# Composition of the Universe can be Derived from PI?

1. Mar 22, 2013

### zeroace

New data from NASA's Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and Planck have found evidence that the composition of the universe:

• Matter - 4.9 %
• Dark Matter - 26.8 %
• Dark Energy - 68.3 %

These numbers seem almost too coincidental to numbers that come from various calculations with π:

The above numbers (I'm sure there are more exact figures but this is the best I found) means that 31.7% of the universe if made up of Matter and Dark Matter.

If you take the universe as 1 and divide it by π, you get right at the total percent of matter/dark-matter above (once again, particularly given the rough percentages)

1 / π = 0.318

The above percent ( 31.8% ) leaves 68.2 %, which is right at the total percent of dark energy in the universe ( 68.3% ).

Is there anything to this? It just seems too coincidental that dividing 1 by π gives you the latest, most accurate totals found by COBE, WAMP, and Planck for the amount of Matter/Dark-Matter in the Universe and the amount of dark energy in the universe from the remainder of 100%.

I had noticed the numbers were close previously but far enough off to forget about, but this new data puts these composition percentages DEAD ON.

Last edited: Mar 22, 2013
2. Mar 22, 2013

### mathman

It is a coincidence. It wouldn't surprise me if the numbers get changed in the future.

3. Mar 22, 2013

### zeroace

These may seem like trivial adjustments, but they are not, says Martin White, an astrophysicist at the University of California at Berkeley and a member of the Planck science team.

"For the working cosmologist, a number of these shifts are significant enough that I feel as though an awful lot of people will be doing calculations and rerunning their computer simulations with the new numbers," he says. "These are not irrelevant shifts. These are quite important."

4. Mar 22, 2013

### DennisN

Coincidence. When you juggle with numbers you can conjure up all sorts of seemingly meaningful connections, when there most likely aren't any. One classic example is the fine-structure constant which is about 1/137, but not quite. There's also the Inverse Symbolic Calculator which can produce a multitude of mathematical expressions from a single number input. Fun to play around with.

5. Mar 22, 2013

### MPKU

I'm sure you don't need to hear it a third time..

Our world isn't even in Euclidean space so I don't see why it would have anything to do with pi

6. Mar 22, 2013

### zeroace

It probably is a coincidence, but I would still like to entertain the notion.

So here's a question: the universe expands outwardly from a single point i.e. the Big Bang; would the initially expansion be equal in all directions? i.e. a circular expansion? If not, what would cause an unequal expansion in certain directions; given this is during the initial expansion when particles would not be formed yet.

7. Mar 23, 2013

### mitchell porter

I know of precisely one cosmological model which produces (through a reasoning process that I never did fathom) predictions for these numbers in terms of pi. This is Louise Riofrio's variable-speed-of-light cosmology. The numbers are supposed to be: 1-3/pi for baryonic matter, 3/4pi for dark matter, 9/4pi left over, i.e. 4.5%, 23.9%, 71.6%.

Meanwhile, the "zeroace cosmological ansatz" ;-) (we can't call it a model yet, but it's a formula) is: 1/pi for baryonic matter plus dark matter, 1-1/pi for dark energy, i.e. 31.8%, 68.2%.

I certainly find it intriguing, and good to know about such relations. Most cosmologists don't have simple formulas for these quantities, but there are a few, e.g. Chernin and Padmanabhan. It would be interesting to know if there's any set of hypotheses at all which could motivate this particular formula.

I have made sure to blog this observation here, just in case this thread disappears.

8. Mar 23, 2013

### Drakkith

Staff Emeritus
As far as we know, this is not true. The universe did not expand outwards from any point, it simply expanded everywhere. You cannot name a location in space and say 'there's the center'.

9. Mar 24, 2013

### Staff: Mentor

The ratio of (baryonic+dark matter) to (dark energy) is time-dependent. It has to be a coincidence, unless you propose something special about the current age of the universe, or a model with a completely different type of dark energy.

10. Mar 24, 2013

### mitchell porter

Arkani-Hamed et al have a paper, "A New Perspective on Cosmic Coincidence Problems", in which they try to explain the existence of a "triple coincidence" of matter, radiation, and dark energy densities, as well as the "why now" problem, of why we live in the epoch of this triple coincidence. Essentially, they construct a model in which the densities are functions of the electroweak scale and the Planck scale, such that all three densities will be of the same order, when the cosmic temperature is of order (electroweak scale)^2 / (Planck scale). (Chernin, who I cited above, presents a form of this scenario.)

They even note that the triple coincidence is "split only by O(1) coefficients such as α and π". One could try to engineer a specific model in this spirit, in which the ratio of "dark energy density" to "density of everything else" is (π-1):1, as required by the current proposal - except that this ratio is evolving, as mfb observes. And I don't see how the window in time, when the coincidence might be observed, is narrow enough for such a specific value to be meaningful.

edit: Perhaps the ultimate contrivance, to produce such a ratio in the context of this type of explanation, would be an anthropic just-so story which argued that the moment in cosmic time when the ratio is (π-1):1, is also a peak (preferably a sharp peak) in the distribution of observers in the universe's history. But at this point the theoretical effort would be getting an A+ for ingenuity and an F for plausibility...

Last edited: Mar 24, 2013
11. Mar 24, 2013

### Chalnoth

Indeed. This is the primary issue. The ratio of dark energy to matter was very different in the early universe, and it will be very different in the far future.

12. Mar 24, 2013

### mitchell porter

mfb's simple observation is a pretty lethal one for any numerology based on cosmic density fractions, so long as you assume anything at all like conventional cosmology.

My preceding comment provides an example. Arkani-Hamed et al actually produce a framework in which the existence of an order-of-magnitude cosmic coincidence has an explanation; but the coincidence is centered on a particular cosmic temperature. But we can express the variation of cosmic temperature through time as a function of "redshift" (in the cosmologist's sense of that word, as a measure of cosmic time). And now consider, for example, Marcus's recent post in which he describes the evolution of the universe according to the latest data from the Planck collaboration. Given the variation of CMB temperature with redshift, one can see that these ratios will evolve by O(1) factors in just a few billion years, so even if one could engineer a physical model to produce that (π-1):1 ratio at a certain moment, it wouldn't hold for very long on either side of that moment.

I have no comparable argument for models in which dark energy is dynamical. But how much scope is there for dynamical dark energy, anyway?

13. Mar 24, 2013

### Chalnoth

If dark energy is dynamic, it has to vary quite slowly with time, and thus there still has to be a significant change over time in the density fractions.

Some dynamical models do purport to have an explanation for how much dark energy is left, but it doesn't eve make sense to attempt to explain the precise current values of ratios that change over time. I'd rather be like going outside at 9AM and attempting to find some deep explanation for the current angle between the horizon and the Sun.

14. Mar 24, 2013

### mitchell porter

But can we be quantitative about this? Suppose, just for the hell of it, that we want the dark energy in our model to stay at 68% of the universe for as long as possible, before and after the present moment. Is there some phenomenological framework which can accept as input, say, empirical data on the expansion of the universe, and a particular scenario for the time evolution of the dark energy density fraction, and which will return as output an estimate of how unlikely this is?

edit: For example, in the cosmic coincidence paper above, when they try to answer "why now?", they concern themselves with the epoch beginning with structure formation and ending with the time when all the hydrogen has been used up. So it would be interesting to know just how implausible it is that Ωd could stay at around 68% for that whole epoch. Also... since we don't know the future... one would also need to consider scenarios in which a big rip occurred long before all the hydrogen was burned up.

Last edited: Mar 24, 2013
15. Mar 24, 2013

### TrickyDicky

This always manages to confuse me. I don't know how relic radiation from when the universe was 380000 years old can tell us what is our current ratio of dynamic dark energy to matter.
Anyone can explain this in not very technical terms?

16. Mar 24, 2013

### Staff: Mentor

If you know the distribution then and know how they evolve, you can calculate the current distribution. For (cold) matter, this is easy: The total amount is (nearly) constant. Radiation drops with the inverse scale of the size, and dark energy increases with the scale cubed (=the density is constant).

17. Mar 24, 2013

### Chalnoth

In order for dark energy to stay at the same energy fraction, it has to behave like matter (i.e. have zero pressure on cosmological scales). It can't both cause the universe to accelerate and behave like matter.

The "why now" problem only really appears if you plot the history of the universe in terms of the expansion factor. If you instead plot it in terms of time, you see that most of the history of the universe has had matter and dark energy being roughly similar in magnitude.

18. Mar 24, 2013

### Chalnoth

The primary thing we get from the CMB is the total matter (normal + dark) density. We then obtain the spatial curvature by comparing the distances between the hot and cold spots on the CMB to the nearby distances between galaxies (since those hot and cold spots are the same differences in density that seeded the nearby galaxies). When we do this, we find that the spatial curvature is very nearly flat (to within about 0.6%, according to the most recent Planck results combined with galaxy observations).

So what we have, then, is 31.75% matter, and 68.75% something else. For the most part, we have to use other observations to nail down that "something else", such as supernova or weak lensing surveys.

That said, there is a minor effect on the CMB fluctuations themselves called the Integrated Sachs-Wolfe effect. The ISW effect comes from the fact that dark energy impacts how structures in the universe form. Specifically, it acts to slowly smooth out differences in density (pushing dense regions apart and pulling voids together). What happens, then, is that if a photon enters a very large gravitational potential well, it gains some energy as it goes in. But in the time since it entered that well, dark energy has smoothed the well out slightly, so that when the photon comes out of the well, it doesn't lose quite as much energy as it gained going in, picking up a little kick (a small blueshift). The reverse happens with voids.

The overall impact of this is that it adds new large-scale fluctuations on top of the primordial CMB fluctuations, bumping up the small-scale power. You can see what happens to the CMB power spectrum due to this effect here:
http://space.mit.edu/home/tegmark/cmb/Ol_CPmovie.html

As you can see, the main effect on the top graph, which is the power spectrum of the hot and cold spots on the CMB, is on the length scale (this is the curvature bit I mentioned earlier). But there's also a blip at the very left of the graph: this is the ISW effect: with more dark energy, gravitational potentials nearby are changed more as photons pass through them.

19. Mar 24, 2013

### TrickyDicky

Thanks for the nice explanation.

That's inferred from the second and third peaks, right?

20. Mar 24, 2013

### mitchell porter

Apart from the lesson in Cosmology 101 being administered by mfb and Chalnoth, for me what's really refuting the original idea of this thread, is that 68.3% isn't an observed quantity, it is extrapolated on the basis of observations of the ancient universe plus some very general assumptions about how the universe works. Even if you wanted to throw out the theoretical framework of modern cosmology and invent some completely new type of theory, you still wouldn't be able to save the idea that this 68.3% somehow derives from a "1/π" appearing in nature, because in abandoning modern cosmology, you would also be abandoning the assumptions which lead you to infer the number 68.3% for the present-day universe!

I see a last-gasp chance for saving the idea, in this remark:
and its apparent contradiction with this remark:
The contradiction must be resolved, by saying that dark energy and matter are similar enough to be "roughly similar in magnitude", but dissimilar enough that dark energy produces a cosmic acceleration that matter does not. "Similar in magnitude" here could just mean that their density fractions differ by less than a factor of 10... close enough to be "roughly similar".

So I think the reasonable position to take is that this "rough similarity" is of interest and deserves explanation, but the detailed numerology involving 1/π does not. However, I do see a way to keep to the unreasonable path. :-)

First, you adopt an analytical framework in which the DE fraction is represented as (1-1/π)+ε(t). Implicitly you assume that the DE fraction is determined by an unknown concatenation of causes which, to a first approximation, yield a constant value of 1-1/π. Then you suppose that there are further considerations which yield the time-dependent correction ε. Finally, you try to fit this against... everything... and then you try to judge just how outlandish the results are.

The real "problem" with this way of proceeding can be seen at the start of this comment: the quantity 1-1/π came up, because of an extrapolation which made certain assumptions. If we relax those assumptions so much, then shouldn't we consider other quantities as well? For example, 2/3. 68.3% may be quite close to 1-1/π, but it's also reasonably close to 2/3...

A more general way to do all this would be to perform the analysis by representing the DE fraction simply as K+ε(t), K an unspecified constant. This could even be counted as a sort of physical hypothesis about the nature of dark energy, that it is "cold matter plus corrections".

edit: Yes, I know it sounds like you should be able to split off the alleged "matter-like part of the dark energy" and simply treat it as part of the universe's matter component. Still, I know that, for example, there are various unified phenomenological models of the dark sector, in which dark matter and dark energy are treated as different aspects of the same thing. If dark energy is "roughly similar in magnitude" to cold matter for so much of the universe's history, does that mean that we can also account for the data with a dynamical dark energy in which the genuinely dynamical part is much smaller in magnitude?

edit #2: OK, probably not, it would have something to do with the equation of state being different...

Last edited: Mar 24, 2013