f(G) Noether cosmology
  We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where
$\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically,
by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq
\mathcal{G}^k$ power-law models where $k$ is a real number. In particular, the
case $k = 1/2$ for $n=4$ results equivalent to General Relativity showing that
we do not need to impose the action $R+f(\mathcal{G})$ to reproduce the
Einstein theory. As a further result, de Sitter solutions are recovered in the
case where $f(\mathcal{G})$ is non-minimally coupled to a scalar field. This
means that issues like inflation and dark energy can be addressed in this
framework. Finally, we develop the Hamiltonian formalism for the related
minisuperspace and discuss the quantum cosmology for this model.
