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arXiv · 2401.14643

Deficit Angles in 4D Spinfoam with Cosmological Constant: (Anti) de Sitter-ness and More

Muxin Han·Qiaoyin Pan
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Abstract

This paper investigates the critical behaviors of the 4-dimensional spinfoam model with cosmological constant for a general 4-dimensional simplicial complex as the discretization of spacetime. We find that, at the semi-classical regime, the spinfoam amplitude is peaked at the real critical points that correspond to zero deficit angles (modulo $4\pi\mathbb{Z}/\gamma$) hinged by internal triangles of the 4-complex. Since the 4-simplices from the model are of constant curvature, the discrete geometry with zero deficit angle manifests a de Sitter (dS) spacetime or an anti de Sitter (AdS) spacetime depending on the sign of the cosmological constant fixed by the boundary condition. The non-(A)dS spacetimes emerge from the complex critical points by an analytic continuation to complex configurations.

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Muxin Han, Qiaoyin Pan. 2024-01-26. Deficit Angles in 4D Spinfoam with Cosmological Constant: (Anti) de Sitter-ness and More. https://arxiv.org/abs/2401.14643

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