A toy model of a fake inflation
  Discontinuities in non linear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on Electrodynamics in the cosmic geometry. Such phenomenon of induced metric is rather general and may occurs for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of non linear scalar field. We show that a class of theories that have been analyzed in the literature, having regular configuration in the Minkowski space-time background is such that the field propagates like free waves in an effective deSitter geometry. The observation of these waves would led us to infer, erroneously, that we live in a deSitter universe. 
M. Novello, E. Huguet and J. Queva