### New Year Challenges

The Edge foundation, which tries but fails to find the cutting edge of science, asked a numbrr of people what they have changed their minds about. From Edge World Question Center, physicist Paul Steinhardt is abandoning the inflationary paradigm. For those who don't know "inflation," it didn't occur so don't bother:

"What created the structure of the universe? Most cosmologists would say the answer is "inflation," and, until recently, I would have been among them. But "facts have changed my mind" — and I now feel compelled to seek a new explanation that may or may not incorporate inflation.

"One often reads that recent measurements of the cosmic microwave background or the large-scale structure of the universe have verified a prediction of inflation. This invariably refers to a prediction based on the naïve classical view. But if the measurements ever come out differently, this could not rule out inflation. According to the quantum view, there are invariably pockets with matching properties."

With a big nod to the wondrous Kea, DARPA has issued an ambitious set of mathematical challenges.

Mathematical Challenge Twenty-two: Settle the Smooth Poincare Conjecture in Dimension 4

• What are the implications for space-time and cosmology? And might the answer unlock the secret of “dark energy”?

Now DARPA is putting "dark energy" on lower case and parentheses. More people agree that it is probably not an ethereal repulsive energy, but could be something like a changing speed of light. The Poincare Conjecture indicates that the Universe is spherical. The Ricci flow can be simplified so that $\partial_t$ g_ij = -2 R_ij = 0. This leads to a lot of math, but it also leads to GM = tc^3. The New Year will be full of challenges!

"What created the structure of the universe? Most cosmologists would say the answer is "inflation," and, until recently, I would have been among them. But "facts have changed my mind" — and I now feel compelled to seek a new explanation that may or may not incorporate inflation.

"One often reads that recent measurements of the cosmic microwave background or the large-scale structure of the universe have verified a prediction of inflation. This invariably refers to a prediction based on the naïve classical view. But if the measurements ever come out differently, this could not rule out inflation. According to the quantum view, there are invariably pockets with matching properties."

With a big nod to the wondrous Kea, DARPA has issued an ambitious set of mathematical challenges.

Mathematical Challenge Twenty-two: Settle the Smooth Poincare Conjecture in Dimension 4

• What are the implications for space-time and cosmology? And might the answer unlock the secret of “dark energy”?

Now DARPA is putting "dark energy" on lower case and parentheses. More people agree that it is probably not an ethereal repulsive energy, but could be something like a changing speed of light. The Poincare Conjecture indicates that the Universe is spherical. The Ricci flow can be simplified so that $\partial_t$ g_ij = -2 R_ij = 0. This leads to a lot of math, but it also leads to GM = tc^3. The New Year will be full of challenges!

## 3 Comments:

Great post! I wish I had more time to think about Ricci flow and the Poincare conjecture, especially using the mathematics of knots, which appear a lot in M theory. Thanks for the nod.

Thanks. The Poincare conjecture favours the spherical space we have been studying. Simplest of all if -2 R_ij = 0.

"

The Edge foundation, which tries but fails to find the cutting edge of science, asked a numbrr of people what they have changed their minds about. From Edge World Question Center, physicist Paul Steinhardt is abandoning the inflationary paradigm. For those who don't know "inflation," it didn't occur so don't bother:

""What created the structure of the universe? Most cosmologists would say the answer is "inflation," and, until recently, I would have been among them. But "facts have changed my mind" — and I now feel compelled to seek a new explanation that may or may not incorporate inflation.

That's good news!

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