String Theory Meets Einstein - As a quick intro, here's a concise lede from the final paragraph of the OP: "Hawking [et al...] have found a way to produce expanding, accelerating universes using a negative cosmological constant. This means that string theory may, after all, describe the universe that we observe."
via +Wade Aaron Inganamort
Stephen Hawking has a big new idea: His 'Escher-verse' could be a theory of everything

Stephen Hawking has come up with a way to describe the universe that suggests it may have the same geometry as mind-boggling images by M. C. Escher

The universe may have the same surreal geometry as some of art's most mind-boggling images. That's the upshot of a study by the world's most famous living scientist, Stephen Hawking of the University of Cambridge.

The finding may delight fans of Dutch artist M. C. Escher, but Hawking's team claim that their study provides a way to square the geometric demands of string theory, a still-hypothetical "theory of everything", with the universe we observe.

Their calculations rely on a mathematical twist that was previously considered impossible. If it stands up, it could explain how the universe emerged from the big bang and unite gravity and quantum mechanics.

"We have a new route towards constructing string theory models of our world," says Hawking's colleague Thomas Hertog of the Institute for Theoretical Physics at the Catholic University of Leuven (KUL) in Belgium.

On the face of it, the idea that Escher's images can describe the layout of the universe seems to contradict what we know about it.

The images in question are tessellations, arrangements of repeated shapes, such as the images of interlocking bats and angels seen in Circle Limit IV. Although these are flat, they serve as "projections" of an alternative geometry called hyperbolic space, rather like a flat map of the world is a projection of a globe. For example, although the bats in the flat projection appear to shrink at an exponential rate at the edges, in hyperbolic space they are all the same size. These distortions in the projection arise because hyperbolic space cannot lie flat. Instead, it resembles a twisting, wiggly landscape of saddle-like hills.
That is not what our universe seems to look like. Measurements of the cosmic microwave background - the echo of the big bang - and distances to supernovae have revealed that our universe is flat, not twisted.

It is also expanding at an accelerating rate, because of a mysterious entity known as dark energy. We don't know what dark energy is or where it came from, but the mathematical language provided by Einstein's theory of general relativity has a way to describe this accelerated expansion. Sticking a constant - known as the cosmological constant - into the general-relativity equations keeps the universe expanding forever, but only if the constant has a positive sign. Until now, saying we live in an ever-expanding universe has been the same as saying our universe has a positive cosmological constant.

There are some outstanding problems, however. General relativity covers this aspect of the universe, but it can't describe the big bang. Nor can it unite gravity, which works on large scales, with quantum mechanics, which works on very small scales. "That means you cannot predict why we live in the universe that we live in," Hertog says.

String theory, in the meantime, offers a beautifully complete picture of the universe's history and connects gravity to quantum mechanics - but is most comfortable in a universe with a negatively curved, Escher-like geometry and with a negative cosmological constant.

This left physicists with a deep chasm to cross: on one side is a universe that works but lacks a complete theory, and on the other is a complete theory that doesn't describe the actual universe.

Now, Hawking, Hertog and James Hartle of the University of California, Santa Barbara, are proposing a bridge. They have found a way to produce expanding, accelerating universes using a negative cosmological constant. This means that string theory may, after all, describe the universe that we observe. The proposal grew from an idea that Hawking and Hartle had in the 1980s to get around general relativity's shortcomings by looking for a quantum picture of cosmology.
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