In a class of models designed to solve the cosmological constant problem by
coupling scalar or tensor classical fields to the space-time curvature, th
e universal scale factor grows as a power law in the age, a proportional to
t(alpha), regardless of the matter content or cosmological epoch. We inves
tigate constraints on such "power-law cosmologies" from the present age of
the Universe, the magnitude-redshift relation, and from primordial nucleosy
nthesis. Constraints from the current age of the Universe and from the high
-redshift supernovae data require "large" alpha (approximate to 1), while c
onsistency with the inferred primordial abundances of deuterium and helium-
4 forces alpha to lie in a very narrow range around a lower value (approxim
ate to 0.55). Inconsistency between these independent cosmological constrai
nts suggests that such power-law cosmologies are not viable. [S0556-2821(99
)02304-8].