Cosmological Moduli Dynamics

TL;DR

This paper investigates cosmological moduli dynamics near extra-species points in string compactifications by constructing a truncated five-dimensional effective field theory with two scalar moduli, φ and χ, coupled through the potential $V(φ,χ)= frac{1}{2}g^{2}φ^{2}χ^{2}$ and specific moduli-space metrics. It demonstrates that classical moduli evolution on this ESP neighborhood exhibits chaotic dynamics, and that classical trapping via the potential is not robust, especially when Hubble friction is included. It also shows that quantum particle production affords a much more efficient stabilization mechanism for the moduli. These results imply that moduli stabilization near ESPs can occur dynamically, offering a potential route to address moduli-related cosmological constraints.

Abstract

Low energy effective actions arising from string theory typically contain many scalar fields, some with a very complicated potential and others with no potential at all. The evolution of these scalars is of great interest. Their late time values have a direct impact on low energy observables, while their early universe dynamics can potentially source inflation or adversely affect big bang nucleosynthesis. Recently, classical and quantum methods for fixing the values of these scalars have been introduced. The purpose of this work is to explore moduli dynamics in light of these stabilization mechanisms. In particular, we explore a truncated low energy effective action that models the neighborhood of special points (or more generally loci) in moduli space, such as conifold points, where extra massless degrees of freedom arise. We find that the dynamics has a surprisingly rich structure - including the appearance of chaos - and we find a viable mechanism for trapping some of the moduli.

Figures (7)

• Figure 1: Two views of the potential $V(\phi,\chi)=\frac{1}{2}g^2\phi^2\chi^2$. The vacuum branches ('arms') $\phi=0$ and $\chi=0$, are thehorizontal and vertical axes. Following Helling:2000kz, we call the central region the 'stadium'.
• Figure 2: Schematic diagram of a Poincaré surface of section. The circles show the points where the phase trajectory cuts the hyperplane. Since the hyperplane is oriented, one can distinguish such points by the direction of the phase trajectory when it passes through. A PSS is a collection of such points with the phase trajectory moving in a specified direction. So this diagram really shows part of two PSS's --- corresponding to the solid and hollow circles.
• Figure 3: Surface of Sections for $\sigma = 10$, $1/2g^2 = 10$, and $E=20$. The points trace out a smooth curve.
• Figure 4: Surface of Sections for $\sigma = 1$, $1/2g^2 = 10$, and $E=20$. Here the points fill out a region of the $\phi,p_{\phi}$ plane, indicating chaotic dynamics.
• Figure 5: Surface of Sections for $\sigma =10$, $1/2g^2 = 10$, and $E=20.0$, for different initial conditions.