Dilaton Stabilization in Brane Gas Cosmology

TL;DR

This work addresses whether a stabilized dilaton can coexist with stable internal dimensions in Brane Gas Cosmology. By introducing a dilaton potential and performing a linear perturbation analysis around a static background, the authors derive a stability matrix ${\bf S}$ and analyze the eigenfrequencies $\omega_i$ under the requirement of real modes. They find that simultaneous dilaton and radion stabilization in the standard BGC setup is not possible: achieving decoupled, stable modes requires fine-tuned cancellations between $V'$ and derivatives of brane-gas pressures, and even with a stabilized dilaton one mode remains unstable. Consequently, the rolling dilaton appears essential for maintaining the negative-pressure winding effects; once stabilization occurs the theory reverts to general relativity with an expanding radion, suggesting that new radion potentials (e.g., from flux compactifications) may be necessary and could connect BGC to flux-based frameworks like GK–Polchinski.

Abstract

Brane Gas Cosmology is an M-theory motivated attempt to reconcile aspects of the standard cosmology based on Einstein's theory of general relativity. Dilaton gravity, when incorporating winding p-brane states, has verified the Brandenberger--Vafa mechanism --a string-motivated conjecture which explains why only three of the nine spatial dimensions predicted by string theory grow large. Further investigation of this mechanism has argued for a hierarchy of subspaces, and has shown the internal directions to be stable to initial perturbations. These results, however, are dependent on a rolling dilaton, or varying strength of Newton's gravitational constant. In these proceedings we show that it is not possible to stabilize the dilaton and maintain the stability of the internal directions within the standard Brane Gas Cosmology setup.