Hydrogen-like spectrum of spontaneously created brane universes with de-Sitter ground state

Aharon Davidson

doi:10.1016/j.physletb.2018.01.044

Abstract

Unification of Randall–Sundrum and Regge–Teitelboim brane cosmologies gives birth to a serendipitous Higgs–deSitter interplay. A localized Dvali–Gabadadze–Porrati scalar field, governed by a particular (analytically derived) double-well quartic potential, becomes a mandatory ingredient for supporting a deSitter brane universe. When upgraded to a general Higgs potential, the brane surface tension gets quantized, resembling a Hydrogen atom spectrum, with deSitter universe serving as the ground state. This reflects the local/global structure of the Euclidean manifold: From finite energy density no-boundary initial conditions, via a novel acceleration divide filter, to exact matching conditions at the exclusive nucleation point. Imaginary time periodicity comes as a bonus, with the associated Hawking temperature vanishing at the continuum limit. Upon spontaneous creation, while a finite number of levels describe universes dominated by a residual dark energy combined with damped matter oscillations, an infinite tower of excited levels undergo a Big Crunch.

Highlights

The no-boundary proposal [1] invokes basic quantum mechanics to avoid the classically unavoidable Big Bang singularity
The simplest model of this kind is constructed at the level of the mini superspace, requires a positive cosmological constant Λ > 0, and can only be implemented for a closed k > 0 space
Exporting the Dirac prescription to the gravitational regime [12] allows us to treat the variety of models as special limits of a single unified brane cosmology

Summary

Introduction

The no-boundary proposal [1] invokes basic quantum mechanics to avoid the classically unavoidable Big Bang singularity. A variant which introduces a supplementary embryonic era can be realized, ad-hoc [2] by including a radiation energy density term, field theoretically by invoking the embedding approach [3], or via the landscape of string theory [4]. The theoretical highlight of the no-boundary proposal is the wave function of the universe, the solution of the Schrodinger Wheeler-deWitt (WdW) equation [6].

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Conclusion