We have recently considered cosmologies in which the universal scale factor
varies as a power of the age of the Universe and concluded that they canno
t satisfy the observational constraints on the present age, the magnitude-r
edshift relation for SN Ia, and the primordial element (D, He-3, He-4, and
Li-7) abundances. This claim has been challenged in a proposal that suggest
ed a high baryon density model (Ohm(B)h(2) similar or equal to 0.3) with an
expansion factor varying linearly with time could be consistent with the o
bserved abundance of primordial helium-il, while satisfying the age and mag
nitude-redshift constraints. In this paper we further explore primordial nu
cleosynthesis in generic power-law cosmologies, including the linear case,
concluding that models selected to satisfy the other observational constrai
nts are incapable of accounting for all the light clement abundances.