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Emergent four-dimensional linearized gravity from a spin foam model

2019; American Physical Society; Volume: 100; Issue: 2 Linguagem: Inglês

10.1103/physrevd.100.024060

2470-0037

Muxin Han, Zichang Huang, Antonia Zipfel,

Cosmology and Gravitation Theories

Spin foam models (SFMs) are covariant formulations of loop quantum gravity (LQG) in four dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying the 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 can arise as a 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 $\ensuremath{\delta}$ becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.