modified gravity explain accelerated cosmic expansion ?

We show that the recently suggested explanations of cosmic acceleration by the modification of gravity at small curvature suffer violent instabilities and strongly disagree with the known properties of gravitational interactions. It seems established that at the present epoch the universe expands with acceleration. It follows directly from the observation of high red-shift supernovae [1] and indirectly from the measurements of angular fluctuations of cosmic microwave background fluctuations (CMBR) [2]. The latter shows that the total mass/energy density of the universe is very close to the critical one (Ω = 1), while the observations of the universe large scale structure indicate that normal gravitating (but invisible) matter can contribute only 30% into the total one. Thus one concludes that the remaining 70% is some mysterious agent that creates the cosmological acceleration. The simplest suggestion is that the source of this acceleration is the vacuum energy (cosmological constant). However such an explanation immediately meets two serious problems. First, vacuum energy remains constant in the course of cosmic expansion (modulo possible phase transitions which could discontinuously change the value of ρ vac by a very large amount). On the other hand, " normal " cosmological energy density scales with time as ρ m ∼ m 2 P l /t 2 and it is quite strange coincidence that ρ vac and ρ m are of the same order of magnitude just today. Second and much more serious, there are known contributions into vacuum energy which are 50-100 orders of magnitude larger than the cosmologically allowed value. At the present day there is no workable scenario to solve the second problem, while the first one may be solved if instead of a constant ρ vac a new massless or very light field is introduced which evolves in the course of the expansion in such a way that its energy density today more or less naturally approaches the energy density of normal matter [3]. Still such field remains mysterious. It would be in much better shape if it simultaneously solved the problem of almost complete elimination of gigantic contributions into vacuum energy by some adjustment mechanism but, alas, it does not happen or, better to say, it is unknown how it can be realized. To avoid an introduction of additional fields (plurality should not be posited without necessity " , W. Ockham) it was suggested recently that gravity itself, if properly modified, could create cosmological …