Exact cosmological solutions from Hojman conservation quantities
  We present a new approach to find exact solutions for cosmological models. By
requiring the existence of a symmetry transformation vector for the equations
of motion of the given cosmological model (without using either Lagrangian or
Hamiltonian), one can find corresponding Hojman conserved quantities. With the
help of these conserved quantities, the analysis of the cosmological model can
be simplified. In the case of quintessence scalar-tensor models, we show that
the Hojman conserved quantities exist for a wide range of V(\phi)-potentials
and allow to find exact solutions for the cosmic scale factor and the scalar
field. Finally, we investigate the general cosmological behavior of solutions
by adopting a phase-space view.
