Reconstruction Procedure in Nonlocal Cosmological Models
  A nonlocal gravity model is considered which does not assume the existence of
a new dimensional parameter in the action and includes a function $f(\Box^{-1}
R)$, with $\Box$ the d'Alembertian operator. Using a reconstruction procedure
for the local scalar-tensor formulation of this model, a function f is obtained
for which the model exhibits power-law solutions with the Hubble parameter
$H=n/t$, for any value of the constant n. For generic n - namely except for a
few special values which are characterized and also specifically studied - the
corresponding function f is a sum of exponential functions. Corresponding
power-law solutions are found explicitly. Also the case is solved in all detail
of a function f such that the model contains both de Sitter and power-law
solutions.
