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We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term m2Râ¡â2R to the Einstein-Hilbert action. The model has the same number of parameters as ÎCDM, with mreplacing Î©Î, and is very predictive. At the background level, after fixing m so as to reproduce the observed value of Î©M, we get a pure prediction for the equation of state of dark energy as a function of redshift, wDE(z), with wDE(0) in the range [â1.165,â1.135] as Î©M varies over the broad range Î©Mâ[0.20,0.36]. We find that the cosmological perturbations are well-behaved, and the model fully fixes the dark energy perturbations as a function of redshift z and wavenumber k. The nonlocal model provides a good fit to supernova data and predicts deviations from General Relativity in structure formation and in weak lensing at the level of 3-4%, therefore consistent with existing data but readily detectable by future surveys. For the logarithmic growth factor we obtain Î³â0.53, to be compared with Î³â0.55 in ÎCDM. For the Newtonian potential on subhorizon scales our results are well fitted by Î¨(a;k)=[1+Î¼sas]Î¨GR(a;k) with a scale-independent Î¼sâ0.09 and sâ2, while the anisotropic stress is negligibly small.
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