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dS/CFT is a form of gauge/gravity duality introduced by Andrew Strominger. It’s quite different from the more-familiar AdS/CFT, which is amenable to string-theoretic methods, and involves a conformal field theory living on the timelike boundary of the hyperbolic Anti-de Sitter space solution to Einstein’s field equations. The boundary has one spatial dimension fewer than the bulk (interior spacetime), and translations in this radial direction come from renormalization group flow on the boundary. In particular, short-distance (high-momentum) physics in the bulk comes from long-distance (low-momentum) physics on the boundary, and vice versa.

On the other hand, dS/CFT is a gauge/gravity duality for the de Sitter space solution to the Einstein equations, which is resistant to string-theoretic methods (but seems to work well with Vasiliev gravity). In this positively-curved space, the conformal field theory has no timelike boundary to live on, and instead lives on the spacelike boundary at future infinity. Now it is the time evolution which emerges from (reverse) renormalization group flow on the boundary! In other words, the long-distance (low-resolution) features of the boundary at future infinity correspond to the bulk’s past, and vice versa. Strominger suggests that the distant past and future of our universe (which indeed appears to be asymptotically de Sitter in both time directions) correspond to conformal fixed points of the boundary renormalization group flow. This means that the future infinity boundary is scale-invariant (looks like a fractal) at very high and very low resolution.

Conformal cyclic cosmology, put forth by Roger Penrose and Vahe Gurzadyan, suggests that the future and past boundaries of FLRW spacetimes with positive cosmological constant (such as dS) should both be described by a conformally invariant theory, and that furthermore these two boundaries are conformally equivalent. As a result, the conformal future of one “aeon”, as they call the period between boundaries, can be sewn onto the conformal past (i.e. big bang) of the next: thus, history loops on a cosmological scale.

Edward Witten - What Every Physicist Should Know About String Theory

The first half of this lecture is a very nice and uncomplicated explanation of how quantum general relativity in 1 dimension (with some matter fields) is equivalent to a quantum field theory on a (possibly curved) manifold, whose dimension is equal to the number of matter fields. This is done in a Euclidean (rather than Lorentzian) signature to avoid technicalities.