  Unimodular gravity is an alternative theory of gravity to general relativity.
The gravitational field equations are given by the trace-free version of
Einstein's field equations. Due to the structure of the theory, unimodular
gravity admits a diffusion term that characterizes a possible non-conservation
of the canonical energy-momentum tensor locally. Employing this feature of
unimodular gravity, in the present work, we explicitly show how to construct an
inflationary phase that can be contrasted with current observations. In
particular, we focus on three different inflationary scenarios of physical
interest. An important element in these scenarios is that the accelerated
expansion is driven by the diffusion term exclusively, i.e. there is no
inflaton. Furthermore, the primordial spectrum during inflation is generated by
considering inhomogeneous perturbations associated to standard hydrodynamical
matter (modeled as a single ultra-relativistic fluid). For each of the
scenarios, we obtain the prediction for the primordial spectrum and contrast it
with recent observational bounds.
