Discontinuities in nonlinear 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 a phenomenon of induced metric is rather general and may occur for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of nonlinear 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 de Sitter geometry. The observation of these waves would lead us to infer, erroneously, that we live in a de Sitter universe.

• Received 12 January 2006

DOI:https://doi.org/10.1103/PhysRevD.73.123531