  According to classical GR, negative-energy (AdS) bubbles in the multiverse
terminate in big crunch singularities. It has been conjectured, however, that
the fundamental theory may resolve these singularities and replace them by
non-singular bounces. Here we explore possible dynamics of such bounces using a
simple modification of the Friedmann equation, which ensures that the scale
factor bounces when the matter density reaches some critical value $\rho_c$.
This is combined with a simple scalar field `landscape', where the energy
barriers between different vacua are small compared to $\rho_c$. We find that
the bounce typically results in a transition to another vacuum, with a scalar
field displacement $\Delta\phi \sim 1$ in Planck units. If the new vacuum is
AdS, we have another bounce, and so on, until the field finally transits to a
positive-energy (de Sitter) vacuum. We also consider perturbations about the
homogeneous solution and discuss some of their amplification mechanisms (e.g.,
tachyonic instability and parametric resonance). For a generic potential, these
mechanisms are much less efficient than in models of slow-roll inflation. But
the amplification may still be strong enough to cause the bubble to fragment
into a mosaic of different vacua.
