Coasting-fluid age bound ($\frac{2}{3}\le H_0{t}_0\le 1$)

For nonnegative matter and coasting-fluid densities, $0\le {\Omega }_m\le 1$. Since $a\le {\Omega }_m+(1-{\Omega }_m)a\le 1$ on the normalized integration interval, the age integrand lies between $\sqrt{a}$ and one. The age of a flat matter-coasting-fluid universe therefore decreases monotonically with the matter fraction and stays between the pure-fluid endpoint ages.