Reconstruction Procedure in Nonlocal Cosmological Models

Understand

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.