Age of a flat barotropic matter-vacuum universe ($t_0=\frac{2\mathrm{artanh}\sqrt{{\Omega }_{\Lambda 0}}}{3(1+w)H_0\sqrt{{\Omega }_{\Lambda 0}}}$)

The flat barotropic matter-vacuum solution has $H_{\Lambda }/H_0=\sqrt{{\Omega }_{\Lambda 0}}$ and therefore the displayed age, measured from its Big Bang. At fixed $H_0$ and density fractions it is $1/(1+w)$ times the dust-plus-vacuum age. Its $w=0$ case is the age of a flat matter-Lambda universe.