Why does dark energy flatten the universe if negative pressure causes expansion?

[HowardTheDuck]

Hi guys, I'm a bit confused. The initial motivation for including dark energy seems to be:

"The Friedmann equation requires a flat universe to have a mass/energy density exactly equal to the critical density. Yet, observationally, including both the baryonic and dark matter, we can only find less than a third of this value."

So a dark energy term is added so the universe can be flat. But then they say the dark energy has negative pressure and so is responsible for expansion which would result in an open universe! So they put in something to make the universe flat, then give it the characteristic which would result in an open universe. So the dark energy is not going to result in a flat universe after all. So what's that all about??

Thanks a lot.

 

[kevinferreira]

If only the action of regular matter (baryonic) and radiation was taken into account, as it was before the introduction of the cosmological constant, the overall behaviour of the universe should be of contraction, because these constituents have an attractive gravitational effect.
To balance these effects, the dark energy/cosmological constant is introduced. To balance, dark energy must have repulsive effects.

 

[HowardTheDuck]

Thanks a lot for your help. I'm still confused.

So, when they say they don't have enough matter to make a flat universe, actually the reverse is true - they've actually got too much matter. Because the universe would be contracting already with the matter they have.

So instead of saying "Yet, observationally, including both the baryonic and dark matter, we can only find less than a third of this value." what they actually mean is "We've got too much matter"?

I'm totally confused now. Any help appreciated.

 

[kevinferreira]

He's a quote from wikipedia:

"The existence of dark energy, in whatever form, is needed to reconcile the measured geometry of space with the total amount of matter in the universe. Measurements of cosmic microwave background (CMB) anisotropies, most recently by the WMAP spacecraft , indicate that the universe is close to flat. For the shape of the universe to be flat, the mass/energy density of the universe must be equal to a certain critical density. The total amount of matter in the universe (including baryons and dark matter), as measured by the CMB, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%"

So, space is flat acording to our measurements. For this to happen the total density must be equal to a certain critical density (theoretically known). Add the known densities of matter and radiation. It's not even 30% of the critical density our universe must have. Then: postulate the existence of something else, dark energy.

 

[marcus]

Hi guys, I'm a bit confused. The initial motivation for including dark energy seems to be:

"The Friedmann equation requires a flat universe to have a mass/energy density exactly equal to the critical density. Yet, observationally, including both the baryonic and dark matter, we can only find less than a third of this value."

So a dark energy term is added so the universe can be flat. But then they say the dark energy has negative pressure and so is responsible for expansion which would result in an open universe! So they put in something to make the universe flat, then give it the characteristic which would result in an open universe. So the dark energy is not going to result in a flat universe after all. So what's that all about??

Thanks a lot.

A fair amount of the confusion over these issues results from unclear words. It's important to distinguish between two very different things "dark matter" and "dark energy"

Also around 1998 it was discovered that you could have a spatially CLOSED universe that would EXPAND FOREVER.

So starting around 1998 the word "closed" took on slightly different connotations. Before that, cosmology popularizers had given the public the impression that closed meant the universe would eventually contract (or even that it was already contracting!) People are still suffering from that misconception.

You have some quotes in your post but you don't tell the source. It's good to give an online source or or at least an author and date. Simply knowing the date can help us to sort things out and explain what's wrong.
OLD pop-cosmology can be an obvious source of misunderstanding.

 

[marcus]

He's a quote from wikipedia:

"The existence of dark energy, in whatever form, is needed to reconcile the measured geometry of space with the total amount of matter in the universe. Measurements of cosmic microwave background (CMB) anisotropies, most recently by the WMAP spacecraft , indicate that the universe is close to flat. For the shape of the universe to be flat, the mass/energy density of the universe must be equal to a certain critical density. The total amount of matter in the universe (including baryons and dark matter), as measured by the CMB, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%"

So, space is flat acording to our measurements. For this to happen the total density must be equal to a certain critical density (theoretically known). Add the known densities of matter and radiation. It's not even 30% of the critical density our universe must have. Then: postulate the existence of something else, dark energy.

We don't know that the universe is flat "according to our measurements". Flat is not the same thing as "close to flat". Measurements by the South Pole telescope (SPT) last year indicated CLOSE to flat but their narrowest 95% confidence interval did not include zero curvature. This is still undecided. Most studies come up with confidence intervals which include zero but are still a bit lopsided on the positive side. SPT was entirely on the positive side. We still cannot say definitely. The overall mean curvature might be EXACTLY zero, or it might not. It might be slightly positive and we might be looking at a spatially CLOSED universe somewhat analogous to the surface of a sphere. Finite spatial volume, finite amount of matter etc.

The motivation for introducing the "dark energy" idea came from observing evidence (around 1998) that the percentage rate of distance expansion was not declining as rapidly as thought earlier.

It is currently measured at 1/140 % per million years and it is on track to continue declining but gradually to level out at 1/165% per million years.

Look at http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
Check the "S=1.000" box and press "calculate". It will show you the standard cosmic model vision of the future, as well as the past. You will see the role played by numbers 14.0 and 16.5 which I referred to in percentage language, and there are pop-up explanations under the blue dots. You will see the gradual leveling out that the standard cosmic model now predicts.

Before 1998 people thought instead of declining to level out at 1/165% the rate was on track to decline to 0%.

So far we do not know that this effect results from any sort of "energy". The safest assumption is simply that the law of gravity has two main constants: Newton's G and Einstein's Lambda constant, a slight intrinsic curvature in space-time that does not change.
The evidence continues to mount that the universe is behaving exactly as if there were a small positive cosmological curvature constant.

The words people use are often confusing. The root meaning of "energy" is "ability to do work" and there is no evidence so far that this small built-in vacuum curvature should be thought of in that way.

So far it is probably best to think of it simply as "cosmological constant" (a very small curvature quantity). And this is how I see a growing number of cosmologists talk and write about it---getting away from the biased language that suggests some exotic "energy" field.

 

[HowardTheDuck]

Also around 1998 it was discovered that you could have a spatially CLOSED universe that would EXPAND FOREVER.

So starting around 1998 the word "closed" took on slightly different connotations. Before that, cosmology popularizers had given the public the impression that closed meant the universe would eventually contract (or even that it was already contracting!) People are still suffering from that misconception.

That's very interesting, thanks. Generally, most places you look say that a closed universe will contract and an open universe will expand. That's still very common. In fact, I'd say its the usual way it is presented. The quote I took was from "Relativity, Gravitation, and Cosmology" by Ta-Pei Cheng, 2010. A really good book. Author is a professor.

Here's another quote from "Cosmology: A Very Short Introduction": "The behaviour of space in these models mirrors the way they evolve in time. A closed universe is a finite space, but it also has a finite duration. If the universe is expanding at any time, and is closed, the expansion will slow down in the future. Eventually the universe will stop expanding and recollapse. The open and flat models will expand forever. Gravity always fights the expansion of the universe in the Friedmann models, but only in the closed model does it actually win".

There's definitely a lot of confusion about this, and this is not very clearly expressed in the literature at all. The big question for me is over the nature of dark energy. The way I understand it, they seem to be treating it as gravitationally attractive like normal matter (hence producing a flat universe, and giving us this 70% value for the amount of dark energy) but also powering the expansion of the universe. Is that right? I don't follow that at all. Surely the end result is just how it contributes to the curvature of spacetime. It can only be one thing or the other. I don't see how it can be both attractive and repulsive.

To be honest, I get the impression that this is just one of those things which is not very well understood and no one wants to admit it.

(Marcus, those figures you gave are very useful. Thanks for your contribution. I am looking at that cosmological calculator and trying to understand it! It looks to me like the scale factor, a, is just increasing at an accelerated rate. So I don't see any levelling out as you seem to suggest. Am I wrong?)

 

[marcus]

... It can only be one thing or the other. I don't see how it can be both attractive and repulsive.

The confusion arises from people trying to think of the cosmo constant Lambda as a sort of "material" or mysterious "energy field". And then that "substance" has to behave in seemingly paradoxical or unintuitive ways.

This is a "manufactured crisis". It isn't necessary.

Some readers might want to read a critique by Carlo Rovelli. Google "rovelli prejudices". It is an article called "Why all these prejudices against a constant?" Fairly simple thorough treatment of the issue.

But reading that article is not necessary either. Most of the popularization talk is garbage sometimes even including that by reputable people and sometime Wikipedia.

Before 1998 we thought Lambda was zero and we still had expanding distances. Lambda is not what "drives expansion". It just contributes a little bit to it. So the percentage rate isn't declining as rapidly. The expansion started a long time ago, in a bounce or some other event.

But the whole Lambda thing is basically SIMPLE. (Once you get the simple basic idea there are lots of exciting measurements to make and intriguing additional questions to ask. Its actually thrilling all the stuff that is coming up in cosmology. But the basic idea of the cosmological curvature constant is simple enough.)

Physical laws have constants in them. Newton gave us the Newton Law of Gravity that has one constand in it: G.

Then in 1915 Einstein gave us an improvement, actually a Law of Gravity AND Geometry. The Einstein law has TWO naturally occurring constants in it, G and Λ.
And for 80 years most people, most of the time, assumed Λ=0.
But on theoretical grounds there is no reason to assume that. And it turned out in 1998 that assuming Λ=0 gives a slightly bad fit. You get a better fit to the data if you give Λ a small positive curvature value.

 

[marcus]

The acceleration of the expansion of the universe is slowing down?

The percentage or fractional rate of growth of cosmic distances is declining.

But if you take a particular large distance, and calculate the SPEED that distance is growing in miles per hour or lightyears per year or meters per second, you will find that the speed is increasing.

The speed of growth of any fixed cosmic distance in increasing.
The percentage rate of growth that all cosmic distances share is decreasing.

Often people are rather vague about what they mean by the word "acceleration". There is no one definite "speed" that distances in the universe is expanding at--it depends on the size of the distance. You see that in a savings account at the bank. If you put money in at a fixed interest rate of 2% then the "speed of growth" in dollars per year depends on the amount you put into start with, and it will gradually increase because of compounding.
The dollars per year would increase even though the interest rate were slowly declining, if the bank is, say, gradually reduced the interest rate from 2% to 1.5%. Even with the interest rate slowly being reduced, the "speed" of growth (dollars per year) of your account could still be increasing.

The "speed" of growth depends on the dollar amount you put into begin with. And in cosmology it depends on the original size of the distance you decided to look at. So it's simpler to look at the fractional or percentage growth rate, which applies to all large-scale distances across the board. (They have to be distances outside bound structures like galaxies, galaxies are held together by gravity so their internal dimensions are not subject to this pattern of distance growth.)

 

[marcus]

Howard I would seriously urge you to explore that calculator I mentioned. Mark the box that says "exactly S=1.000" and press calculate. It will tabulate for you both the past and the future of the universe (according to currently accepted standard cosmic model.)

Here's something fun that some readers may want to try.

You know I think that "dark energy" is actually a FICTITIOUS energy that corresponds to the cosmological curvature constant Λ. We might eventually find out some exotic type of energy that is responsible. It would be an energy density measured (according to the metric system) in joules per cubic meter. That unit is also called "pascals" and can serve to measure pressure. So we can see how to calculate what that energy would be if it were real and were causing the observed intrinsic curvature.

If you have checked out Jorrie's calculator you see the quantity 16.5 billion years playing a big role. It is all over the place.

The reciprocal is 1/16.5 per billion years. As an instantaneous growth rate that is the same as 1/165% per million years. (Just taking the rate per a different span of time.) So basically we just SQUARE that rate and multiply it a quantity that converts a squared growth rate to pascals (or IOW to joules per cubic meter).

The right physical quantity to multiply by is 3c²/(8 pi G). The Google calculator thinks of this as 3 c^2/( 8 pi G) and it uses * to mean multiplication. The squared fractional rate is (1/16.5 per billion years)^2

Google calculator knows what c is, and what G is, so we can just type this into the Google box.

3 c^2/( 8 pi G) *(1/16.5 per billion years)^2

Try pasting that into the Google box. You may need to type a space or an equal sign afterwards to get the calculator to work. The box normally works as a calculator. If it does, then you should get
something like 0.59 nanopascals = 0.59 nanojoules per cubic meter.
That is the density of the fictitious energy which would supply the observed intrinsic curvature and the consequent constant growth rate 1/165% per million years that according to standard model is never expected to go away.

A more meaningful number would be the critical MATTER density (nanopascal equivalent of combined ordinary and dark matter needed to achieve spatial flatness given the two key parameters 14.0 and 16.5 billion years.)

Try pasting this into Google:

3 c^2/( 8 pi G) *(1/14.0^2 - 1/16.5^2) per (billion years)^2

Again you may need to prod it by typing a space or an equal sign. If it works it should get the critical density for actual MATTER. 0.23 nanopascal. As far as anyone knows that is, indeed, the average density of ordinary and dark matter that we actually have (expressed in equivalent energy) for as far out as we can see.

 

[Chalnoth]

We've also done some fairly detailed measurements of how fast our universe has expanded over time, and these are consistent with a flat universe with a cosmological constant, but inconsistent with nearly all other competing theories (note: many dynamic models of dark energy can be made indistinguishable from a cosmological constant).

 

[marcus]

We've also done some fairly detailed measurements of how fast our universe has expanded over time, and these are consistent with a flat universe with a cosmological constant,...

I agree, and also the detailed measurements are consistent with NON-flat universe with a cosmological constant (the spatially "nearly flat" case that cosmologists so often refer to).
About equally consistent, wouldn't you say?

Howard, here are some expansion history curves, showing how fast expansion of distances has occurred over time:
http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
You get different ones by varying the model parameters and then you see which gives the best fit to all the combined evidence of observational data. The heavy solid curve is the one that gives the best fit.

 

[Chalnoth]

I agree, and also the detailed measurements are consistent with NON-flat universe with a cosmological constant (the spatially "nearly flat" case that cosmologists so often refer to).
About equally consistent, wouldn't you say?

Well, the problem with that statement is that it will always be true. There is no universe in which it couldn't be true. It's impossible to state with certainty that our universe is flat, because there will always be some uncertainty to the measurement.

But we can now say that our universe is highly flat, meaning that the spatial curvature contributes no more than 1% to the current expansion rate, and probably significantly less.