Scalar speed limits and cosmology: Acceleration from D-cceleration
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Abstract
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 regime of the field theory and extend the analysis to cosmological systems obtained by coupling this type of field theory to four-dimensional gravity. This leads to a mechanism for slow roll inflation for a massive scalar at sub-Planckian vacuum expectation value without need for a flat potential (realizing a version of k inflation in a microphysical framework). It also leads to a variety of novel Friedman-Roberston-Walker cosmologies, some of which are related to those obtained with tachyon matter.