In this thesis we will discuss several issues concerning cosmological applications of non-canonical scalar fields, which are generically referred to as k-essence. First, we consider two examples of k-essence. These are the rolling tachyon and static spherically symmetric solutions of non-canonical scalar fields in flat space. We find constraints on the form of the allowed interactions in the first case and on the choice of boundary conditions in the latter. For the rolling tachyon we find that at late times the tachyon matter behaves like a non-relativistic dust, thus making it a dark matter candidate. For the static spherically symmetric solutions we show that solutions which are finite at the origin must have negative energy density there.

Next, we consider static spherically symmetric solutions of non-canonical scalar fields coupled to gravity as a way to explain dark matter halos as a coherent state of the scalar field. Consistent solutions are found with a smooth scalar profile which can describe observed rotation curves. The non-trivial solutions have negative energy density near the origin, though the total energy is positive. We also reconsider the no scalar hair theorems for black holes with emphasis on asymptotic boundary conditions and superluminal propagation.

After this we show that, for general scalar fields, stationary configurations are possible for shift symmetric theories only. This symmetry with respect to constant translations in field space should either be manifest in the original field variables or reveal itself after an appropriate field redefinition. In particular this result implies that neither k-essence nor quintessence can have exact steady state/Bondi accretion onto black holes. Finally, we find that stationary field configurations are necessarily linear in Killing time, provided that shift symmetry is realized in terms of these field variables.

The next discussion outlines a general program for reconstructing the action of non-canonical single field inflation models from CMBR power spectrum data. This method assumes that an action depends on a set of undetermined functions, each of which is a function of either the inflaton field or its time derivative. The scalar, tensor and non-gaussianity of the curvature perturbation spectrum are used to derive a set of reconstruction equations whose solution set can specify up to three of the undetermined functions. This method is used to find the undetermined functions in various types of actions assuming power law type scalar and tensor spectra.

Finally, we study a novel means of coupling neutrinos to a Lorentz violating k-essence background. We first look into the effect k-essence has on the neutrino dispersion relation, and derive the neutrino velocity in a k-essence background. Next, we look at the effect on neutrino oscillations. It is found that if k-essence couples non-diagonally to the neutrino flavor eigenstates, this leads to an oscillation length that varies with the neutrino energy like λ ∼ E^-1. This is to be compared with the λ ∼ E dependence seen in mass-induced neutrino oscillations. While such a scenario is not favored experimentally, it places tight constraints on the possible interaction that a k-essence background can have with neutrinos.