Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and
  their cosmological applications
  We study higher derivative terms associated with scalar field cosmology. We
consider a coupling between the scalar field and the geometry inspired by the
Pais-Uhlenbeck oscillator, given by
$\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We
investigate the cosmological dynamics in a phase space. For $\alpha>0$, we
provide conditions for the stability of de Sitter solutions. In this case the
crossing of the phantom divide $w_{DE}=-1$ occurs once; thereafter, the
equation of state parameter remains under this line, asymptotically reaching
towards the de Sitter solution from below. For $\alpha<0,$ which is the portion
of the parameter space where in addition to crossing the phantom divide, cyclic
behavior is possible, we present regions in the parameter space where,
according to Smilga's classification the ghost has benign or malicious
behavior.
