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De Sitter Cosmic Model Revival

Posted June 04, 2012 9:00 AM by Jorrie

Dutchman Willem de Sitter developed an expanding cosmological solution[1] to Einstein's field equations (EFEs) in the same year that Einstein made his "biggest blunder" - 1917.

The "blunder" was adding a cosmological constant (Λ) to the EFE's in order to keep his cosmos from collapsing or expanding. On the other hand, de Sitter's expanding model sported only Λ and nothing else - no matter, no radiation, or at least the latter two had no effect on the expansion dynamics. What's more, de Sitter's model was a rigorous solution to the EFEs.

Although Einstein could not find any mathematical error in de Sitter's work, he argued that it could not possibly have any physical meaning and must hence be just an artifact of the math. After all, the real cosmos had both matter and radiation energy and it was static, as far as observations went at the time. Further, his general theory was all about matter curving spacetime and how curved spacetime affects the movements of radiation and matter.

When Hubble discovered that the universe was indeed expanding, Einstein dropped Λ from the EFEs, but the fact that his own theory did allow a solution with zero matter remained a puzzle. This was 'resolved' by the fact that Friedman and Lemaitre had already found other workable expanding solutions to the EFEs, which did not only allow radiation and matter to enter the model, but they did not need Λ at all.

The de Sitter cosmic model was all but forgotten, until in the 1980s, when cosmologists attempted to solve the 'flatness' and the 'horizon' problems of the standard model that cropped up out of observations.[2] Alan Guth's inflation theory solved both problems and it was found that it is compatible with de Sitter cosmology, with Λ of course. When accelerating expansion was discovered in the late 1990s, it was soon realized that as time goes on, the cosmos may be heading more and more towards a de Sitter type expansion. The de Sitter model was then taken very seriously, because it seemed to describe the 'opening' and the 'end games' pretty adequately. (Picture on right from http://www.science20.com/hammock_physicist/geometry_big_bang-90461. See final paragraph below.)

But what about the 'middle game', which is all we can really observe? We surely see a lot of radiation, especially in the early mid-game and we observe a lot of matter. Well, maybe not all that much, because today the radiation energy density is negligible and the normal matter density is about 4% of what is needed for the 'flatness' we observe. The rest is dark matter and dark energy - unobserved, with only "circumstantial evidence".

Since our observational accuracy on things like large-scale distances (and hence the Hubble constant) does not really make the ±4% mark, it makes one uncomfortable, to say the least. Granted, there are many corroborating pieces of evidence that point towards the 'best-buy' values used by cosmologists today. But, they are invariably all interpreted along the lines of the currently preferred Lambda Cold Dark Matter (ΛCDM) model. What if they would be interpreted using the de Sitter model?

To do such an interpretation is beyond my knowledge, but fortunately there are more capable people around, e.g. the Blog from where I ripped the picture above. Johannes Koelman did an excellent job of explaining the science at the heart of the present thinking in an accessible way. I suggest you give it a read and if you feel intimidated by the heavyweights on that Blog, you are welcome to comment here.

-J

[1] http://en.wikipedia.org/wiki/De_Sitter_universe

[2] The 'flatness problem' centers on the question: why is space (not spacetime) of the cosmos appearing to be so near flat on the large scale? The 'horizon problem' is about answering the difficult question: why do we observe the CMB to have virtually the same temperature everywhere we look?

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#1

Re: De Sitter Cosmic Model Revival

06/04/2012 1:45 PM

Thanks, Jorrie.

I have read the linked blog and have not had the time to dig too much deeper, but what needs further discussion is the "mechanics" that drive the big bounce from a forward perspective.

So far, everything we have seen points to an open universe and not one that will contract again. If our universe is simply in one of many phases of expansion followed by a subsequent contraction, there has been no discussion on how that will happen.

What are your thoughts?

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#2
In reply to #1

Re: De Sitter Cosmic Model Revival

06/04/2012 2:51 PM

Hi AH. Tough question.

I'm reasonably comfortable with a time-symmetrical, 'infinite' cosmos without a singularity, but I'm not very comfortable when thinking about 'what started it and how'. Nevertheless, if something or else, "this side of the infinite past", caused a vacuum energy-only cosmos, it could have had a 50:50 chance of starting to contract or expand. In this de Sitter model we may be living in, it had to be born contracting, then later bounced and is now expanding towards an infinite future.

This reminds me of a Roger Penrose lecture, where he posed an infinitely expanding vacuum cosmos that 'pinched off' an empty area. This area contracted and then bounced into an expanding phase again. This could be repeated an infinite number of times, but the mechanics is however not clear to anyone, I guess.

The present thinking on the bounce seems to be some poorly understood quantum gravity effects. The pure vacuum-only model is unrealistic for the bounce, because we know there are least some normal general relativistic matter and radiation around - and they seem to dominate vacuum energy during the dense phases. In his Blog, Johannes gave a link in one of his comments that talks about some new vacuum energy physics. Highly technical - I'm still trying to understand what they are saying...

-J

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#3

Re: De Sitter Cosmic Model Revival

06/05/2012 8:53 PM

Hi Jorrie,

Having read through your links, I wish your confirmation or denial of my deductions. I take it that a de Sitter universe has an infinite past, no singularity, an infinite expanding future, and does not account for matter. The bottleneck (big bounce?) was not infinite density, but was a minimum. Any idea how dense? It seems to me that matter must be accounted for, especially at the minimum when gravity is at its maximum. How is the contraction phase explained (the causation)?

-S

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#4
In reply to #3

Re: De Sitter Cosmic Model Revival

06/06/2012 12:28 AM

Hi S.

Your deductions are spot-on. The only density that is defined in the model is vacuum energy, which is easy to calculate from the cosmological constant (if one knows it!). It does however not really predict a high energy density at the bottle-neck - actually, a very low density.

Since it cannot handle matter and radiation with our present knowledge, and we know the stuff is around, the model needs modification at the denser levels. Perhaps the 'new physics' that everyone is searching for at the high energy density levels will provide clues.

An 'infinite' past does not need any cause or beginning; as Stephen Hawking wrote in A brief History of Time, "It would just BE". Why did it contact? Perhaps the 50:50 possibility of expansion or contraction, as it was with Einstein's original 'static' cosmos (his "blunder").

We know that a lot of work is presently being done on high energy physics and quantum gravity. Perhaps better ideas will be forthcoming in our lifetimes...

-J

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#5

Re: De Sitter Cosmic Model Revival

06/06/2012 10:30 AM

Jorrie-

In one of the later comments to the reference you provided, one of the participants noted that the cosmological constant appears to be the inverse of the perceived age of the universe- a potential correlation that I have never seen discussed to any length, other than in passing, as in this case. As I have commented before, I have always felt that the perceived age of the universe is too short- 13.7 billion years just does not seem to be sufficient time to build all the structures we can observe, and some of the earliest images we have are surprisingly full of unanticipated structure (gallaxies, etc.). I am wondering if it is not possible that some sort of artifact arising from our observational techniques (i.e., what we chose to measure), the way these observations are analyzed and interpreted, including a bias for rejecting observations that do not comply with current theory as noise or erroneous readings? That is, something in our methods dictates how old we perceive the universe to be, rather than actual physics...

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#6
In reply to #5

Re: De Sitter Cosmic Model Revival

06/06/2012 2:00 PM

Hi cwarner7_11, you wrote: "one of the participants noted that the cosmological constant appears to be the inverse of the perceived age of the universe".

I guess you mean the Hubble constant (Ho) that is the near the inverse of the age, if the right units are chosen. I tried to answer this coincidence in the reply to the post that you referred to. It is just one of many coincidences in the cosmos we live in, I guess.

If a more de Sitter-like expansion model is used (and can be justified), the coincidence disappears. This is however not strong enough evidence to overthrow the current model, which explains most of our observations. It is true that many of the observations, even independent ones, are interpreted using the standard model (at least to some extent).

I think if a new high-energy physics should emerge, there may well be an upward correction to the age of the cosmos. According to my calculations, a hypothetical (pure) de Sitter universe would have a time since the bounce of near 100 billion years, while Ho could still be what we measure today. We determine Ho relatively locally (relative to cosmic scales) and those distances will not change to any appreciable extent. We then use this Ho to calculate other distances, using the standard model.

-J

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#7
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Re: De Sitter Cosmic Model Revival

06/06/2012 5:13 PM

Ah, I was not aware of the hope of extending the age of the universe to a more reasonable value through high-energy physics! I will be able to sleep tonight! I assume your answer to the apparent relationship between H0 and the age of the universe is the response showing what appears to be a straight line fit to a theoretical curve that appears hyperbolic. Reasonable in accordance with current available information, but, again, currently available information is based on only about 75 years of trying to fit the data to the theory...

With the age of the earth estimated to be on the order of 4.2 billion years, and the age of the Milky Way on the order of 13.2 billion years, it just does not seem possible that all that we observe could have magically come in to being in only 13.7 billion years...This makes the whole process sound too similar to other creation myths- some infinite agency waves a magic wand, and everything suddenly appears.

I originally discovered the relationship of H0, as you refer to it, and the age of the universe by running through an exercise of evaluating the consistency of units for H0 in an equation appearing in one of the popular science magazines maybe 10 years ago. Back then, H0 was not so well-defined as it is today, but the correlation was apparent when one got the units matching. Since no one else at the time seemed to be interested in this, I assumed that I had erred in my evaluation, or that the equation was an overly simplified version of the model, and left it sleeping for a while. Now I see it being recognized...

de Sitter would be more attractive to me if it included mass/gravity. I eagerly await news of the Higgs boson...

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#8
In reply to #7

Re: De Sitter Cosmic Model Revival

06/07/2012 9:23 AM

The new high-energy physics is essentially only needed to prevent a singularity in the past - in other words, create a 'bounce' instead of a 'bang'. In standard relativity, any mass present results in a singularity in the past. There are many attempts at using quantum gravity to overcome that, but no consistent solution has been found so far.

Such a solution will not necessarily predict an increase in the time since the bang, unless it simultaneously decreases the influence of mass and increases the influence of vacuum energy, i.e., becoming more de Sitter-like. The Blog article of Johannes Koelman, as I understand it, speculates on such attempts and the references of de Sitter relativity that he gave in a reply go somewhat deeper into it. ("De Sitter Special Relativity is discussed here. Some nice visualisations: here.")

You wrote: "I assume your answer to the apparent relationship between H0 and the age of the universe is the response showing what appears to be a straight line fit to a theoretical curve that appears hyperbolic."

Yes, but it is actually only the slope of the LCDM model's curve at a=1 (now), which roughly equals the slope of the linear curve, that causes the coincidence. The slope of the LCDM curve at a=1 equals Ho in units 1/Gy.

Also remember that 13.7 to 13.2 billion equals 500 million years. That's a reasonable amount of time for galaxies to form. Granted, I would also like to see an longer time. It does not seem that any reply to my age question to Johannes is forthcoming - it looks like those bloggers lose interest in 'old' threads very rapidly.

-J

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#9
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Re: De Sitter Cosmic Model Revival

06/07/2012 11:12 PM

An 'infinite' past does not need any cause or beginning

I didn't mean a cause of the universe, I meant a cause of the contraction. I don't understand the prediction of the "bounce".

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#10
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Re: De Sitter Cosmic Model Revival

06/08/2012 12:57 AM

S:"I don't understand the prediction of the "bounce"".

Taking into account that the de Sitter model may not represent reality in the real high-density past, it is reasonably easy to argue why the model "bounces", provided that it once contracted. The exponential curve would have contracted to some near steady state value in terms of radius (near a=0) and then the smallest 'disturbance' would have made it either contract further or start expanding again. Remember, it is all about Lambda with its positive gravity, but negative pressure...

This similar to what we discussed some time ago for an expanding universe that may reach an equilibrium. I could not readily find our discussion again, but I knew I used the graph again in this reply to an Anonymous. That one was for an over-dense state (Ωm=2) and does not show the future expansion or contraction, but I think the mechanism is the same.

A bounce could also occur in LCDM if at some stage of contraction, Lambda increased due to quantum effects and dominate matter/radiation-gravity ever so slightly (not Alan Guth's inflation, but a gradual one). I think this is perhaps the most realistic possibility.

-J

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#11
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Re: De Sitter Cosmic Model Revival

06/08/2012 8:00 AM

Further to my reference in reply to S above, I have run a similar simulation farther out in time and it looks like this:

It could have gone up or down after 60 Gyr, but my program seems to have an automatic 'seed' to perturb it upwards (I think it is just rounding errors in the computations). Nevertheless, for the values I chose, it does reach a mathematical quasi-stable state around there.

Because the laws of physics should be reversible, one could start this simulation from say a=1 at 100 Gyr and run it backwards. It should then reach the same quasi-stable state at around 60 Gyr. If the perturbation is again upwards, it will expand again and avoid the singularity, almost like the 'cooling tower' of the opening post. And that with a significant mass content, which is eventually overridden by Lambda.

This is not a realistic case, because we know from the CMB redshift that the universe was once about 1000 times denser than it is today. Hence the 'bounce' at a=0.5 could not be right. However, it illustrates that it is possible in principle, and perhaps with certain tweaks to the models, it may even become realistic (i.e. agreeing with observations).

What do you think?

-J

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#12
In reply to #10

Re: De Sitter Cosmic Model Revival

06/08/2012 2:28 PM

Hi Jorrie,

Thanks for the explanation. We probably did discuss this before. I remember a curve like this one, but it was because of a math error. I think the spreadsheet was not intended to go that far. You might want to look for that curve in old posts to confirm that.

So do you have reason to believe that there is recent interest in de Sitter cosmology?

-S

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#13
In reply to #12

Re: De Sitter Cosmic Model Revival

06/09/2012 4:41 AM

Hi S, OK. I found the discussion hidden in that looong 'CR4 balloon' thread. You actually discovered this interesting case.

I rechecked everything and there is no math error, it is just that that spreadsheet cannot handle collapsing scenarios, like Ωm= 0.4, ΩΛ= 2.0, since it forces a to only increase.

The two ΛCDM equations that I gave in the later post:

expansion rate: (ΔR/dt)2 = R2Ho2 ((1-Ω)/a2 + Ωm/a3r/a4 + ΩΛ)

acceleration: ΔR2/dt2 = R Ho2 (ΩΛ - Ωm/2a3)

do in fact give exact zero values for a = R/Ro = 0.5, Ωm= 0.5, ΩΛ= 2.0. It is actually only the factors in brackets that matter. The trivial solutions R=0 or Ho=0 will also give results as zero, but are not applicable here. They may refer to a pre-inflation state, though...

The only errors are numerical integration issues (like never reaching a=0.5 precisely), causing the divergence from the quasi-static state. This will in fact also happen in reality, due to non-homogeneity, etc, except that it can also diverge downwards.

Do I have reason to believe de Sitter cosmology (and de Sitter relativity) is worth investigation? For sure, as indicated in my OP and also in the links provided by Johannes (my reply #2 above).

-J

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#14
In reply to #13

Re: De Sitter Cosmic Model Revival

06/09/2012 5:24 AM

Hi S, sorry, 'the discussion' is here.

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