An algebraic view allows one to compute properties of physical states without having to introduce an explicit Hilbert space. In relational systems without absolute time, a state cannot be completely positive once a choice for a (possibly local) internal time has been made. A more general class of `almost-positive' states is introduced in this talk, together with a discussion of their constrained dynamics.
We hope to find clues about the particle physics of the primordial (inflationary?) universe in the statistics of the cosmological perturbations. However, if the fluctuations are non-Gaussian the statistics we observe can differ significantly from the global, mean predictions of an inflationary model. I will discuss how the conclusions we draw about the primordial degrees of freedom can be affected in interesting ways by the finiteness of our observable universe.