Scalar speed limits and cosmology: Acceleration from D-cceleration

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.

Poly-instanton inflation

“…Explicit examples of this kind of Calabi-Yau three-folds with additional del Pezzo divisors have been analysed in [26] using the powerful tools of toric geometry. Here we shall just focus on the simplest of such manifolds whose volume takes the form: 12) where t 1 is the volume of the P 1 base, τ 1 = λ 1 t 2 2 is the size of the K3 or T 4 fibre, and τ 3 = 3λ 2 t 2 3 controls the volume of a blow-up mode (the other four-cycle volume is given by τ 2 = 2λ 1 t 1 t 2 ). Notice that the fibre is a K3 surface if its Euler characteristic is χ = 24 whereas it is a T 4 divisor if χ = 0 [34].…”

“…The progress in moduli stabilisation also opened up the possibility of realising inflation in the moduli sector. String inflationary models based on single-field slow-roll can be broadly classified, based on the origin of the inflaton field [9], into open string models [10][11][12] and closed string models [13][14][15][16][17][18][19][20].…”

Inflation and String Theory

“…We will discuss this further in §2.3.4, where we also emphasize the need to UV-complete theories such as (2.84). In §5.3, we present DBI inflation [38,40] as a specific example in string theory.…”

“…Enforcing the restrictions imposed by ultraviolet completion winnows the possible models, leading to improved predictivity. For example, the DBI scenario [38] may be viewed as a special case of k-inflation [39]. While most versions of k-inflation are radiatively unstable, string theory makes it possible to control an infinite series of higher-derivative terms.…”

“…The geometric perspective afforded by compactifications, and by D-branes moving inside them, complements the more algebraic tools used to construct effective theories in particle physics. The effective theories in D-brane inflation [41,42], DBI inflation [38], fibre inflation [43], and axion monodromy inflation [34], for example, all exist in their own right as low-energy theories, but would likely have gone undiscovered without the approach provided by string theory. Generating effective theories from the top down in string theory also leads to modified notions of what constitutes a natural inflationary model, or a minimal one.…”