Energy conditions and constraints on the generalized non-local gravity   model
  We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity (GR) obtained by adding a term $m^{2n-2}R\Box^{-n}R$ to the Einstein-Hilbert action. Moreover, in order to get some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter $\varepsilon$ for different $n$. By analysis we give the constraints on the model parameters $\varepsilon$. 
Ya-Bo Wu, Xue Zhang, Bo-Hai Chen, Nan Zhang and Meng-Meng Wu
gr-qc