Signal-to-Noise Eigenmode Analysis of the Two-Year COBE Maps

To test a theory of cosmic microwave background fluctuations, it is natural to expand an anisotropy map in an uncorrelated basis of linear combinations of pixel amplitudes --- statistically-independent for both the noise and the signal. These $S/N$-eigenmodes are indispensible for rapid Bayesian analyses of anisotropy experiments, applied here to the recently-released two-year COBE {\it dmr} maps and the {\it firs} map. A 2-parameter model with an overall band-power and a spectral tilt $\nu_{\Delta T}$ describes well inflation-based theories. The band-powers for {\it all} the {\it dmr} $53,90,31$ $a$+$b$ GHz and {\it firs} 170 GHz maps agree, $\{(1.1\pm 0.1)\times 10^{-5}\}^{1/2}$, and are largely independent of tilt and degree of (sharp) $S/N$-filtering. Further, after optimal $S/N$-filtering, the {\it dmr} maps reveal the same tilt-independent large scale features and correlation function. The unfiltered {\it dmr} $53$ $a$+$b$ index $\nu_{\Delta T}+1$ is $1.4\pm 0.4$; increasing the $S/N$-filtering gives a broad region at (1.0--1.2)$\pm$0.5, a jump to (1.4--1.6)$\pm$0.5, then a drop to 0.8, the higher values clearly seen to be driven by $S/N$-power spectrum data points that do not fit single-tilt models. These indices are nicely compatible with inflation values ($\sim$0.8--1.2), but not overwhelmingly so.Comment: submitted to Phys.Rev.Letters, 4 pages, uuencoded compressed PostScript; also bdmr2.ps.Z, via anonymous ftp to ftp.cita.utoronto.ca, cd to /pub/dick/yukawa; CITA-94-2

Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant

The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this paper this data is fit to models for the equation of state with w = -1, w = const, and w(z) = w_0+w_a(1-a). The last model is poorly constrained by the distance data, leading to unphysical solutions where the dark energy dominates at early times unless the large scale structure and acoustic scale constraints are modified to allow for early time dark energy effects. A flat LambdaCDM model is consistent with all the data.Comment: 19 pages Latex with 8 Postscript figure files. A new reference and constraint, w vs w' contour plots updated. Version accepted by the the Ap

Constraining Large Scale Structure Theories with the Cosmic Background Radiation

We review the relevant 10+ parameters associated with inflation and matter content; the relation between LSS and primary and secondary CMB anisotropy probes; COBE constraints on energy injection; current anisotropy band-powers which 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 $\Lambda$CDM, $\Lambda$hCDM and oCDM model sequences with age 11-15 Gyr, consisting of mixtures of baryons, cold (and possibly hot) dark matter, vacuum energy, and curvature energy 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 is used, and for $\Lambda$CDM when LSS data is combined with CMB; with both, a nonzero value of $\Omega_\Lambda$ is strongly preferred ($\approx 2/3$ for a 13 Gyr sequence, similar to the value from SNIa). The $o$CDM sequence prefers $\Omega_{tot}<1$, but is overall much less likely than the flat $\Omega_\Lambda \ne 0$ 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.Comment: 20 pages, LaTeX, 5 figures, 2 tables, uses rspublic.sty To appear in Philosophical Transactions of the Royal Society of London A, 1998. "Discussion Meeting on Large Scale Structure in the Universe," Royal Society, London, March 1998. Text and colour figures also available at ftp://ftp.cita.utoronto.ca/bond/roysoc9

Increasing the quality of seismic interpretation

Acknowledgments E. Macrae was funded by an NERC Open CASE Ph.D. award (NE/F013728/1) with Midland Valley Exploration Ltd. as the industry partner. We thank 763 geoscientists for their participation, and in particular, the REs who gave their time freely to the project. M. Scott (University of Glasgow, UK) is thanked for assisting with the statistical analysis. Four reviewers are thanked for their constructive comments that improved the manuscript.Peer reviewedPublisher PD

Effects of high and low barometric pressures on susceptibility and resistance to infection Quarterly status report, 1 Apr. - 30 Jun. 1970

Effects of high and low barometric pressures on susceptibility and resistance to infectio

A Way to Dynamically Overcome the Cosmological Constant Problem

The Cosmological Constant problem can be solved once we require that the full standard Einstein Hilbert lagrangian, gravity plus matter, is multiplied by a total derivative. We analyze such a picture writing the total derivative as the covariant gradient of a new vector field (b_mu). The dynamics of this b_mu field can play a key role in the explanation of the present cosmological acceleration of the Universe.Comment: 5 page

CMB Likelihood Functions for Beginners and Experts

Although the broad outlines of the appropriate pipeline for cosmological likelihood analysis with CMB data has been known for several years, only recently have we had to contend with the full, large-scale, computationally challenging problem involving both highly-correlated noise and extremely large datasets ($N > 1000$). In this talk we concentrate on the beginning and end of this process. First, we discuss estimating the noise covariance from the data itself in a rigorous and unbiased way; this is essentially an iterated minimum-variance mapmaking approach. We also discuss the unbiased determination of cosmological parameters from estimates of the power spectrum or experimental bandpowers.Comment: Long-delayed submission. In AIP Conference Proceedings "3K Cosmology" held in Rome, Oct 5-10, 1998, edited by Luciano Maiani, Francesco Melchiorri and Nicola Vittorio, 343-347, New York, American Institute of Physics 199

Cosmological Consequences of String Axions

Axion fluctuations generated during inflation lead to isocurvature and non-Gaussian temperature fluctuations in the cosmic microwave background radiation. Following a previous analysis for the model independent string axion we consider the consequences of a measurement of these fluctuations for two additional string axions. We do so independent of any cosmological assumptions except for the axions being massless during inflation. The first axion has been shown to solve the strong CP problem for most compactifications of the heterotic string while the second axion, which does not solve the strong CP problem, obeys a mass formula which is independent of the axion scale. We find that if gravitational waves interpreted as arising from inflation are observed by the PLANCK polarimetry experiment with a Hubble constant during inflation of H_inf \apprge 10^13 GeV the existence of the first axion is ruled out and the second axion cannot obey the scale independent mass formula. In an appendix we quantitatively justify the often held assumption that temperature corrections to the zero temperature QCD axion mass may be ignored for temperatures T \apprle \Lambda_QCD.Comment: 27 pages, 4 figures; v2: References corrected; v3: Assumptions simplified, minor corrections, conclusions unchange

Comparing Cosmic Microwave Background Datasets

To extract reliable cosmic parameters from cosmic microwave background datasets, it is essential to show that the data are not contaminated by residual non-cosmological signals. We describe general statistical approaches to this problem, with an emphasis on the case in which there are two datasets that can be checked for consistency. A first visual step is the Wiener filter mapping from one set of data onto the pixel basis of another. For more quantitative analyses we develop and apply both Bayesian and frequentist techniques. We define the ``contamination parameter'' and advocate the calculation of its probability distribution as a means of examining the consistency of two datasets. The closely related ``probability enhancement factor'' is shown to be a useful statistic for comparison; it is significantly better than a number of chi-squared quantities we consider. Our methods can be used: internally (between different subsets of a dataset) or externally (between different experiments); for observing regions that completely overlap, partially overlap or overlap not at all; and for observing strategies that differ greatly. We apply the methods to check the consistency (internal and external) of the MSAM92, MSAM94 and Saskatoon Ring datasets. From comparing the two MSAM datasets, we find that the most probable level of contamination is 12%, with no contamination only 1.05 times less probable, and 100% contamination strongly ruled out at over 2 X 10^5 times less probable. From comparing the 1992 MSAM flight with the Saskatoon data we find the most probable level of contamination to be 50%, with no contamination only 1.6 times less probable and 100% contamination 13 times less probable. [Truncated]Comment: LaTeX, 16 pages which include 16 figures, submitted to Phys. Rev.

Cosmic Microwave Background Anisotropy Window Functions Revisited

The primary results of most observations of cosmic microwave background (CMB) anisotropy are estimates of the angular power spectrum averaged through some broad band, called band-powers. These estimates are in turn what are used to produce constraints on cosmological parameters due to all CMB observations. Essential to this estimation of cosmological parameters is the calculation of the expected band-power for a given experiment, given a theoretical power spectrum. Here we derive the "band power" window function which should be used for this calculation, and point out that it is not equivalent to the window function used to calculate the variance. This important distinction has been absent from much of the literature: the variance window function is often used as the band-power window function. We discuss the validity of this assumed equivalence, the role of window functions for experiments that constrain the power in {\it multiple} bands, and summarize a prescription for reporting experimental results. The analysis methods detailed here are applied in a companion paper to three years of data from the Medium Scale Anisotropy Measurement.Comment: 5 pages, 1 included .eps figure, PRD in press---final published versio