In this thesis we will present a comprehensive set of formalisms for comparing, evolving, and constraining primordial non-Gaussian models through the CMB bispectrum. First, we introduce the idea of a shape function for characterising the primordial non-Gaussianity. The shape function can also be used to construct a correlator between the models which we use to group the space of possible models into four main classes: equilateral, squeezed, flattened, and scale dependent. Next, we use a common property of the shape function to create a method for calculating, without approximation, the CMB bispectrum from a general primordial model. There are two techniques we use to speed up the calculation. The first is to use the flat sky approximation for large <i>l</i>, and the second is to exploit the smoothness of the reduced bispectrum to calculate the bispectrum first on a sparse grid then interpolate to obtain the remaining points. We then discuss methods for calculating estimators by decomposing the bispectrum, either today or at primordial times, into the product of eigenmodes. First we deal with the primordial bispectrum and describe how the decomposition can be used to both constrain primordial models and to estimate the primordial bispectrum from observations. Then we repeat the analysis for the CMB bispectrum and describe how this process can be used to constrain models, but this time allowing for the inclusion of late time effects. It also presents a method for generating maps with an arbitrary bispectrum and power spectrum.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:598987 |
| Date | January 2009 |
| Creators | Fergusson, J. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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