I will explain how theories with analytic functions of derivatives are
connected to strings and in particular arise in string field theory
(SFT) and will spent the most part of my talk on the good
and unrevealed properties of analytic infinite derivative (AID) gravity.
In particular, I will discuss questions of avoiding singularities as
well as possible observational evidences for such a non-local
modification of Einstein’s theory. Namely, imprints in inflationary
spectra including non-gaussianities. On top of this I will raise several
purely mathematical questions which need to be solved in order to push
the physics developments further.