10 + 1 to 3 + 1 in an Early Universe with mutually BPS Intersecting Branes

TL;DR

This paper models an early universe dominated by intersecting branes in M theory, showing three spatial dimensions expand indefinitely while others stabilize, with a time-varying Newton's constant exhibiting log periodic oscillations.

Contribution

It provides analytical and numerical analysis of a brane-world cosmology, revealing mechanisms for spatial dimension stabilization and time-varying gravitational constant in an M theory framework.

Findings

Three spatial dimensions expand indefinitely.

Remaining dimensions stabilize at fine-tuned values.

Newton's constant exhibits log periodic oscillations.

Abstract

We assume that the early universe is homogeneous, anisotropic, and is dominated by the mutually BPS 22'55' intersecting branes of M theory. The spatial directions are all taken to be toroidal. Using analytical and numerical methods, we study the evolution of such an universe. We find that, asymptotically, three spatial directions expand to infinity and the remaining spatial directions reach stabilised values. Any stabilised values can be obtained by a fine tuning of initial brane densities. We give a physical description of the stabilisation mechanism. Also, from the perspective of four dimensional spacetime, the effective four dimensional Newton's constant G_4 is now time varying. Its time dependence will follow from explicit solutions. We find in the present case that, asymptotically, G_4 exhibits characteristic log periodic oscillations.