Over the last 40 years or so, the Standard Models of Particle Physics and Cosmology have enjoyed unrivalled phenomenological successes. Unfortunately, this has also meant that High Energy Physics has had very little observational help in moving forward. Consequently, model builders have relied heavily on theoretical prejudices, and I will talk about one such prejudice, that of requiring our universe to be singularity free. In particular, I will discuss whether covariant non-local theories can resolve some of the classical and quantum singularities of their local counterpart, and whether we can hope to find observational signatures of these new models.