Isotropic universe with almost scale-invariant fourth-order gravity
  We study a broad class of isotropic vacuum cosmologies in fourth-order
gravity under the condition that the gravitational Lagrangian be
scale-invariant or almost scale-invariant. The gravitational Lagrangians
considered will be of the form L = f(R) + k(G) where R and G are the Ricci and
Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) =
G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat
Friedmann space-time and interpret their asymptotic early-time and late-time
behaviour as well as their inflationary stages. One unique example which we
discuss is the case of a very small negative value of the parameter b in the
Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de
Sitter solution from L = R^2 (being a local attractor) to a power-law inflation
exact solution also representing a local attractor. This shows how one can
modify the dynamics from de Sitter to power-law inflation by the addition of
the G ln G-term.
