Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity

Abstract

We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term m2R □−2R to the Einstein-Hilbert action. The model has the same number of parameters as ΛCDM, with m replacing ΩΛ.At the background level, after fixing m so to reproduce the observed value of ΩM, we get a pure prediction for the equation of state of dark energy as a function of redshift, wDE(z), withwDE(0) in the range [−1.165,−1.135] as ΩM varies over the broad range ΩM∊[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 γ ≃ 0.53, to be compared withγ ≃ 0.55 in ΛCDM. For the Newtonian potential on subhorizon scales our results are well fitted byΨ(a;k) = [1+μsas]ΨGR(a;k)with a scale-independent μs ≃ 0.09 and s ≃ 2, while the anisotropic stress is negligibly small.