Einstein–de Sitter universe

An Einstein-de Sitter universe is a spatially flat expanding model containing only pressureless matter, with zero cosmological constant. Conservation of matter gives $\rho \propto a^{-3}$; inserting this into the Friedmann equations gives $a\propto t^{2/3}$ in cosmic time. Since $dt=ad\tau$, it also gives $a\propto {\tau }^2$ and $\mathcal{H}=2/\tau$ in conformal time. These simple powers make the model useful for isolating gravitational growth, rather than representing the full matter content at every epoch of the actual universe.