  This paper contains a critique of the standard inflationary account of the
origin of cosmological structures from quantum fluctuations in the early
universe. This critique can be thought to be purely philosophical in nature,
but I prefer to view it, rather, as arising from the need to put the
interpretational aspects of the theory -which quite obviously lie at the basis
of any comparison with experiments- on the firm grounds required by the unique
features of the problem at hand. This discussion is followed by a proposal to
complement that treatment to deal with the unsatisfactory aspects of the
standard account of the problem, using Penrose's ideas about the quantum
gravity induced collapse of the quantum states of matter fields. The formalism
developed to carry out this analysis was first introduced in [1] and leads to
unexpected predictions and to novel avenues to confront some of the details of
the proposal with observations. In my view, this is, therefore, the most
promising path towards quantum gravity phenomenology.
