Tuesday, September 05, 2006

Inflation Leaking


Thank you, ST LOUIS for being gateway to the American West, building a great arch, financing Lindbergh's flight and being home to the McDonnell-Douglas plant, among other things. Many pilots have enjoyed the "Viking" takeoff, when an F-15 fresh from the factory lifts off and does an immediate 90 degree climb. Thank you also for reaching the milestone of 1000+ viewings! Welcome, PARIS to the 100 viewings club. I would love to hear from you sometime.

Concerning Steve Irwin, we should all applaud those willing to take risks. Today it is easy to be anonymous hiding behind a computer terminal. Sticking one's neck out invites criticism, slings and arrows. If not for the Steven Irwins, the Jacqueline Cochrans, or the Einsteins the world would not move forward. We need to encourage potential leaders not snipe at them.

When Stephen Hawking first proposed that Black Holes give off radiation, the idea seemed to defy common sense. The moderator of his talk got up and said, "Sorry Stephen, but this is absolute rubbish." Fortunately, others checked Hawking's calculation and the idea was soon accepted. Hawking's startling idea began his climb to fame.

Alan Guth first proposed the inflationary idea to explain problems with Big Bang cosmology, like uniformity in the microwave background and the apparent flatness. Inflation predicts that quantum density fluctuations expanded to form the seeds of structures. Because this idea was couched in the language of particle physics, it was quickly accepted. Now that the older generation is preparing to move on, new ideas are needed. Even the inflationary paradigm is leaking.

To answer Mahndisa's wise question: It is fashionable to say that the Universe is flat, like the Earth. Even the tiniest mass causes it to be curved. If you squeeze a cosmologist, they will admit that it must have begun with a finite topology, like a sphere. Inflation would have expanded a sphere so big that it would appear flat to our experience. Like an insect's view of the Earth, it is only flat if you can't conceive all of it!

It is also fashionable to say that WMAP "proves" inflation. The incredible force that would make the Universe expand at warp speed is still just a speculation. Inflation predicts that density fluctuations are the same at all scales. In fact, fluctuations are virtually zero for angles greater than 60 degrees, disproving inflation's prediction.

The above graph was given to me by Dr. Ned Wright of the WMAP team. As you can see, inflation's predicted spectrum is ruled out by both WMAP and COBE. The red line is a prediction of a Unified Space/Time. This prediction is hard to distinguish from the data points. Lack of large-scale fluctuations shows that the Universe is curved, just as a ship disappearing over the horizon shows that Earth is round.

Some people refused to peer in Galileo's telescope for fear of upsetting their Ptolemaic worldview. A growing number of cosmologists are aware of deficiencies in the "standard model." The WMAP team's latest report concludes: "An alternative model that better fits the low l data would be an exciting development." Time to look at those new models, boys!

13 Comments:

Blogger Kea said...

Wow, another pretty graph! It's like all our christmases coming at once!

2:09 PM  
Blogger Kea said...

Unfortunately, the term 'flatness' means SO many different things mathematically. In a sense, a volume V = 2 pi^2 r^3
= (pi r^2)(2 pi r) is just the volume of a torus with 'barely a hole' in the middle - a nice 'flat' space.

2:25 PM  
Blogger Mahndisa S. Rigmaiden said...

09 05 06

Thanks Louise:
Yes Kea I see what you mean. One of the papers I read by Thomas Thiemann did LQG in an asymptotically flat spacetime. However I have read that the Einstein equations admit chaotic solutions and that there even may be some fractal discretizations of black hole boundaries. These are curiosities and I will cite the sources so you guys can comment.

Also, if there is a fractal discretization of spacetime, then the thought of flatness really takes on another meaning because of how the Hausdorff dimension is defined and the fact that some fractals have Lesbesge measure zero. In that context, Einstein's equations admit many differing solutions. Perhaps some solutions describe some sectors of the universe and others describe other sectors. Hmmm Interesting post Louise:)

3:52 PM  
Blogger Mahndisa S. Rigmaiden said...

09 05 06

OK guys here are some of the links I was referring to. In particular, I wonder how this fits in with changing C according to your theory Louise:)

1. Chaos and Fractals around Black Holes, Dettman et al.

2.Fractals and Symbolic Dynamics as Invariant Descriptors of Chaos in General Relativity, Cornish et al.

4:04 PM  
Blogger L. Riofrio said...

Thanks, all. Kea, the toroidal model may also work. Great that you know the 2 pi^2 r^3 formula for volume! Much confusion comes from multiple definitions of "flat." the model I've been working on has a "flat" density but is geometrically curved.

Mahndisa, I just speed-read through those papers. From what I have seen, a fractal discretization works within the very broad envelope I am proposing. The first paper notes that fractal geometry can be seen in Saturn's Rings and other places. The paper does use the annoying h=c=1, which prevents one from seeing c change. It also uses the static metric, which works better in a static Universe. The results for Hawking radiation are changed very little by c change.

Second paper is entertaining too. It is very possible that spacetime is quantized. What I came up with just gives the very broad dimensions. If h changes, that may increase the amount of quantization. These discussions are the best on blogger!

6:02 PM  
Blogger Kea said...

Thanks, Mahndisa, but I'm not sure when I'll get a chance to look carefully at these papers. The second one certainly looks interesting. In the abstract they mention 'coordinate independent' ways of looking at chaos. Symbolic dynamics comes up naturally in the relation between knot theory and dynamical systems. My collaborator and I are not looking at this directly at present, but we are looking at some related algebraic structures for black holes and quantum computation.

6:32 PM  
Blogger InsightAction said...

Okay here we go, I think I can put this in words.

I still don't understand why, if you are willing to hypothesize that 'c' is time dependent, why 'G' or 'M' can't be time dependent either. Which leads to the ugly question how do you define 'M' the total mass/energy of the universe? Isn't this an observer depenendent quantity? Now clearly if two observers can be mapped into each offer by diffeomorphic local Lorentz boosts(causally related) then the conservation of energy requires that 'M' is the same for both; however if one has even a modest acceleration in space (e.g. Rindler Spaces) there are observers that cannot be causually related. So which 'M' is to be used and by whom?

8:47 AM  
Blogger L. Riofrio said...

Mass M = density rho times volume V. Kea has the formula for V.

Both Dirac and Eddington tried varying-G cosmologies. These were disproven by multiple experiments, including one that used Viking lander data to show that Mars' orbital period wasn't changing. If G varied, planetary orbits would not be stable and life could not have evolved on Earth.

Varying M invokes continuous creation of matter. Below the stable density (Omega=1) matter can be created through pair production. A lot of this may have happened near the Big Bang. Net change in M would be close to zero today, since we are near the stable density.

9:18 AM  
Blogger InsightAction said...

Hmmm,

Solar system observations only show that G hasn't changed in our neighbourhood.

But more tricky is this idea of volume. Do you mean all volume of all of space-time past and future? Or do you mean a specific sectioning of space-time, ie volume coincident with an observer like earth? In which case again volume is an observer dependent quantity, which if you assume isotropic matter density makes the mass term an observer dependent quantity.

9:50 AM  
Anonymous Eirik said...

That graph looks really convincing. How do you get that power spectrum from your model? I have no idea how calculations like that are done. Please show how you derive it.

1:05 PM  
Blogger Kea said...

...which if you assume isotropic matter density makes the mass term an observer dependent quantity.

insightaction

The way I look at it (from QG) everything is observer dependent, but here we are always talking about one kind of observer, a human on Earth. One needs to start with the question 'what is it I am looking at from here?'. Given the constraints of Louise's cosmological evolution, such as the fixed M from our local late-universe perspective, the relation between various quantities then follows.

2:13 PM  
Blogger L. Riofrio said...

eirik, those are spherical harmonics, which are more than I can fit here. I have found that you can model the graph with Legendre polynomials too. The WMAP website links to papers with some of the math.

Here is a way you can try with a graphing calculator. Theory says that R = ct, and the biggest possible density fluctuation has wavelength 2pi.

Graph \sum {cos(nx)} from x = 0 to x = 90 degrees, with n running from 1 to as high as you want. The harmonics cancel each other out above 60 degrees.

The inflationary paradigm says that the universe has infinite size, and density fluctuations occur at all scales. This prediction is ruled out by WMAP and COBE.

6:41 PM  
Anonymous Dr. Health said...

Because this idea was couched in the language
of particle physics, it was quickly accepted.

3:01 AM  

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