  We investigate the influence of boundary terms in the warm inflationary
scenario, by considering that in the Einstein-Hilbert action the boundary can
be described in terms of a Weyl-type geometry. The gravitational action, as
well as the field equations, are thus extended to include new geometrical
terms, coming from the non-metric nature of the boundary, and depending on the
Weyl vector, and its covariant derivatives. We investigate the effects of these
new boundary terms by considering the warm inflationary scenario of the early
evolution of the Universe, in the presence of a scalar field. We obtain the
generalized Friedmann equations in the Universe with a Weylian boundary by
considering the Friedmann-Lemaitre-Robertson-Walker metric. We consider the
simultaneous decay of the scalar field, and of the creation of radiation, by
appropriately splitting the general conservation equation through the
introduction of the dissipation coefficient, which can depend on both the
scalar field, and the Weyl vector. We consider three distinct warm inflationary
models, in which the dissipation coefficients are chosen as different functions
of the scalar field and of the Weyl vector. The numerical solutions of the
cosmological evolution equations show that the radiation is created during the
very early phases of expansion, and, after the radiation reaches its maximum
value, the transition from an accelerating inflationary phase to a decelerating
one takes place. Moreover, it turns out that the the Weyl vector, describing
the boundary effects on the cosmological evolution, plays a significant role
during the process of radiation creation.
