Scalar Speed Limits and Cosmology: Acceleration from D-cceleration

TL;DR

This work shows that strong-coupling dynamics in ${\cal N}=4$ SYM imposes a speed limit on moduli-space motion, realized holographically by a DBI-probe D3-brane in AdS and leading to markedly different cosmological dynamics than in conventional two-derivative theories. By coupling this speed-limited field to four-dimensional gravity, the authors derive novel slow-roll–like inflation and a spectrum of FRW cosmologies, including power-law inflation at sub-Planckian VEVs and dust-like or accelerating phases depending on the potential structure and throat geometry. They develop a Hamilton–Jacobi framework to analyze these cosmologies, address backreaction and perturbative stability, and discuss higher-derivative and curvature corrections, showing that the DBI kinetic terms can dominate inflationary dynamics while problematic tachyonic instabilities are avoided at strong coupling. The results connect AdS/CFT, warped throat geometry, and k-inflation-like mechanisms, offering a microphysical route to inflation and exotic cosmologies without requiring flat potentials, while highlighting caveats related to backreaction, mass generation from additional sectors, and the need for explicit compactification models. Overall, the paper demonstrates how a speed limit arising from higher-derivative corrections can dramatically alter scalar field dynamics and open new avenues for string-inspired cosmology.

Abstract

Causality on the gravity side of the AdS/CFT correspondence restricts motion on the moduli space of the 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 Poincare 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 subPlanckian VEV without need for a flat potential (realizing a version of k-inflation in a microphysical framework). It also leads to a variety of novel FRW cosmologies, some of which are related to those obtained with tachyon matter.