Observational Constraints On Power-Law Cosmologies
  In a class of models designed to solve the cosmological constant problem by coupling scalar or tensor classical fields to the space-time curvature, the universal scale factor grows as a power law in the age, $a \propto t^\alpha$, regardless of the matter content or cosmological epoch. We investigate constraints on such "power-law cosmologies" from the present age of the Universe, the magnitude-redshift relation, and from primordial nucleosynthesis. Constraints from the current age of the Universe and from the high-redshift supernovae data require "large" $\alpha$ ($\approx 1$), while consistency with the inferred primordial abundances of deuterium and helium-4 forces $\alpha$ to lie in a very narrow range around a lower value ($\approx 0.55$). Inconsistency between these independent cosmological constraints suggests that such power-law cosmologies are not viable. 
M. Kaplinghat, G. Steigman, I. Tkachev, and T. P. Walker