  The leading candidate for the very early universe is described by a period of
rapid expansion known as inflation. While the standard paradigm invokes a
single slow-rolling field, many different models may be constructed which fit
the current observational evidence. In this work we outline theoretical and
observational studies of non-Gaussian fluctuations produced by models of
inflation and by cosmic strings - topological defects that may be generated in
the very early universe during a phase transition. In particular, we consider
the imprint of cosmic strings on the cosmic microwave background (CMB) and
describe a formalism for the measurement of general four-point correlation
functions, or trispectra, using the CMB. In addition we describe the
application of our methodology to non-Gaussian signals imprinted in the large
scale structure of the universe. Such deviations from Gaussianity are generally
expressed in terms of the so-called bispectrum and trispectrum.
