Singularity Avoidance in Nonlinear Quantum Cosmology

Abstract

Abstract. We extend our previous study on the effects of an information-theoretically motivated nonlinear correction to the Wheeler-deWitt equation in the minisuperspace scheme for FRW universes. Firstly we show that even when the geometry is hyperbolic, and matter given by a cosmological constant, the nonlinearity can still provide a barrier to screen the initial singularity, just as in the case for flat universes. Secondly, in the flat case we show that singularity avoidance in the presence of a free massless scalar field is perturbatively possible for a very large class of initially unperturbed quantum states, generalising our previous discussion using Gaussian states.

Information and Particle Physics

“…[4,5] needs motivation: It can be constructed axiomatically [6,7] as the simplest measure satisfying constraints suitable to the context, just as the Gibbs-Shannon entropy measure is the simplest expression satisfying the requirements for statistical mechanics [1,8]. Relaxing the constraints gives generalised measures [9], such as the Kullback-Liebler entropy [10], which then lead within the maximum uncertainty approach to nonlinear Schrodinger equations whose properties have been further investigated [11,12,13,14]; an application to quantum cosmology [15,16] used the nonlinear equations to model expected new physics at the Planck scale: it was found that even a weak nonlinearity could replace the Big Bang singularity by a bounce.…”