Mathematics – Logic
Scientific paper
Sep 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003phdt.........9d&link_type=abstract
Thesis (PhD). THE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL, Source DAI-B 64/03, p. 1286, Sep 2003, 73 pages.
Mathematics
Logic
Scientific paper
The discovery of the dark energy through type Ia supernova distance-magnitude measurements is the most important cosmological discovery of recent years. The most pressing problem for cosmologists since has been to understand the properties and the source of dark energy. The proliferation of increasingly precise observations of the cosmic microwave background anisotropy, measurements of large-scale structure and surveys of supernovae is rapidly constraining the values of a myriad of cosmic parameters. In this thesis, we suggest possible ways of extracting information from microwave background measurements and supernova counts. We address the effect of dark energy on the position of the first acoustic peak in the CMB power spectrum. We derive an analytic formula for the first peak, ℓ1, and with the aid of the computer program CMBFAST compare our results to the current Microwave Anisotropy Probe limits on ΩM and ΩΛ. The accelerated expansion rate due to the negative pressure of dark energy can significantly alter the value of ℓ 1 and CMB measurements should soon be precise enough to tightly constrain the equation of state with this method. We also suggest the possibility of applying the classical number count test to type Ia supernova. We derive formulae for the rate of type Ia supernovae in as a function of redshift, ΩM, Ω Λ and the dark energy equation of state. Future surveys should amass large catalogs of 1000's of supernovae. Due to the extremely high detection efficiency predicted for the SuperNova Acceleration Probe, it is estimated that only a modest improvement in measurements of the cosmic star formation rate and initial mass function should make this type of analysis at least as useful for measuring cosmological observables as number count tests proposed for galaxies and clusters.
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