Unraveling the Mystery of Dark Energy in the Expanding Universe

[exDark]

if the expansion of the universe seems to be accelerating the farther away in distance(and time) we look,
then since we're looking into the past because light has a finite speed,
and the further you go in the past, the faster the universe's expansion was.
why should there be any dark energy at all? shouldn't that be what is expected?

 

[marcus]

exDark, this is a perspective on what you are asking about. You might like it and find it useful, or you might not. Try looking at things this way, if you want, and see if it makes sense: space has no known size or boundary. Since the universe has no size that we can pin down, it has no defined speed of expansion.

Instead of a speed, what is inferred from observations is a percentage rate of distance growth. Currently it is estimated to be about 1/144 of one percent per million years.

As far as we can tell, at any given moment of universe time this rate is the same everywhere.
It changes only very slowly (at least by our standards). It is complicated to infer what it has been here and what it will be at distant regions, so as to be able to check that it has been the same everywhere at any given moment. It's not obvious how to check that and it requires fitting data to an equation model. You have to be able to reconstruct the past to check it, at least in broad outline.

Since we're talking about a fractional or percentage growth rate, naturally at any given moment in the history of the cosmos the LARGER distances are growing proportionally FASTER.

If the percentage growth rate would stay constant this would lead to exponential growth of any given distance you choose to watch. that's the kind of "acceleration" you'd naturally expect from a constant percentage growth rate. whether it's money in a savings account, or a population of bacteria.

Actually for essentially the whole history of the universe's expansion the percentage growth rate has been DECLINING. But even with a declining growth rate,if the decline is slow enough, you can still get "almost" exponential growth and you can still see a detectable acceleration if you watch some chosen distance.

That's enough for now. A kind of preparation to try to respond to your question. If you are comfortable with this approach let me know, ask a question or something. this approach is mainstream but it does not necessarily have anything you would call "dark energy". It just has a naturally occurring small constant curvature that turns up in the main equation. It doesn't need to correspond to anything you would really consider an "energy".

Instead of 1/144% per million years being on track to eventually decline to zero there is this constant percentage rate 1/173% per million years that it is on track to decline to, and level off at. And there's no reason there shouldn't be a longterm positive stop to the decline. That 1/173% is a way of stating the "cosmological constant". It's as simple as that.

 

[exDark]

thank you! I see what you're saying about the "percentage growth rate" and I think that is what was confusing me.
I still feel a bit of slight confusion, when thinking about how the perceived rate of growth for space in the past made the objects in space to appear to be decelerating, then begin to accelerate away from one another, after a certain volume of space that is generated during the expansion is reached. or maybe I am still trying to process correctly an understanding of this property, most likely.edit: the only thing I'm stuck on, is suppose the universe is actually decelerating in its expansion, but any light we receive will be from the past where things were moving faster apart than they are now. wouldn't this produce the illusion of accelerated expansion?

 

[marcus]

Hi exDark, thanks for getting back to me. I want to answer but it's too late and I'm falling asleep. I'll have to try to respond tomorrow. What I want to suggest the basic observation data are a plot of redshift z (or actually z+1) the factor by which wavelengths and distances are stretched while the light is in transit, and the present DISTANCE to the object (estimated using "standard candle" objects of known brightness).

So if you try working with a calculator that runs the standard cosmic model and VARY the cosmological constant you can see how present distance (Dnow) changes as a function of redshift z (or S=z+1).

You can see how they could have arrived at the present estimate of the size of the cosmological constant.

But I'm too slowed down at the moment to try to get into this
In the meantime you might click on
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
and see how Dnow relates to S=z+1

You can narrow the range to be from S=10 down to S=1 (the present) so you don't go too far into the past and don't project into the future. S=10 down to 1 is a more practical range in terms of actual astronomical observation.

It may be totally confusing, but it's worth getting some exposure to. Hovering sometimes brings up info tips for some of the quantities. I'll try to explain it tomorrow. It is a hands-on version of the standard cosmic model that allows one to vary model parameters and see the effect.
Sorry to be wimping out.

 

[marcus]

It's morning. So most people hear words like "dark energy" and "acceleration" and get some idea--then it's reasonable to wonder (as you exDark may wonder) how that idea is supported by observational evidence.

I'm going to try to clarify this using the Lightcone calculator. I click on the link, and change S_upper to 10 and S_lower to 1 (narrowing the redshift range to between z=9 and z=0 because that's the range we actually observe stars and galaxies in, for the most part) and I get this standard model version of the universe history from year 545 million (around the time of the first stars) up to the present year 13.8 billion:
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.000&0.5454&0.8196&30.684&3.068&4.717&2.13&3.74\\ \hline 0.126&7.943&0.7707&1.1568&28.684&3.611&5.687&1.99&3.12\\ \hline 0.158&6.310&1.0886&1.6308&26.444&4.191&6.804&1.84&2.57\\ \hline 0.200&5.012&1.5362&2.2939&23.938&4.776&8.066&1.66&2.08\\ \hline 0.251&3.981&2.1646&3.2127&21.143&5.311&9.452&1.47&1.65\\ \hline 0.316&3.162&3.0412&4.4626&18.045&5.706&10.920&1.25&1.28\\ \hline 0.398&2.512&4.2500&6.1052&14.651&5.833&12.396&1.02&0.96\\ \hline 0.501&1.995&5.8828&8.1349&11.008&5.517&13.780&0.76&0.68\\ \hline 0.631&1.585&8.0151&10.4035&7.226&4.559&14.962&0.50&0.44\\ \hline 0.794&1.259&10.6685&12.6018&3.483&2.767&15.863&0.24&0.22\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline \end{array}}$$

I want to encourage you to try and see if you get this table when you change the S range to be from 10 to 1, and press "calculate". The default S range is 1090 to 0.01 and this gives us extensive stretches of the past (before first stars) and the future, which might distract, so let's trim the range for this discussion.

What we observe is essentially just S and Dnow. S is told from the shift of spectral lines (in the received light) and Dnow is told by the dimness of known sources.

All the other stuff can essentially be derived from those two columns using the 1915 GR equation (which has been checked many times in many ways, so is used until something better shows up)

Because the other stuff can be distracting, we can click on the "column select" button and get the column menu and UNselect all the other stuff and get this:
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&D_{now} (Gly) \\ \hline 10.000&30.684\\ \hline 7.943&28.684\\ \hline 6.310&26.444\\ \hline 5.012&23.938\\ \hline 3.981&21.143\\ \hline 3.162&18.045\\ \hline 2.512&14.651\\ \hline 1.995&11.008\\ \hline 1.585&7.226\\ \hline 1.259&3.483\\ \hline 1.000&0.000\\ \hline \end{array}}$$

and then we can remove the decimal point in R_∞ = 17.3, making it 173. And recalculate.
This has the effect of making the cosmological constant much smaller, so the percentage growth rate declines more sharply heading towards nearly zero instead of to 1/173% per million years.
All the sources (at every value of S) are predicted to be LESS DIM:
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&173&3400&67.9&0.007&0.993\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&D_{now} (Gly) \\ \hline 10.000&19.732\\ \hline 7.943&18.618\\ \hline 6.310&17.368\\ \hline 5.012&15.966\\ \hline 3.981&14.391\\ \hline 3.162&12.625\\ \hline 2.512&10.642\\ \hline 1.995&8.419\\ \hline 1.585&5.924\\ \hline 1.259&3.127\\ \hline 1.000&0.000\\ \hline \end{array}}$$

 

[exDark]

thank you again for the explanation, its clear to me now what I was overlooking, or at least its apparent to me that the observations we see are not obvious when applying the intuition I was using in my OP. very interesting stuff, cheers.

 

[marcus]

I SHOULD THANK YOU! I'm not doing a great job explaining. Don't worry. What I'm trying to find a way to make intuitive is that in 1998 they found that certain supernovae "standard candles" were DIMMER THAN EXPECTED at the given redshifts (corresponding to around S=1 or 1.5 and later 2). that dimness was the key observation

 

[marcus]

I'd say you are being remarkably patient and considerate. At present I'm struggling with an unintuitive mess. they knew how bright this class of supernovae were in reality, having observed them at known distance. Now look at row S = 1.995 (call it 2) in the table. That corresponds to light being wavestretched by a factor of 2. Wavelengths twice as long (aka redshift z=1). So supernova light came in with that S=2, and they expected it to have brightness corresponding to distance Dnow=8.4

But it didn't! The supernova was DIMMER, corresponding to a Dnow=11.0.

Big excitement. BTW the percentage growth rate is called the Hubble rate H(t) and the simplified GR equation cosmologists use tells how it evolves over time based on a small number of parameter inputs. The two most important are the current rate H(now)=H₀ and the longterm eventual rate H_∞

In the Lightcone calculator the reciprocal parameter R₀ = c/H₀ = 14.4 billion lightyears is used as a handle on H₀=1/144% per million years. And the same thing for what plays the role of the cosmological constant:
R_∞ = c/H_∞ = 17.3 billion lightyears is used as a handle on H_∞ = 1/173% per million years.
Say if you want to see the algebra worked out.

 

[marcus]

OK here is what I think is the key intuitive idea. The Hubble rate controls both the rate that distances are growing and the rate that wavelengths are being stretched.
The Hubble rate H(t) is declining over time.

If the decline is steep (e.g. H(t) heading for zero) then as you go back in time it rises more sharply.
So at a given distance you expect MORE WAVESTRETCH to have occurred while the light was on its way.
(That translates into expecting a shorter distance corresponding to a given redshift.)

If the decline is more gradual (e.g. H(t) heading to level out at some positive value like 1/173%) then as you go back in time it rises more gradually and, at a given Dnow distance you expect LESS wave stretch or redshift.

That translates into a LONGER distance corresponding to a given redshift. And that was what they found:
the standard candle supernovae were DIMMER at each given z (or each given S=z+1) than their old model with its zero cosmological constant predicted. So they in effect

increased H_∞ from zero% per million years to 1/173% per million years, to get a good fit to the data.

That slowed the decline in H(t) the percentage distance growth rate, and as we discussed earlier if the growth rate declines slowly enough you get behavior approximating exponential growth of some distance you choose to watch over time, increasing slope to the curve, "acceleration".

 

[marcus]

FRESH START: Let's try to boil it down and get a simple intuitive handle on the topic.

The Hubble rate H(t) is declining over time. The issue is how steeply and does it level off at a positive value or go all the way to zero.

This is controlled by one simple parameter that appears naturally in the 1915 Einstein GR equation.
So if we can measure the steepness we can determine that constant.

A steeper decline means when we look back a given distance we should see comparatively HIGHER values of H, so light reaching us from those distances should be MORE redshifted.

A more gradual decline means when we look back a given distance we should see H comparatively less elevated, so light reaching us from those distances should be less redshifted.

So all we need to do is measure redshift of sources at various distances and we can determine that constant.

One more thing, a kind of footnote. A recent (Planck mission) estimate for H(now) is somewhere around 67.9 km/s per Mpc. To get that in more convenient units, paste this into google:
"67.9 km/s per Mpc in percent per million years"

Google's built in calculator should do the units conversion for you and give you back:
"0.00694406728 percent per million years"
That is H(now) expressed as a fractional growth rate. And 1/.00694406728 = 144.0… (very close) so we can use 1/144 percent per million years as current value of the Hubble growth rate.

A similar calculation shows that the cosmological constant estimate translates into an eventual value H_∞ = 1/173 percent per million years. In the standard cosmic model (as derived from GR) the past and future trajectory of the Hubble rate is determined by these two quantities. Under simple uniformity assumptions they are the two main parameters you have to supply to the model. So you see parameter input boxes for them in the upper left when you open Lightcone calculator.