Mathematics – Logic
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........19b&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF CALIFORNIA, BERKELEY, 1995.Source: Dissertation Abstracts International, Volume: 56-09, Section: B
Mathematics
Logic
23
Cold Dark Matter
Scientific paper
The recent discovery of spatial variations in the temperature of the cosmic microwave background (CMB) radiation provides a powerful tool for testing cosmological theories; however, the process of comparing theoretical predictions with the data is far from trivial. We develop several techniques for facilitating this confrontation between theory and experiment, and apply these techniques to recent observations of CMB anisotropy, with particular emphasis on the two-year COBE DMR data. Because no CMB anisotropy experiment observes the entire sky, it is impossible to estimate the individual multipole moments of the anisotropy. These moments, unfortunately, are precisely what theoretical models predict. It is, however, possible to compute Bayesian likelihoods for theoretical models. These likelihoods can then be used to constrain theories. We develop an optimal set of basis functions for use in such an analysis. These functions are defined on only the observed portion of the sky and are optimized to have the maximum possible rejection power for incorrect models. We then use these basis functions to test the data from the COBE DMR experiment for consistency with a variety of models, including among others the popular Cold Dark Matter (CDM) model. The amplitude of fluctuations seen by the DMR is found to be somewhat too large to fit a standard CDM model, although we can improve the fit by adopting any number of slight variants of the model. In particular, we explore in detail the effects of adding a cosmological constant to the CDM theory. Such models can have fluctuation amplitudes that fit the DMR data quite well, but the CMB angular power spectra they predict tend to have shapes that fit the data poorly. As the quality and quantity of the data improve, it is beginning to be possible to identify particular localized features in the CMB with high statistical significance. Because the data have low signal-to-noise ratios, filtering is required to achieve this goal. We apply a Wiener filter to the COBE DMR data and use the filtered map to make predictions for the Tenerife experiment, which probes angular scales similar to the DMR.
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