Cosmological non -Gaussianity and reionization
In this thesis we discuss how probes of cosmological non-Gaussianity and reionization affect our ability to constrain the epoch of inflation. The principle predictions of inflation can be divided into three broad categories, an epoch of inflation will generally produce: (i) a stochastic background of primordial curvature perturbations with a nearly scale-invariant power spectrum; (ii) a stochastic background of gravity waves; and (iii) make the prediction that primordial curvature perturbations should obey Gaussian statistics to great precision. This thesis will focus on the first and the third predictions.
There is a proposal to measure the shape of the primordial power spectrum in an effort to learn about the epoch of inflation by conducting a high redshift galaxy survey. We show that the imprint of inhomogeneous reionization on the galaxy power spectrum exceeds the desired primordial signal, thus uncertainties in the epoch of reionization will make extraction of the primordial signal quite difficult. The standard inflationary scenario predicts that the amplitude of primordial non-Gaussianity should be observationally negligible. An observation of primordial non-Gaussianity would be a strong indication that our understanding of the epoch of inflation is inadequate. We analyze the use of cosmic microwave background observations to constrain primordial non-Gaussianity. The dependence of the primordial bispectrum's shape on the details of the epoch of inflation is examined. Then the use of polarization information and the contamination of the signal by gravitational lensing is studied. Finally, it is demonstrated that standard method of constraining the bispectrum amplitude is optimal, which means that no other statistical procedure can better produce statistical constraints on the bispectrum amplitude with the same data set.
Since the information provided by the cosmic microwave background appears to be unable to allow us to draw strong conclusion about primordial non-Gaussianity, we turn to a new cosmological observable: high redshift 21cm fluctuations. In principle, the limitations of using cosmic microwave background fluctuations to probe primordial non-Gaussianity can be overcome with high redshift 21cm fluctuations. As part of the effort to model this radiation, we calculate the polarization features of the high redshift 21cm emission.