Increase of dark energy with expansion of universe

[Vighnesh Nagpal]

Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it doesn't please correct me

 

[phinds]

It does and is well known to. It's not clear to me why it should, but the density of the "dark energy", whatever it is, remains constant as spacetime expands, so the total amount increases.

 

[Suraj M]

The dark energy density/concentration, remains a constant, ..as the universe expands, the dark energy also increases, to maintain it's concentration a constant
..also resulting in the accelerated expansion of the universe

 

[wabbit]

I don't know if there is a reason why dark energy density is - or should be - constant, but my (non expert) understanding of the reason it is usually assumed to be constant is that
- this is the only simplest form compatible with standard general relativity ;
- there is so far no observational evidence that forces cosmologists to abandon this assumption and go for something more general.
(Though alternative models do exist of course)

Edit : corrected, thanks PeterDonis

 

[PeterDonis]

this is the only form compatible with standard general relativity

Not really. It is the simplest form compatible with standard GR. A scalar field that varies with space and time but has an appropriate equation of state can also act like dark energy and is compatible with standard GR, but it's more complicated.

 

[wabbit]

Not really. It is the simplest form compatible with standard GR.

Thanks for the correction, edited that - I guess I was using "standard" in an unduly restrictive sense here.

 

[Chalnoth]

It does and is well known to. It's not clear to me why it should, but the density of the "dark energy", whatever it is, remains constant as spacetime expands, so the total amount increases.

I think the way you worded this is slightly confusing.

The density of dark energy remains constant, but everything else dilutes with the expansion. So over time, the dark energy makes up a larger fraction of the energy density. It doesn't increase: everything else just decreases.

 

[phinds]

I think the way you worded this is slightly confusing.

The density of dark energy remains constant, but everything else dilutes with the expansion. So over time, the dark energy makes up a larger fraction of the energy density. It doesn't increase: everything else just decreases.

Excellent correction. Thanks. I was going to add, and clearly should have, that the implication of (or really just another way of saying) "density of dark energy remains constant" is that it does not dilute within a given cosmologically large volume but the matter density does dilute.

 

[Vighnesh Nagpal]

oh ok. thanks guys!

 

[Uollises]

Never thought about it. But, does this dark energy have sources of..uhm..energy?)

 

[Chronos]

Im stuck on the Peter Donis explanation, what part of that you find incomprehensible?

 

[wabbit]

there is so far no observational evidence that forces cosmologists to abandon this assumption and go for something more general

To qualify this somewhat, the following paper (not completely sure if this is an acceptable source - will remove if not) assesses current observational constraints on dark energy anisotropy and inhomogeneity (and hints of a possible large scale dipole moment in dark energy) : Leandros Perivolaropoulos : Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy

A wide range of large scale observations hint towards possible modifications on the standard cosmological model which is based on a homogeneous and isotropic universe with a small cosmological constant and matter. These observations, also known as "cosmic anomalies" include unexpected Cosmic Microwave Background perturbations on large angular scales, large dipolar peculiar velocity flows of galaxies ("bulk flows"), the measurement of inhomogenous values of the fine structure constant on cosmological scales ("alpha dipole") and other effects. The presence of the observational anomalies could either be a large statistical fluctuation in the context of {\lcdm} or it could indicate a non-trivial departure from the cosmological principle on Hubble scales. Such a departure is very much constrained by cosmological observations for matter. For dark energy however there are no significant observational constraints for Hubble scale inhomogeneities. In this brief review I discuss some of the theoretical models that can naturally lead to inhomogeneous dark energy, their observational constraints and their potential to explain the large scale cosmic anomalies.

 

[stevebd1]

Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it doesn't please correct me

I always thought this was a good overview of dark energy and the expanding universe-

http://preposterousuniverse.com/writings/skytel-mar05.pdf

 

[phinds]

I always thought this was a good overview of dark energy and the expanding universe-

http://preposterousuniverse.com/writings/skytel-mar05.pdf

Excellent reference. I really like Carroll; I think he's a good explainer. I have a "Teaching Company" set of 12 half-hour video lectures by him on "Dark Matter; Dark Energy" and they're excellent.

 

[marcus]

Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it doesn't please correct me

Vighnesh, I don't know of any scientific reason to think that "dark energy" actually arises from any form of energy. Some people think of it that way and others don't. All we observe is a small residual expansion rate that corresponds to a curvature constant that appears naturally on the lefthand side of the GR equation. In my experience it confuses people to think of it as some kind of energy---it's just a slight built-in spacetime curvature.

If you want to know the exact value in metric units, based on current observational measurements, it corresponds to a distance growth rate of 1.83 x 10^-18 per second. No mysterious "energy" needs to be involved.
The present fractional rate of distance growth (between things at cosmic rest, not gravitationally or otherwise bound together) is
2.20 x 10^-18 per second.
Each second, a large-scale distance distance grows by that small fraction of its length.

This fractional distance growth rate was much larger in the early universe and has been steadily declining ever since. It is expected to continue declining but not to reach zero. Instead it is expected to level off at 1.83 x 10^-18 per second.
Einstein included in his GR Equation the curvature constant Lambda which turns out to be three times the square of this rate.

If you google "general relativity" and get the Wikipedia article, you immediately see this Lambda in the standard form of the equation in the box on the right of the page.

Its value according to current estimates is about 10.0 x 10^-36 per second².
You can easily see how that works out: if you square 1.83 and multiply by 3 you get about 10, squaring 10^-18 gives 10^-36 and of course if you square "per second" you get "per second per second" or per second²

 

[Vighnesh Nagpal]

Hi. Thanks for your replies guys, really cleared it up for me :)

 

[Phynos]

This fractional distance growth rate was much larger in the early universe and has been steadily declining ever since. It is expected to continue declining but not to reach zero. Instead it is expected to level off at 1.83 x 10^-18 per second.

If the expansion is accelerating, why is this fractional distance growth rate decreasing? Doesn't that imply the acceleration is actually negative and that things are slowing down? Or am I misunderstanding what you're saying?

 

[phinds]

If the expansion is accelerating, why is this fractional distance growth rate decreasing? Doesn't that imply the acceleration is actually negative and that things are slowing down? Or am I misunderstanding what you're saying?

Think about this: You are going 100mph and you are accelerating at 20mph per hr, so in an hour you will be going 120 mph. At that point, your acceleration decreases to 19mph per hr, so in one more hour you will be going 139mph. Does that seem to you like "slowing down"?

 

[marcus]

If the expansion is accelerating, why is this fractional distance growth rate decreasing? Doesn't that imply the acceleration is actually negative and that things are slowing down? Or am I misunderstanding what you're saying?

that is a verbal problem, Phyrnos. the word "accelerating" is confusing people. the expansion rate has always been decreasing since the very early universe and according to the standard cosmic model (called LambdaColdDarkMatter, or LCDM) we expect it to continue decreasing, just not to get down to zero but to kind of level out at a longterm rate.

The big discovery in 1998 was that the longterm rate is not zero but is actually a small positive rate.

There are two ways they could have announced the 1998 result, which way sounds better to you?

===announcement one===
The present rate of distance growth is 1/144 of one percent per million years and we found that it is declining more slowly than was thought. Instead of gradually tailing off to zero it has been acting as if it is going to level out at 1/173 percent per million years.
==endquote==

The alternative would use scientific notation, to express these very small fractional growth rates, and the metric unit of time, the second. Each second the distance grows by a tiny tiny fraction of itself.

===announcement two===
The present rate of distance growth is 2.20 x 10^-18 per second and we found that it is declining more slowly than was thought. Instead of gradually tailing off to zero it has been acting as if it is going to level out at 1.83 x 10^-18 per second.
==endquote==

I don't like the word "acceleration" in this context because for most of us it has mental associations with driving a car. Driving a car is not a good metaphor for the pattern of cosmic distance growth described by Hubble Law. The analogies are weak, and awkward, and lead to confusion. A better analogy would be money in a savings account at the bank where the interest rate is gradually declining. If the fractional growth rate is declining GRADUALLY ENOUGH then the account can still grow each year by a larger dollar amount (because the principal is increasing). AFAICS the minute you use the word "acceleration" and start thinking about driving a car you have lost touch with the actual process occurring in nature.

 

[wabbit]

Oh you just corrected a deep misunderstanding of mine, thanks marcus. Plus that makes sense, I actually thought either statement true depending on what I was thinking about !

Back from deleting my post about this in another thread : )

I find it strange that we hear that expression "accelerating expansion" all the time when it is in fact not accelerating... This is just confusing, why make it so hard for us poor laymen to get even a broad understanding of what's going on !

Edit : Well I suppose it's accelerating in comparison to one that would be decreasing... kind of like my country's public spending is said to decrease whenever it increases less than previously expected : )

 

[marcus]

Wabbit, thanks for the encouraging comment. Now let's open the door a crack and let the word "accelerating" back in :grin: It's the idea of exponential growth, and quasi-exponential or near-exponential growth with a gradually declining rate.

I know I'm being ambiguous and wish-washy about this but having said that about the Hubble expansion rate H(t) which is indeed declining towards a longterm rate H_∞, there is also the SCALE FACTOR a(t) which is the size of a generic distance normalized to a(now) = 1.

Cosmologists need both H(t) and a(t), both those handles on distance growth are useful. As a fractional growth rate, H = a'/a
the small fraction of itself that a generic distance grows by, per unit time.

The Friedmann equation, as usually written, governs H. It tells you what H² is. and it shows how it is declining.

You could say that H, the "Hubble rate" is our main handle. But a(t) is in there too. And it is "accelerating" in a sense, because after about year 8 billion the second derivative of a(t) became positive. a'(t) has always been positive as long as the U has been expanding. But a'' was negative until around that time and then became positive. So there is a "scale factor" sense in which growth IS accelerating. think of a(t) as the size of the savings account. For a long time it grew by decreasing dollar amount each year because the bank was ramping down the interest rate so rapidly, but then the bank continued to decrease the rate, but more gradually, so it becomes quasi-exponential growth and the annual dollar amount increment grows.

the a(t) curve changes from convex to concave at an inflection point around year 8 billion. Some people use the notation R(t) for the scale factor.
Sorry to be adding to the confusion. But want to be fair to the scale factor, another important handle on the process.

 

[Phynos]

Think about this: You are going 100mph and you are accelerating at 20mph per hr, so in an hour you will be going 120 mph. At that point, your acceleration decreases to 19mph per hr, so in one more hour you will be going 139mph. Does that seem to you like "slowing down"?

No, I didn't mean the recession speed of far away galaxies was decreasing, but that the acceleration of that recession was decreasing. Poor wording on my part.

that is a verbal problem, Phyrnos. the word "accelerating" is confusing people. the expansion rate has always been decreasing since the very early universe and according to the standard cosmic model (called LambdaColdDarkMatter, or LCDM) we expect it to continue decreasing, just not to get down to zero but to kind of level out at a longterm rate.

The big discovery in 1998 was that the longterm rate is not zero but is actually a small positive rate.

I don't like the word "acceleration" in this context because for most of us it has mental associations with driving a car. Driving a car is not a good metaphor for the pattern of cosmic distance growth described by Hubble Law. The analogies are weak, and awkward, and lead to confusion. A better analogy would be money in a savings account at the bank where the interest rate is gradually declining. If the fractional growth rate is declining GRADUALLY ENOUGH then the account can still grow each year by a larger dollar amount (because the principal is increasing). AFAICS the minute you use the word "acceleration" and start thinking about driving a car you have lost touch with the actual process occurring in nature.

The second one makes sense to me, it just runs counter to what I have been previously told. Why would a astronomy professor use the term acceleration in this context in an introductory class if the word poses issues? Just because it's an introductory class?

I understand the distance growth rate, and I like it explained that way, but it seems to convert into the language of velocity and acceleration just fine unless I'm missing something? From what you explained above, it seems to me this is the situation:

(1) The distance between galaxies is increasing (radial velocity between distant galaxies is positive, positive being the direction away from us).
(2) This radial velocity is increasing (Positive acceleration caused by Dark Energy).
(3) However this acceleration is not increasing, but rather decreasing (AKA there is a negative jerk), and is presently creeping towards a minimum.

 

[marcus]

Human language is sometimes mysterious and once words get started it is hard to change them. Maybe someone can summarize this situation better than I. I want to be fair to the scale factor and its INFLECTION POINT which came about 5 billion or 6 billion years ago. You can see the inflection point around year 8 billion, that is around -5 or -6 on the time axis.

This is from a Lineweaver 2003 article. I'm a fan of Lineweaver. He's a world-class cosmologist and also good at presenting information. Even though it's old and in some ways out of date this Lineweaver article can be helpful to read. The title is "Inflation and the Cosmic Microwave Background".
Nowadays there are alternatives to inflation, maybe other things happened that achieved the same or similar observable effects. But so what? He is a good writer, and it is not all about inflation by a long shot. 90% about other stuff.

 

[wabbit]

And following this I checked other definitions for a few expressions we hear, hope I got this right:

Hubble scale = scale factor = a(t) or R(t), the characteristic scale of the universe, its size if finite.
Hubble parameter = Hubble rate = H(t) =$\dot a(t)\over a(t)$, the logarithmic growth rate of that scale.

Hubble constant = current value of the Hubble rate = H₀

Just need to be careful...

 

[wabbit]

Thanks marcus, actually your explanation makes perfect sense, I was just forgetting that "acceleration" mathematically can be an ambiguous term.

In fact it was even fine to think "accelerating" in one context and "slowing down" in another - but I needed to realize that:
- one is about the (increasing) growth rate of the scale factor,
- the other is about the Hubble rate, i.e. the (decreasing) logarithmic growth rate of the scale factor.

Thanks for clearing this up. Oh and nice chart you have here, just saw your last post - this wraps it up perfectly.

And I even get now that it isn't an evil conspiracy by physicists to keep the masses in the dark

 

[marcus]

And following this I checked other definitions for a few expressions we hear, hope I got this right:

Hubble scale = scale factor = a(t) or R(t), the characteristic scale of the universe, its size if finite.
Hubble parameter = Hubble rate = H(t) =$\dot a(t)\over a(t)$, the logarithmic growth rate of that scale.

Hubble constant = current value of the Hubble rate

Just need to be careful...

Perfect! That's probably how I should have started off.

And a simple way to write the (spatial flat) Friedmann equation that the whole cosmic model LCDM runs on is:

H² - H_∞² = const ρ

Where rho ρ is the combined energy density of radiation and matter (dark and ordinary)
and where "const" is a constant that converts energy density to squared growth rate
The constant that does this in the Friedmann equation is 8πG/(3c²).

 

[marcus]

Except for a pesky factor of c², Λ in the Einstein GR equation is equal to 3H_∞²

So that form of the Friedmann equation in the previous post could also be written (except for that c^2)

H² - Λ/3 = const ρ

Darn that c², it doesn't look so clean when I include it:
H² - Λc²/3 = const ρ

The conventional Lambda is in units of reciprocal area. In metric it would be m^-2
But relativists often switch between time and distance and sometimes Lambda is expressed in terms of seconds^-2. If that were understood, I wouldn't have to include the c².
It is there just to convert m^-2 to s^-2

 

[wabbit]

This is disappointing. Far too simple : )

 

[marcus]

You are always one hop ahead, Wabbit. Suppose we just cut the Gordian tangle by agreeing that Lamda is 10^-35 seconds^-2 as some relativists would have it. Then we get the clean form.

 

[wabbit]

Thanks but that's undeserved, I didn't notice a missing factor, was just impressed by the simplicity !

But anyway, c=1 so no big deal. (Other than, why do we move so fast in time and so desperately slowly in space? But that's for another thread, another day...)