No-naked-singularity conjecture for cosmological spacetimes

Let $(\widetilde{M}, \widehat{g})$ be a smooth, time-oriented, globally hyperbolic Lorentzian $(3+1)$-dimensional spacetime with $\widetilde{M} \cong M \times \mathbb{R}$, where $M$ is a closed, connected, oriented three-manifold. Suppose $\widehat{g}$ satisfies the Einstein field equations

$$\operatorname{Ric}_{\widehat{g}} - \tfrac{1}{2} R_{\widehat{g}} \widehat{g} + \Lambda \widehat{g} = \mathcal{T}.$$

Here $\Lambda \in \mathbb{R}$ is the cosmological constant and $\mathcal{T}$ is a smooth energy-momentum tensor obeying the dominant energy condition and representing physically reasonable matter and radiation content. No-naked-singularity conjecture. For an open and dense set of smooth initial data prescribed on a Cauchy hypersurface $M \times \{t_0\}$ satisfying the Einstein constraint equations, the maximal globally hyperbolic development $(\widetilde{M}, \widehat{g})$ does not develop a future naked singularity; that is, any future singularity, if it forms, is not visible to any future-directed timelike curve originating from the initial hypersurface. This is a cosmological analogue of weak cosmic censorship. The supplied text gives no resolution or established range of validity, so the conjecture remains open.