Emergent 4-dimensional linearized gravity from spin foam model

Abstract

Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity is indeed the low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter $\delta$ becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.

arXiv comment15+5 pages, 4 figures. V2 improves the presentation, and expands the discussion on the geometrical correspondence of spinfoam large-j critical points

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• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
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• Modified Graviton Dynamics From Spin Foams: The Area Regge Action
• A saddle-point finder and its application to the spin foam model