Numerical solution of the ekpyrotic scenario in the moduli space approximation

A numerical solution to the equations of motion for the ekpyrotic bulk brane scenario in the moduli space approximation is presented. The visible universe brane has positive tension, and we use a potential that goes to zero exponentially at large distance, and also goes to zero at small distance. In the case considered, no bulk brane, visible brane collision occurs in the solution. This property and the general behavior of the solution is qualitatively the same when the visible brane tension is negative, and for many different parameter choices.

Figure 1

$A(t)$ increases slowly as the system evolves.

Figure 2

$B(t)$ starts out slowly, but becomes very steep.

Figure 3

$C(t)$ falls significantly during the evolution.

Figure 4

The bulk brane bounces without colliding.

Figure 5

The bulk brane does not collide with the visible universe.

Figure 6

The four-dimensional effective scale factor decreases as the system evolves.

Figure 7

The physical length of the orbifold dimension increases on the whole during the evolution, but displays small dips when the bulk brane is close to the visible brane.