Instability of an emergent universe

Abstract

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.

Classically and quantum stable emergent universe from conservation laws

“…Therefore our model is free of the instability towards collapse described in Refs. [1][2][3][4]. The conserved quantity Π φ = 0 provides in this case with a protection towards collapse to a equal zero.…”

“…It has been recently pointed out by Mithani-Vilenkin [1][2][3][4] that certain emergent universe scenarios which are classically stable are nevertheless unstable semiclassically to collapse.…”

“…The parameter β represents the ambiguity in the ordering of the non-commuting factors a and p a in the Hamiltonian. The value of β does not affect the wave function in the semiclassical regimen, and usually in the study of semi-classical stability of EU it is chosen to be zero, see [1][2][3][4]. In order to obtain the potential U(a) for the case of the EU, we have to select one of the solutions Eqs.…”

Exploring eternal stability with the simple harmonic universe

“…Recent work arguing for the existence of a past singularity and a 'beginning of time' [8,9,[29][30][31][32] in the context of the universe has focused on the generation and role of entropy or on the presence of specific decay modes. It is not clear, however, that these arguments apply to our class of solutions, particularly in the static limit and with the addition of Casimir energy described in section 4.…”

Tunneling decay rate in quantum cosmology

“…Such models can be classically stable with respect to small perturbations [2][3][4], but it was pointed out in [5,6] that they are generically unstable with respect to decay through quantum tunneling to zero size. Our goal in the present paper is to calculate the corresponding decay rate.…”