Scalar speed limits and cosmology: Acceleration from D-cceleration

Causality on the gravity side of the AdS/CFT correspondence restricts motion on the moduli space of the $\mathcal{N}=4$ super Yang-Mills theory by imposing a speed limit on how fast the scalar field may roll. This effect can be traced to higher-derivative operators arising from integrating out light degrees of freedom near the origin. In the strong coupling limit of the theory, the dynamics is well approximated by the Dirac-Born-Infeld Lagrangian for a probe D3-brane moving toward the horizon of the AdS Poincar\'e patch, combined with an estimate of the (ultimately suppressed) rate of particle and string production in the system. We analyze the motion of a rolling scalar field explicitly in the strong coupling…