Instability of an emergent universe

Oscillating solutions to the effective equations of Loop Quantum Cosmology have been suggested for the role of an `eternal seed', providing a possible starting point for the emergent universe scenario. We investigate the stability of a particular model, sourced by a homogeneous massless scalar field and a negative cosmological constant, with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to collapse by quantum tunneling to zero size. We discuss the possibility that the state resulting from the collapse is non-singular, so it may tunnel back to the oscillating regime. We argue that the universe is then likely to evolve to states of very large size with large particle occupation numbers.