  Inflationary dynamics driven by multiple fields, especially with nonminimal
couplings, allow for highly interesting features such as isocurvature,
non-Gaussianity, and preheating. In this paper, we study two-field inflation in
the context of purely affine gravity, where the metrical structure results from
the dynamics of the spacetime affine connection. We introduce a covariant
formulation in the new framework and show that it leads to a curved field space
which can produce conspicuous departure from the purely metric gravity. In the
case where the fields are canonical, the field manifold gains a conformally
flat shape. Interestingly, while the manifold is generally curved, it is
possible to be flattened by allowing specific non-canonical field kinetic
terms. This in turn simplifies the inflationary dynamics significantly while
allowing for new predictions due to the effects of the nonminimal coupling
function on the potential solely. We use this new feature in studying two-field
inflation driven by quartic potentials for given parameter constants. We
perform a numerical solution of the slow-roll dynamics and track the possible
non-Gaussianity. We focus on field parameters that allow for spectral indices
within the favored region of the Planck results. These are associated to tiny
tensor-to-scalar ratios, $r \sim 10^{-6}$ for single field and $r \sim 10^{-4}$
for two-fields. We also show that two-field Higgs inflation may favor a curved
field manifold.
