The cosmological evolution of p-brane networks

TL;DR

This paper derives the acceleration components of p-branes from the Nambu-Goto action, extends the velocity-dependent one-scale model, and shows that in decelerating universes, p-brane interactions do not cause frustration unless finely tuned.

Contribution

It provides a direct derivation of p-brane acceleration from fundamental action principles and extends the evolution model to include these effects.

Findings

Interactions do not lead to frustration in typical cosmological scenarios.

Fine-tuned non-relativistic networks with small curvature can frustrate.

The model clarifies the cosmological impact of p-brane networks.

Abstract

In this paper we derive, directly from the Nambu-Goto action, the relevant components of the acceleration of cosmological featureless $p$-branes, extending previous analysis based on the field theory equations in the thin-brane limit. The component of the acceleration parallel to the velocity is at the core of the velocity-dependent one-scale model for the evolution of $p$-brane networks. We use this model to show that, in a decelerating expanding universe in which the $p$-branes are relevant cosmologically, interactions cannot lead to frustration, except for fine-tuned non-relativistic networks with a dimensionless curvature parameter $k \ll 1$. We discuss the implications of our findings for the cosmological evolution of $p$-brane networks.