Gravity assisted dark energy dominance and cosmic acceleration
  It is proposed that dark energy may become dominant over standard matter due to universe expansion (curvature decrease). Two models: non-linear gravity-matter system and modified gravity may provide the effective phantom or effective quintessence dark energy which complies with the conjecture. It is interesting that future of such universe is not necessary finite time singularity (Big Rip). The effective quintessence naturally describes current cosmic speed-up. 
Shin'ichi Nojiri and Sergei D. Odintsov