A solution of the $(4+n)$-dimensional vacuum Einstein equations is found for which spacetime is compactified on an $n$-dimensional compact hyperbolic manifold ($n\ge 2$) of time-varying volume to a flat four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmology undergoing a period of accelerated expansion in the Einstein conformal frame. This shows that the “no-go” theorem forbidding acceleration in “standard” (time-independent) compactifications of string or M theory does not apply to “cosmological” (time-dependent) hyperbolic compactifications.

• Received 19 March 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.061302