It is shown that all scalars built from the stress-energy tensor must have vanishing space-time average values in any nonrotating singularity-free universe in which the strong energy condition is satisfied. Application to the real universe, where observations seem to rule out such an “empty” universe, suggests that the hope of a reasonable realistic singularity-free cosmological model has to be abandoned.

• Received 27 December 1996

DOI:https://doi.org/10.1103/PhysRevLett.80.654