  An alternative scenario about the phenomenology of primordial Universe is
k-inflation. According to this concept, inflation can be achieved by
nonstandard kinetic term of scalar field, namely the inflaton. In this project
we focus on k-essence models in the presence of a higher order and a linear
kinetic term. Furthermore, the inflationary phenomenology with a
Dirac-Born-Infeld scalar field is briefly examined, which arises from quantum
theories of gravity such as superstring theory. Our approach about the
inflationary era is that it can be described in the context of Einstein's
gravity involving quantum corrections such as the Chern-Simons string inspired
parity violating gravitational term. The equations of motion namely, the
Friedmann equation, the Raychadhuri equation and the Klein-Gordon equation for
an expanding background are extracted from the gravitational action utilizing
the variational principle. The consequential system of differential equations
with respect to Hubble's parameter and the inflaton field was quite perplexed
in order to be solved with an analytic way. Therefore, the slow-roll conditions
during inflationary era were imposed and terms with minor numerically
contribution were neglected. From the overall phenomenological analysis it is
proved that, models with exotic kinetic terms can generate viable results in
consistency with the latest Planck data. Finally, the presence of Chern-Simons
quantum corrections shifts the primordial spectral tensor index to blue. Even
though blue gravitational waves have yet to be observed, if detected,
compatibility with the aforementioned theory can be achieved.
