First-order formalism for scalar field in cosmology
  We present a general procedure to solve the equations of motion for cosmological models driven by real scalar fields with first-order differential equations. The method seems to have great power, since it works for closed, flat or open space-time, for scalar fields with both standard and tachyonic dynamics. We illustrate the procedure solving several examples which model situations of current interest to modern cosmology. 
D. Bazeia, L. Losano, J.J. Rodrigues