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

We discuss the modified gravity which includes negative and positive powers of the curvature and which provides the gravitational dark energy. It is shown that in GR plus the term containing negative power of the curvature the cosmic speed-up may be achieved, while the effective phantom phase (with $w$ less than -1) follows when such term contains the fractional positive power of the curvature. The minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fliud may describe the (effective phantom) dark energy. The account of $R^2$ term (consistent modified gravity) may help to escape of cosmic doomsday.Comment: LaTeX file, 9 pages, based on the talk given by S.D. Odintsov (Int. Conference Mathematical Methods in Physics, Rio de Janeiro, Augest, 2004), to appear in CQG, Letter

One-loop f(R) gravity in de Sitter universe

Motivated by the dark energy issue, the one-loop quantization approach for a family of relativistic cosmological theories is discussed in some detail. Specifically, general $f(R)$ gravity at the one-loop level in a de Sitter universe is investigated, extending a similar program developed for the case of pure Einstein gravity. Using generalized zeta regularization, the one-loop effective action is explicitly obtained off-shell, what allows to study in detail the possibility of (de)stabilization of the de Sitter background by quantum effects. The one-loop effective action maybe useful also for the study of constant curvature black hole nucleation rate and it provides the plausible way of resolving the cosmological constant problem.Comment: 25 pages, Latex file. Discussion enlarged, new references added. Version accepted in JCA