Reconstruction of inflationary scenarios in non-conservative unimodular gravity

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.