model neutrinos may therefore be warm dark matter candidates.Comment: 5 pages, 5 figures, LaTeX file uses revtex packag

Simulating Cosmic Microwave Background maps in multi-connected spaces

This article describes the computation of cosmic microwave background anisotropies in a universe with multi-connected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multi-connected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps.Comment: 33 pages, 55 figures, submitted to PRD. Higher resolution figures available on deman

Cosmic Strings Lens Phenomenology: Model of Poisson Energy Distribution

We present a novel approach for investigating lens phenomenology of cosmic strings in order to elaborate detection strategies in galaxy deep field images. To account for the complexity of the projected energy distribution of string networks we assume their lens effects to be similar to those of a straight string carrying a {\em random} lineic energy distribution. In such a model we show that, unlike the case of uniform strings, critical phenomena naturally appear. We explore the properties of the critical lines and caustics. In particular, assuming that the energy coherence length along the string is much smaller than the observation scale, we succeeded in computing the total length of critical lines per unit string length and found it to be $4/\sqrt{3} {\bf E}(3/4)$. The length of the associated caustic lines can also be computed to be $16/(\pi \sqrt{3}) {\bf E}(3/4)$. The picture we obtain here for the phenomenology of cosmic string detection is clearly at variance with common lore.Comment: 10 pages, 5 figures. Minor correction