Instability of the time dependent Hořava-Witten model

We consider scalar perturbations in the time dependent Hořava-Witten model in order to probe its stability. We show that during the nonsingular epoque the model evolves without instabilities until it encounters the curvature singularity where a big crunch is supposed to occur. We compute the frequencies of the scalar field oscillation during the stable period and show how the oscillations can be used to prove the presence of such a singularity.

Figure 1

Potential ${\alpha }^2+m^2{H}^{1/2}$ for ${\alpha }^2=1$, $m=0.1$.

Figure 2

Evolution of the massless (left panel) and massive (right panel) scalar field $\Psi$ at the position of the negative tension brane $y=0$ for several values of $h$.

Figure 3

Evolution of the massless (left panel) and massive (right panel) scalar field $\Psi$ at a bulk position $y=L/2$ between the two branes for several values of $h$.

Figure 4

Evolution of the massless (left panel) and massive (right panel) scalar field $\Psi$ at the position of the positive tension brane $y=L$ for several values of $h$.