Scalar speed limits and cosmology: Acceleration from D-cceleration

Causality on the gravity side of the AdS/CFT correspondence restricts motionon the moduli space of the N=4 super Yang Mills theory by imposing a speedlimit on how fast the scalar field may roll. This effect can be traced tohigher derivative operators arising from integrating out light degrees offreedom near the origin. In the strong coupling limit of the theory, thedynamics is well approximated by the Dirac-Born-Infeld Lagrangian for a probeD3-brane moving toward the horizon of the AdS Poincare patch, combined with anestimate of the (ultimately suppressed) rate of particle and string productionin the system. We analyze the motion of a rolling scalar field explicitly inthe strong coupling regime of the field theory, and extend the analysis tocosmological systems obtained by coupling this type of field theory to fourdimensional gravity. This leads to a mechanism for slow roll inflation for amassive scalar at subPlanckian VEV without need for a flat potential (realizinga version of k-inflation in a microphysical framework). It also leads to avariety of novel FRW cosmologies, some of which are related to those obtainedwith tachyon matter.Comment: 39 pages. v2: References added. v3: comments on conformal and curvature couplings revise