  Inflationary era of our Universe can be characterized as semi-classical
because it can be described in the context of four-dimensional Einsteins's
gravity involving quantum corrections. These string motivated corrections
originate from quantum theories of gravity such as superstring theories and
include higher gravitational terms as, Gauss-Bonnet and Chern-Simons terms. In
this paper we investigated inflationary phenomenology coming from a scalar
field, with quadratic curvature terms in the view of GW170817. Firstly, we
derived the equations of motion, directly from the gravitational action. As a
result, formed a system of differential equations with respect to Hubble's
parameter and the inflaton field which was very complicated and cannot be
solved analytically, even in the minimal coupling case. Based on the
observations from GW170817, which have shown that the speed of the primordial
gravitational wave is equal to the speed of light, our equations of motion
where simplified after applying this constraint, the slow-roll approximations
and neglecting the string corrections. We described the dynamics of
inflationary phenomenology and proved that theories with Gauss-Bonnet term can
be compatible with recent observations. Also, the Chern-Simons term leads to
asymmetric generation and evolution of the two circular polarization states of
gravitational wave. Finally, viable inflationary models are presented,
consistent with the observational constraints. The possibility of a blue tilted
tensor spectral index is briefly investigated.
