This work concentrates on theoretical cosmology in the aspect of modelling the inflationary
cosmology, and the central work investigates Non-Canonical inflation (NCI) through the Kinflation
paradigm. In this work the objective NCI models can be classified to three classes
which are summation-separable models, product-separable models and an ansatz for NCI
models, respectively. For simplicity of discussion, the application of the methods, and also
the generality of the resulting predictions, I studied NCI models which are associated with
the single-term polynomial potential V (�) = A�m.
By means of several methods, which include scalar field redefinition and the asymptotic
method, as well as the efficient approximations such as slow-roll approximation, for the
first time I formulated and revealed the degeneracy and the correlations for the model
parameters, in for instance both the scalar potential and the kinetic energy for different
investigated NCI models in the work.
The work also introduces one developed code, namely Kinetic Model (KMC) for the
considered NCI models which implements and extends the scope of ModeCode based on the
CosmoMC packages from the conventional canonical inflation to the generic NCI models.
The results from numerical exploration helps in illustrating the constraints on the model
parameters without the limits of slow-roll assumptions, and the generated results present
the consistency as well as similar correlations to those derived from theoretical calculations.
Specifically, all investigated NCI models which are driven by a quartic potential ��4
present a novel explanation as a viable candidate theory in modelling our universe given
the current high precise observational data, such as from Wilkinson Microwave Anisotropy
Probe (WMAP) satellite and Planck satellite.