  Cosmic inflation, which describes an accelerated expansion of the early
Universe, yields the most successful predictions regarding temperature
anisotropies in the cosmic microwave background (CMB). Nevertheless, the
precise origin of the primordial perturbations and their quantum-to-classical
transition is still an open issue. The continuous spontaneous localization
model (CSL), in the cosmological context, might be used to provide a solution
to the mentioned puzzles by considering an objective reduction of the inflaton
wave function. In this work, we calculate the primordial power spectrum at the
next leading order in the Hubble flow functions that results from applying the
CSL model to slow roll inflation within the semiclassical gravity framework. We
employ the method known as uniform approximation along with a second order
expansion in the Hubble flow functions. We analyze some features in the CMB
temperature and primordial power spectra that could help to distinguish between
the standard prediction and our approach.
