### Decelerating the Universe

It's Christmas day here in Sydney, and the rain has fallen incessantly; it feels like when I was growing up in Wales.

Anyway, I thought a short post. Over at In The Dark, Peter Coles was talking about the new results from the WMAP satellite, the latest of the probes of the Cosmic Microwave Background; I've mentioned before that I am old enough to remember the results from COBE, especially this front page story.
Basically, Peter's article points out that these observations have radically changed your understanding of the Universe. Mind you, looking at the above newspaper, and seeing "Bosnia ceasefire crumbles", tells me that in the same period, humans haven't advanced very far in the same period.

Anyway, in the comments, there was an interesting issue raised by Phillip Helbig (hi Phil!). Phillip and I are of the same vintage, and were raised on a diet of VMS before Unix became all pervasive in astronomy. Essentially, it is to do with the coincidence problem.

This is a simple problem to understand. Over cosmic history, as the universe has expanded, it was previously dominated by matter, but the density of matter has continued to thin out as the Universe got larger. However, the energy density of the other major component in the Universe, namely dark energy, remains constant even though the Universe expands.

So, in the past, the Universe was "matter-dominated", and in the future it will be "dark energy-dominated". Here's a piccy to illustrate this
The solid-line is the density of matter, and the dotted-line is the density of dark energy (normalized to the universal "Critical Density"). It's important to understand the time-scale on the x-axis, as it is logarithmic (rather than linear), so it includes everything from the tiny-time-scales of inflation, to the extensive time scale into the distant Universe. Look how rapidly (on this time axis) the change from matter dominated to dark energy dominated is.

The weird thing is that we currently find ourselves at a time where roughly a quarter of the energy density of the Universe is in matter and the other three-quarters is dark energy - so we find ourselves in the very narrow change over. We have a coincidence!!

So, where is my part in this story? Well, it's in a paper called "Through the Looking Glass: Why the "Cosmic Horizon" is not a horizon", but then MSc student, Pim van Oirschot, and then PhD student, Juliana Kwan (both of whom have moved on to better and brighter things).

The focus of the paper was not on cosmic coincidences, but we found one. We were looking at something called the deceleration parameter (normally called q).

How is q defined? It a combination of things that characterise the expansion of the Universe, its size, velocity and acceleration (for those in the know, these are the zeroth, first and second derivatives of the expansion factor with respect to cosmic time).

This is easy to understand - if the expansion of the universe is constant, then q is zero. If, however, the universe is decelerating, then q is positive. And vice-versa for acceleration.

Now, we know that during the time that dark matter dominated, then the Universe was decelerating, but now the Universe is becoming dominated by dark energy, it is accelerating. So, the question is, what is the average of the deceleration and then acceleration over cosmic history?

This is one of the things we calculated in the paper. Basically, we took the cosmic parameters as we have currently measured them and calculated the time averaged value of q. Here's what we got
So, these have the same matter and dark energy densities noted above. Along the bottom is time, where zero is today, positive is into the future, and negative is into the past. The different coloured lines are for different equations of state of dark energy (the cosmological constant is the red line with w=-1).

Let's look first at the dashed lines, as these are the normalized densities of matter in each of these cosmologies (right-hand y-axis). In the past, in all of them, the Universe was more matter dominated, and into the future the matter density continues to diminish. But notice how on this linear scale, the "coincidence" of the matter density being not to dissimilar to one is no longer so spectacular.

Now check out the solid curves (left-hand y-axis) which presented the time averaged value of q. In the past, where matter was dominating, q was positive and so the time averaged value of q was positive.

As the Universe expands and dark energy comes to dominate, then the expansion starts to accelerate, and so q becomes smaller, and (for some of the models) becomes negative. For these, there is a switch in the time averaged value of q from positive to negative. For the black model, it was in the past. For the green model it appears to be in the future. But for the red model, the cosmological constant model, it appears to be - eerrrm - right now!

If we plug in the values of the cosmological parameters as we have now measured them, and included their uncertainties, how big do we expect the time averaged value of q to be? Well -
To within the uncertainty, it is zero. The switch over is right now!

What's the significance of this? I don't know. Some think that it's a fundamental property of the Universe, telling us something deep about the cosmos that we currently don't really understand. Others think that essentially its numerology, and if you play around with enough numbers, some combinations will surprisingly be close to zero, or pi, or one, or ten etc.

But, we now have the new numbers from WMAP, telling us the parameters of the Cosmos. These have changed slightly from the last numbers, and the errors have become tighter. The question is, has the time averaged value of q changed significantly with the new numbers, and has it become even closer to zero? If it has, it is interesting.

I will get to this, but being Christmas it may not be until the New Year. Something to think about during the Twilight Zone that this week is.

Have a Merry Christmas and Happy New Year :)

1. I've re-read this post several times because some of the arguments are not at all easy for me to comprehend.

However, I get the main thrust, that "we currently find ourselves at a time where roughly a quarter of the energy density of the Universe is in matter and the other three-quarters is dark energy - so we find ourselves in the very narrow change over. We have a coincidence!!"

Why is a coincidence a problem? Maybe it would also have been a 'coincidence' if we found ourselves in an epoch of the Universe which is dominated by just one of them!

Questions:

(1) Is it right to assume that because dark energy is at about 73%, (with baryonic matter plus dark matter at 27%), that the changeover period itself is therefore also 73% completed?

(2) The logarithmic scale of the first graph(a) squeezes time so much at the "Now" point. Can you elaborate about (i) how long ago the changeover began? (ii) how much longer it will take? and (iii) whether there will ever be any effect on the local galactic scale?

Happy New Year!

2. Good questions. Coincidence are important things to look for in science. While things might be just a coincidence, they might be telling us something deeper about the universe. So, why do the proton and neutron have such similar masses? We now know it is because they are made of very similar things, and the coincidence in mass pointed towards this.

But people don't like to think we live in any kind of a special time. In the early universe, we would have seen the universe as being completely matter dominated, in the future, we will see it as being completely dark energy dominated, so why do we find ourselves in the transition between the two.

Some call on the anthropic principle as an excuse, namely that life could not have arisen in the very early universe, and it has taken to now to get to a state where we have intelligent life. In the distant future, the rapid expansion of the universe and the end of star formation means that it is likely that life could not arise then.

Others say that the coincidence means that all we know about cosmology is wrong (I am not in that boat).

1) No, the change over is non-linear. If you look at the relative matter density in the picture up there, you can see that in roughly 10 billion years, the matter density will be insignificant.

2) In the same picture, you can see how the transition has gone on in linear time. Over what we have considered as cosmic time (measured in billion of years) then matter has been steadily falling in important from the start, but in the early parts of the universe, where matter was forged etc, then dark energy was irrelevant. The answer to the last part is yes. In 10 billion years, the accelerated expansion due to dark energy will empty out the universe, leaving only the local group in this part of the universe (with nothing else to see). If, however, dark energy is phantom energy, then the milky way will be ripped apart, then individual stars, and then individual atoms, an even known as the big rip.

On that happy note, have an excellent new year :)

1. I think you mean atheists dont like coincidences because everyone else doesnt call them coincidences -they call them design. The second scientists strayed from their field into philosophy--they betrayed the public trust. They went into this trying to prove the world only appears designed--and the bias started when Einstein fudged his ad hoc static universe.

Now that they have found out it is designed==something everyone already could clearly see in all of 3 seconds--they're still trying to hide their results with ad hoc junk like multiverse and pretending that its not blatantly absurd.

Its not even intellectuality dishonest--its just dishonest. By calling the clear design they find "a problem" is the most laughable form of bias. Its Embarrassing. Just report your data and let people who can actually reason without a pathological, self refuting, bias such as atheism, sort it out.

Design has been found in countless parameters--not only in cosmology, but in our very DNA. Its time to admit that-- even though it means atheists beliefs are doomed(which is the reason the bias exists in the first place--who admits their worldview is garbage?) These guys should let the truth be the truth and stop hiding in the corner like scarred children.
I long for the day when this demented crop of fools is replaced by people who are not afraid of what the find. Its over..those who flocked to the fields of origins to prove the world is not designed have been defeated by the data 120 places to the right of the decimal point.

3. Thanks, Geraint.

To me, it only looks narrow in the logarithmic sense. On a linear time scale of tens of Gyr, the changeover seems to last for much of our mere 13 billion year history. So, some might well argue that it is not really a narrow changeover, (unless you changed the scale to hundreds of Gyr).

I guess everything is relative (or logarithmic). Have a 'ripping' New Year. :)

4. "Phillip and I are of the same vintage, and were raised on a diet of VMS before Unix became all pervasive in astronomy."

I still run a VMS cluster at home, and will upgrade to VMS 8.4 soon. In the last few days, I upgraded to faster disks. Outside of astronomy, VMS is still alive and well in many areas.

I'm sure Geraint realizes this, but the fact that the average value of q, <q>, up to now is zero is not exactly the same as the change from matter-dominated to lambda-dominated happening about now.

I think the first coincidence is similar to the fact that the Sun and the Moon have the same angular size. It is a coincidence, and one that happens only now. Any other explanation would mean something quite different than the standard cosmological framework. Not impossible, but unlikely. In other words, any explanation must make sure that the cure is not worse than the disease. :-)

If the universe expands forever, is the question why we are living near the time of transition from matter-dominated to lambda-dominated (only universes which expand forever are ever lambda-dominated) different than asking why, if the universe will last forever, are we near the beginning? (The second question can be asked at any time and so is more puzzling than the first. Thus, if the second one doesn't bother you, why should the first?) (I mention this briefly in my latest paper (written, LaTeXed and figures made with Fortran on a VMS machine): http://www.astro.multivax.de:8000/helbig/research/publications/info/flatness.html .)

5. "Essentially, it is to do with the coincidence problem."

The figure you link to in this sentence above is perhaps a bit misleading for some readers. It's not very clear in the figure, but the arrows show the direction of motion in the lambda-Omega parameter space (something seen more clearly, though without arrows, in my flatness-problem paper mentioned above).

The caption mentions that the universe is unstable in the sense that it is evolving, as if this is somehow strange. However, the first impression from the figure is that our universe is very close or even on the diagonal line, which means that it is very close to being flat or is exactly flat, but that has nothing to do with the evolution from matter to vacuum. There are flat universes which move in this diagram and those which don't, and also non-flat universes which move in this diagram and those which don't.