Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary
  Models
  We study the statistical descriptors for some cosmological inflationary
models that allow us to get large levels of non-gaussianity and violations of
statistical isotropy. Basically, we study two different class of models: a
model that include only scalar field perturbations, specifically a subclass of
small-field slow-roll models of inflation with canonical kinetic terms, and
models that admit both vector and scalar field perturbations. We study the
former to show that it is possible to attain very high, including observable,
values for the levels of non-gaussianity f_{NL} and \tao_{NL} in the bispectrum
B_\zeta and trispectrum T_\zeta of the primordial curvature perturbation \zeta
respectively. Such a result is obtained by taking care of loop corrections in
the spectrum P_\zeta, the bispectrum B_\zeta and the trispectrum T_\zeta .
Sizeable values for f_{NL} and \tao_{NL} arise even if \zeta is generated
during inflation. For the latter we study the spectrum P_\zeta, bispectrum
B_\zeta and trispectrum $T_\zeta of the primordial curvature perturbation when
\zeta is generated by scalar and vector field perturbations. The tree-level and
one-loop contributions from vector field perturbations are worked out
considering the possibility that the one-loop contributions may be dominant
over the tree level terms. The levels of non-gaussianity f_{NL} and \tao_{NL},
are calculated and related to the level of statistical anisotropy in the power
spectrum, g_\zeta . For very small amounts of statistical anisotropy in the
power spectrum, the levels of non-gaussianity may be very high, in some cases
exceeding the current observational limit.
