Where new gravitational physics comes from: M-theory?

It is suggested \cite{CDTT} that current cosmic acceleration arises due to modification of General Relativity by the terms with negative powers of curvature. We show that time-dependent (hyperbolic) compactifications of string/M-theory lead to the effective 4d gravity which naturally contains such terms. The same may be achieved in braneworld by the proper choice of the boundary action. Hence, such a model which seems to eliminate the need for dark energy may have the origin in M-theory.