Cosmological perturbations and structure formation in nonlocal infrared
  modifications of general relativity
  We study the cosmological consequences of a recently proposed nonlocal
modification of general relativity, obtained by adding a term
$m^2R\,\Box^{-2}R$ to the Einstein-Hilbert action. The model has the same
number of parameters as $\Lambda$CDM, with $m$ replacing $\Omega_{\Lambda}$,
and is very predictive. At the background level, after fixing $m$ so as to
reproduce the observed value of $\Omega_M$, we get a pure prediction for the
equation of state of dark energy as a function of redshift, $w_{\rm DE}(z)$,
with $w_{\rm DE}(0)$ in the range $[-1.165,-1.135]$ as $\Omega_M$ varies over
the broad range $\Omega_M\in [0.20,0.36]$. 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 $\gamma\simeq 0.53$, to be
compared with $\gamma\simeq 0.55$ in $\Lambda$CDM. For the Newtonian potential
on subhorizon scales our results are well fitted by $\Psi(a;k)=[1+\mu_s
a^s]\Psi_{\rm GR}(a;k)$ with a scale-independent $\mu_s\simeq 0.09$ and
$s\simeq 2$, while the anisotropic stress is negligibly small.
