Initial conditions and degrees of freedom of non-local gravity

  • Gianluca Calcagni
  • Leonardo Modesto
  • Giuseppe Nardelli
Open Access
Regular Article - Theoretical Physics


We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are both characterized by four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.


Classical Theories of Gravity Models of Quantum Gravity Nonperturbative Effects 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Instituto de Estructura de la Materia, CSICMadridSpain
  2. 2.Department of PhysicsSouthern University of Science and TechnologyShenzhenChina
  3. 3.Dipartimento di Matematica e FisicaUniversità Cattolica del Sacro CuoreBresciaItaly
  4. 4.TIFPA — INFN c/o Dipartimento di FisicaUniversità di TrentoTrentoItaly

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