 The singularity theorems proved in the 60s (see, in particular, Hawking &amp; Ellis 1973) show that the universe is finite to the past in a broad class of cosmological models. Past singularities, signaled by the existence of inextendible geodesics with bounded length, must be present in models with a number of plausible features. (Geodesics are the curves of extreme length through curved spacetime, and freely falling bodies follow timelike geodesics.) Intuitively, extrapolating backwards from the present, an inextendible geodesic reaches, within finite distance, an “edge” beyond which it cannot be extended. There is not a uniquely defined “cosmic time”, in general, but the maximum length of these curves reflects the finite age of the universe. The singularity theorems plausibly apply to the observed universe, within the domain of applicability of general relativity. There are various related theorems differing in detail, but one common ingredient is an assumption that there is sufficient matter and energy present to guarantee that our past light cone  refocuses.[31]  The energy density of the CMB alone is sufficient to justify this assumption. The theorems also require an energy condition: a restriction on the types of matter present in the model, guaranteeing that gravity leads to focusing of nearby geodesics. (In eqn. (\(\ref{eq:Ray}\)) above, this is the case if \(\rho_{\textit{grav}} &gt; 0\) and \(\Lambda=0\); it is possible to avoid a singularity with a non-zero cosmological constant, for example, since it appears with the opposite sign as ordinary matter, counteracting this focusing effect.)