Oldness/Flatness Problem

[otseng]

This has been mentioned a couple of times in different threads: Anthropic Principle and Intelligent Creation (God) as opposed to Evolution. But, I'd like to put this in its own thread.

So for debate. Why is the universe flat? That is, why does it have Euclidean geometry?

[Goat]

This has been mentioned a couple of times in different threads: Anthropic Principle and Intelligent Creation (God) as opposed to Evolution. But, I'd like to put this in its own thread.

So for debate. Why is the universe flat? That is, why does it have Euclidean geometry?

It is 'flat' because the inital conditions of the universe had a period of what is called 'inflation'.. where there was a spurt of very very fast expansion. This drove the numbers that we look at to figure out if a universe if 'flat' or 'open' close to the blance point. (maybe exactly on the balance point).

[juliod]

That is, why does it have Euclidean geometry?

I'm not entirely sure of my philosophophysics, but are we sure we have Euclidean geometry? IIRC, Euclid's 5th postulate has never been proven (the one about parallel lines). We assume it is true, and that gives us our geometry.

But some looney mathameticians have proven that other geometries were the 5th postulate is false are equally valid. It's not clear that if the universe had one of these other geometries that we could tell the difference.

It all goes to my view that math is a convention, not a philosophy or quasi-religious belief system.

DanZ

[otseng]

I'm not entirely sure of my philosophophysics, but are we sure we have Euclidean geometry?

All measurements confirm that the universe is flat (Euclidean).

To astronomers, flat means that the usual rules of geometry are observed - light not being bent by gravity travels in straight lines, not curves. But since Albert Einstein proposed that the Universe may be "curved", the debate has been open.

Scientific opinion has moved towards a flat Universe and the latest data confirm this with greater certainty than ever before.

http://news.bbc.co.uk/1/hi/sci/tech/727073.stm

The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were open, the brightest microwave background fluctuations (or "spots") would be about half a degree across. If the universe were flat, the spots would be about 1 degree across. While if the universe were closed, the brightest spots would be about 1.5 degrees across.

Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know that the universe is flat with only a 2% margin of error.

http://map.gsfc.nasa.gov/m_uni/uni_101shape.html

The results of the first flight of the MAXIMA balloon-borne study of the cosmic microwave background radiation, released May 9, 2000, agree with the results of the BOOMERANG Antarctic flight, announced April 26, in the all-important conclusion that the universe is flat.

http://www.lbl.gov/Science-Articles/Arc ... sults.html

[otseng]

One consequence of general relativity is that the curvature of space depends on the ratio of rho to rho(crit). We call this ratio Ω = rho/rho(crit). For Ω less than 1, the Universe has negatively curved or hyperbolic geometry. For Ω = 1, the Universe has Euclidean or flat geometry. For Ω greater than 1, the Universe has positively curved or spherical geometry.

The figure above shows a(t) for three models with three different densities at a time 1 nanosecond after the Big Bang. The black curve shows the critical density case with density = 447,225,917,218,507,401,284,016 gm/cc. Adding only 1 gm/cc to this 447 sextillion gm/cc causes the Big Crunch to be right now! Taking away 1 gm/cc gives a model with Ω that is too low for our observations. Thus the density 1 ns after the Big Bang was set to an accuracy of better than 1 part in 447 sextillion. Even earlier it was set to an accuracy better than 1 part in 10E59! Since if the density is slightly high, the Universe will die in an early Big Crunch, this is called the "oldness" problem in cosmology. And since the critical density Universe has flat spatial geometry, it is also called the "flatness" problem -- or the "flatness-oldness" problem. Whatever the mechanism for setting the density to equal the critical density, it works extremely well, and it would be a remarkable coincidence if Ω were close to 1 but not exactly 1.

http://www.astro.ucla.edu/~wright/cosmo_03.htm

So, 1 nanosecond after the Big Bang, the density was the universe was exactly 447,225,917,218,507,401,284,016 gm/cc. Any deviation of 1 gm/cc would cause the universe to be non-Euclidean. So, as the article states, "it is quite remarkable that Ω is anywhere close to 1 now."

[QED]

Like Goat said,

The solution to both the flatness and horizon problems is due to a phase of the Universe called inflation. Currently, inflation is the only theory that explains why the observable Universe is both homogeneous and causally connected.

(No particular authority on the subject but I thought the above lecture notes gave a good brief)

We have a major selection effect here as well. The Anthropic Principle has already been mentioned, and as it instructs, we must accept that any universe observed by carbon based life can only be one with properties conducive to carbon based life. While this tells us nothing about how this situation has come to be, it can present us with possibilities that would make our presence (and the apparent fine-tuning of the dimensionless constants of nature) unremarkable. So we are not compelled to be surprised.

[otseng]

However, it does not address why the cosmic lottery picked the number 447,225,917,218,507,401,284,016 which happens to be the winning jackpot number.

Statistically, we are compelled to be surprised and even at awe.

[Goat]

However, it does not address why the cosmic lottery picked the number 447,225,917,218,507,401,284,016 which happens to be the winning jackpot number.

Statistically, we are compelled to be surprised and even at awe.

That is what the inflationary theory addresses. .. why the universe is so flat.

[juliod]

However, it does not address why the cosmic lottery picked the number 447,225,917,218,507,401,284,016 which happens to be the winning jackpot number.

Statistically, we are compelled to be surprised and even at awe.

Why awe? Why surprise? That seems like a "random" number. No mystical significance, no signature of god.

For any physical principle you care to define there has to be a specific numerical value associated with it. No particular value is more rare or unusual than any other.

DanZ

[otseng]

That is what the inflationary theory addresses. .. why the universe is so flat.

Please present how inflationary theory addresses how it came to be 447,225,917,218,507,401,284,016.

Why awe? Why surprise? That seems like a "random" number. No mystical significance, no signature of god.

For any physical principle you care to define there has to be a specific numerical value associated with it. No particular value is more rare or unusual than any other.

Any other number would result in a non-Euclidean geometry of the universe. That is what makes it special. It is the only number that fulfills this.