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Ricci Flow Approach to the Cosmological Constant Problem

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Abstract

In order to resolve the cosmological constant problem, the notion of reference frame is re-examined at the quantum level. By using a quantum non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame is proposed. The underlying mathematical structure is a new geometry endowed with intrinsic second central moment (variance) or even higher moments of its coordinates, which generalizes the classical Riemannian geometry based on only first moment (mean) of its coordinates. The second central moment of the coordinates directly modifies the quadratic form distance which is the foundation of the Riemannian geometry. At semi-classical level, the second central moment introduces a flow which continuously deforms the Riemannian geometry driven by its classical Ricci curvature, which is known as the Ricci flow. A generalized equivalence principle of quantum version is also proposed to interpret the new geometry endowed with at least second moment. As a consequence, the spacetime is stabilized against quantum fluctuation, and the cosmological constant problem is resolved within the framework. With an isotropic positive curvature initial condition, the long flow time solution of the Ricci flow exists, the accelerating expansion universe at cosmic scale is an observable effect of the spacetime deformation of the normalized Ricci flow. A deceleration parameter − 0.67 consistent with measurement is obtained by using the reduced volume method introduced by Perelman. Effective theory of gravity within the framework is also discussed.

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Acknowledgements

This work was supported in part by the National Science Foundation of China (NSFC) under Grant No. 11205149, and the Scientific Research Foundation of Jiangsu University for Young Scholars under Grant No. 15JDG153.

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  1. Department of Physics, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    M. J. Luo

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Luo, M.J. Ricci Flow Approach to the Cosmological Constant Problem. Found Phys 51, 2 (2021). https://doi.org/10.1007/s10701-021-00405-4

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