  We show how the recently developed string-inspired, projectively-invariant
gravitational model Thomas-Whitehead gravity (TW gravity) naturally gives rise
to a field acting as the inflaton. In the formulation of TW gravity, a field
$\mathcal{D}_{ab}$ is introduced into the projective connection components and
is related to a rank-two tensor field $\mathcal{P}_{ab}$. Through the dynamical
action of TW gravity, in terms of projective curvature, the tensor field
$\mathcal{P}_{ab}$ acquires dynamics. By decomposing $\mathcal{P}_{ab}$ into
its trace and traceless degrees of freedom, and choosing the connection to be
Levi-Civita, we demonstrate that TW gravity contains a non-minimally coupled
scalar field with a specific potential. Considering only the trace degrees of
freedom, we demonstrate that the scalar field acts as an inflaton in the slow
roll approximation. We find a range of values for the parameters introduced by
TW gravity that fit the experimental constraints of the most recent
cosmological data.
