Nonlocal gravity and the diffusion equation
  We propose a nonlocal scalar-tensor model of gravity with pseudodifferential
operators inspired by the effective action of p-adic string and string field
theory on flat spacetime. An infinite number of derivatives act both on the
metric and scalar field sector. The system is localized via the diffusion
equation approach and its cosmology is studied. We find several exact dynamical
solutions, also in the presence of a barotropic fluid, which are stationary in
the diffusion flow. In particular, and contrary to standard general relativity,
there exist solutions with exponential and power-law scale factor also in an
open universe, as well as solutions with sudden future singularities or a
bounce. Also, from the point of view of quantum field theory, spontaneous
symmetry breaking can be naturally realized in the class of actions we
consider.
