  We consider multidimensional gravity with a Lagrangian containing the Ricci
tensor squared and the Kretschmann invariant. In a Kaluza-Klein approach with a
single compact extra space of arbitrary dimension, with the aid of a
slow-change approximation (as compared with the Planck scale), we build a class
of spatially flat cosmological models in which both the observed scale factor
$a(\tau)$ and the extra-dimensional one, $b(\tau)$, grow exponentially at large
times, but $b(\tau)$ grows slowly enough to admit variations of the effective
gravitational constant $G$ within observational limits. Such models predict a
drastic change in the physical laws of our Universe in the remote future due to
further growth of the extra dimensions.
