What could we learn about high energy particle physics from cosmological observations at largest spatial scales ?

The very well known example of cosmology testing particle physics is the number of relativistic particles (photons and three active neutrinos within the Standard Model) at primordial nucleosynthesis. These days the earliest moment we can hope to probe with present cosmological data is the early time inflation. The particle physics conditions there and now are different because of different energy scales and different values of the scalar fields, that usually prohibits a reliable connection between the particle physics parameters at the two interesting epochs. The physics at the highest energy scales may be probed with observations at the largest spatial scales (just somewhat smaller than the size of the visible Universe). However, we are not (yet) ready to make the tests realistic, because of lack of a self-consistent theoretical description of the presently favorite cosmological models to be valid right after inflation