Dark Energy and Cosmic Speed-Up from Consistent Modified Gravity
  We review some modified gravity models which describe the gravitational dark energy and the possibility of cosmic speed-up. The new consistent version of such theory which contains inverse and HD curvature terms as well as new type of coupling with matter is proposed. The accelerating cosmologies are discussed there. The structure of finite-time (sudden) singularities is investigated. 
Shin'ichi Nojiri and Sergei D. Odintsov