 Third, FLRW models with ordinary matter have a singularity at a finite time in the past. Extrapolating back in time, given that the universe is currently expanding, eqn. (\(\ref{eq:Ray}\)) implies that the expansion began at some finite time in the past. The current rate of expansion is given by the Hubble parameter, \(H_0 = (\frac{\dot{R}}{R})_0\). Simply extrapolating this expansion rate backward, from eqn. (\(\ref{eq:Ray}\)) the expansion rate must increase at earlier times, so \(R(t) \rightarrow 0\) at a time less than the Hubble time Hubble time \(H_0^{-1}\) before now, if \(\rho_{\textit{grav}}\geq 0\). As this “big bang” is approached, the energy density and curvature increase without bound provided \(\rho_{\textit{inert}}\coloneqq (\rho+p)&gt;0\) (which condition guarantees that \(\rho \rightarrow\infty\) as \(R\rightarrow0\)). This reflects gravitational instability: as \(R(t)\) decreases, the energy density and pressure both increase, and they both appear with the same sign on the right hand side of eqn. (\(\ref{eq:Ray}\)), hence pressure \(p&gt;0\) does not help avoid the singularity. Work in the 1960s, discussed below in  §4.1,  established that the existence of a singularity holds in more realistic models, and is not an artifact of the symmetries of the FLRW models.