Abstract
We present a class of nonsingular, bouncing cosmologies that evade singularity theorems through the use of vorticity in compact extra dimensions. The vorticity combats the focusing of geodesics during the contracting phase. The construction requires fluids that violate the null energy condition (NEC) in the compact dimensions, where they can be provided by known stable NEC violating sources such as Casimir energy. The four dimensional effective theory contains an NEC violating fluid of Kaluza-Klein excitations of the higher dimensional metric. These spacetime metrics could potentially allow dynamical relaxation to solve the cosmological constant problem. These ideas can also be used to support traversable Lorentzian wormholes.
Highlights
Could the Universe have gone through a bounce? This question is of significant import: a bouncing universe could be past eternal and avoid the big bang singularity
As we will describe below, a spatially flat bouncing cosmology may permit a solution to the grandest hierarchy problem in physics—namely, the cosmological constant problem
Every element of our construction is necessary to evade the power of the singularity theorems: null energy condition (NEC) violation along compact directions and nonzero vorticity for 4D geodesics evades gravitational focusing, while the restriction of vorticity into just compact dimensions prevents the formation of closed timelike curves enabling the space-time to be globally hyperbolic
Summary
This question is of significant import: a bouncing universe could be past eternal and avoid the big bang singularity It could even potentially permit a new background for cosmological relaxation processes to explain hierarchy problems [1,2], or provide an alternative to the inflationary paradigm [3,4] as the origin of the hot, radiation dominated epoch in our past, see e.g. The space-time geometry is of the form R4 × X where X is a compact manifold with dimensionality ≥ 3 We endow this manifold with a nonfactorizable metric containing vorticity.1As we will show, the existence of vorticity enables a nonsingular bouncing cosmology without the need for NEC violation along the noncompact. V we comment on possible applications of our ansatz to solve the cosmological constant problem and support traversable wormholes
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