Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss modified gravity which includes negative and positive powers of curvature and provides gravitational dark energy. It is shown that in GR plus a term containing a negative power of curvature, cosmic speed-up may be achieved while the effective phantom phase (with w less than −1) follows when such a term contains a fractional positive power of curvature. Minimal coupling with matter makes the situation more interesting: even 1/ R theory coupled with the usual ideal fluid may describe the (effective phantom) dark energy. The account of the R 2 term (consistent modified gravity) may help to escape cosmic doomsday.