Abstract
We propose a lower limit on the size of a single discrete gravitational extra dimension in the context of an effective field theory for massive gravitons. The limit arises in this setup from the requirement that the Casimir energy density of quantum fields is in agreement with the observed dark energy density of the universe ρobs≃10−47GeV4. The Casimir energy densities can be exponentially suppressed to an almost arbitrarily small value by the masses of heavy bulk fields, thereby allowing a tiny size of the extra dimension. This suppression is only restricted by the strong coupling scale of the theory, which is known to be related to the compactification scale via an UV/IR connection for local gravitational theory spaces. We thus obtain a lower limit on the size of the discrete gravitational extra dimension in the range (1012GeV)−1⋯(107GeV)−1, while the strong coupling scale is by a factor ∼102 larger than the compactification scale. We also comment on a possible cancelation of the gravitational contribution to the quantum effective potential.
Highlights
Recent observations suggest that the universe is currently in a phase of accelerated expansion [1,2,3,4,5], that is assumed to be driven by an energy form with negative pressure called Dark Energy (DE)
The paper is organized as follows: In Sec. 2, we review the model for a single discrete gravitational extra dimension and briefly discuss the strong coupling behavior as the origin of the UV/IR connection
The underlying model of a discrete gravitational extra dimension exhibits a strong coupling behavior at an energy scale Λ, which depends via an UV/IR connection non–trivially on the size R of the extra dimension
Summary
Recent observations suggest that the universe is currently in a phase of accelerated expansion [1,2,3,4,5], that is assumed to be driven by an energy form with negative pressure called Dark Energy (DE). We consider a vacuum energy contribution to DE, which is generated from the Casimir effect in a single discrete gravitational extra dimension. For this purpose, we treat the gravitational theory space as a flat background for quantum fields propagating in the latticized five–dimensional (5D) bulk. In determining the Casimir energy densities of the latticized bulk fields, we assume linearized gravity and truncate the theory at the 1–loop level Since these energy densities contribute to the CC, they have to lie below the observed value ρobs ∼ 10−47 GeV4, associated with the accelerated expansion of the universe.
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