12 problems

Let an expanding universe have a positive cosmological constant. Cosmic no-hair conjecture. All such universes asymptotically admit the de Sitter universe as a solution. This conje…

Positivity conjecture. Under these assumptions, $E_\lambda\geq 0$. The spacelike mean-curvature-vector conditions ensure that the quasi-local energy is well defined. This is the de…

Forbidden mass interval conjecture. The interval

Consider a pair of non-overlapping modes, with the formal proof restricted to modes having super-Hubble support. Non-overlapping-mode extension conjecture. The result applies to an…

Let $RH$ denote the dimensionless product of the mode's support scale $R$ and the Hubble parameter $H$. Proposition vNgeneral concerns single modes supported in super-Hubble region…

Strominger's dS/CFT conjecture. Such a duality could happen between the bulk and the future or past infinity of de Sitter spacetime, or between the bulk and the cosmological horizo…

Generalized entropy conjecture. The generalized entropy $\mathcal{S}_\text{gen}$ can only decrease when any type of matter is added. This conjecture proposes a generalized second l…

In an accelerated expanding universe, consider a nonlinear wave equation whose nonlinear term is either $|u|^p$ or $|\nabla_x u|^p$, where $p>1$. Blow-up conjecture. The equation a…

Global existence, no-bubble formation, and convergence conjecture. For smooth initial conditions, a smooth solution exists globally for all time; under some initial conditions, no…

Let $g_{ab}$ be a solution of the Einstein vacuum equations … with positive cosmological constant $\Lambda>0$. Consider inhomogeneous and anisotropic expanding solutions. Cosmic no…

Let $V(\tau,t_q)$ be the volume of a causal diamond of fixed duration $\tau$ at cosmological time $t_q$ in a spacetime solving the vacuum Einstein equations with positive cosmologi…

Cosmic no-hair conjecture. Generic elements of $\mathcal{A}$ yield maximal globally hyperbolic developments that are future asymptotically de Sitter like.