De Sitter gravitates towards holography

Kyoto University

Kyoto, Japan — Our expanding understanding of the universe may not be as exponential as the expansion of the universe itself. And in some cases, our theories about cosmic inflation may feel as if they are deflating into a black hole.

Actually, black holes may be the exact analogy needed to mathematically approximate the universe’s expansion period. This may require some thinking outside of the box, or in this case, under a ‘microscope’.

Now emerging from Kyoto University’s Yukawa Institute for Theoretical Physics is a novel approach that uses the holographic principle to describe the expanding universe in de Sitter space, in which we exist.

A hologram, which may conjure up images of interstellar video calls in sci-fi flicks, is actually a mathematical, microscopic model encoding higher-dimensional information onto a lower-dimensional structure such as a surface. With entropy-filled black holes, scientists posit that the information content encoded on its event horizon is proportional to that surface area, not the volume as in Euclidean geometry.

“To better understand the events following the Big Bang, we need a consistent theory of quantum gravity, and de Sitter universe provides a solution to Einstein’s general relativity equation with a positive cosmological constant,” says author Tadashi Takayanagi.

The mathematical microscopic model, which excludes gravity, provides a two-dimensional framework to approximate the expansion period of our three-dimensional universe. This has enabled the author to identify his first example of the two-dimensional conformal field theory or CFT that typically realizes a positive value for its cosmological constant.

“A special feature of our proposed model is to go beyond a negative cosmological constant to account for gravity on anti-de Sitter space by extending the two-dimensional microscopic model,” adds Takayanagi, “thus highlighting the importance of the holographic principle for de Sitter gravity.”

While holography for anti-de Sitter space was first proposed in 1997, the results produced from the computational model demonstrated that basic quantities agreed between classical Einstein gravity and CFT.

The author concludes, “Quantum information theory has played an essential role in black hole physics and holographic principle, raising expectations for a deeper understanding of the space-time structure of our higher-dimensional universe.”

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