Degree Name

Doctor of Philosophy


School of Physics


In the currently accepted theory of inflation, the early universe is permeated by a quantum scalar field, which has small inhomogeneities, referred to as primordial perturbations, and these perturbations grow over time to form lumps of matter such as stars, galaxies, and clusters. Numerous predictions of this theory including the near scale invariance of the power spectrum, the Gaussianity, and the adiabatic nature of these perturbations have been supported by observations. Nonetheless, the uncertainties in the observations still leave some room for other theories with similar predictions. One such theory is a theory with multiple scalar fields, which naturally leads to slight deviations from the Gaussianity and adiabaticity of the perturbations that can still be within the uncertainty range of the observations. The aim of my master project is to use the clustering of galaxies as a tool to test these predictions thereby constraining models of inflation, since galaxy clustering across the sky can be mapped out via observations.

We first developed expressions for the non-Gaussianity and the non-adiabaticity in the primordial perturbations generated in a theory of inflation with two scalar fields (the predictions are essen-tially the same in a theory with more fields). Non-adiabatic perturbations, known as isocurvature perturbations, are relative perturbations in energy densities of di˙erent energy components, such as baryonic matter and radiation. This is unlike the case of single field inflation, where only the total energy density is perturbed. These features were then incorporated into our galaxy bias expansion, which is a technique developed to relate galaxy density/distribution (an observable) to the primordial perturbations. The possibility of non-Gaussian initial conditions had already been considered in the existing theory of galaxy bias expansion while that for the isocurvature perturbations had not. In particular, we incorporated compensated isocurvature perturbations, which are perturbations between baryonic matter and dark matter, as these would directly a˙ect the distribution of galaxies and hence their densities. Subsequently, theoretical expressions for the galaxy statistics (power spectrum and bispectrum) were determined and plotted, which along with observational data, can be used to constrain the initial conditions and hence the models of inflation in the future.

FoR codes (2008)




Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.