A layman's guide to the accelerating expansion of space

[rootone]

I think part of the confusion with the term 'singularity' arises from the usage of the term 'singular', to indicate a condition of an object (could be anything), which is very peculiar, unusual, unexpected, or hitherto thought to be impossible.
That is a legitimate usage of the word but is no longer commonly used, though it was quite popular in the earlier parts of the last century.
IIRC Conan Doyle's Sherlock Holmes detective character used 'singular' in that context a number of times when he had discovered mysterious evidence, but of course Holmes was not implying that he believed that the evidence was unphysical and had zero dimensions.

 

[JDoolin]

Last summer I subscribed to the International Astronomical Union long enough to download a whole bunch of CBET###.txt files from Harvard's database. This summer I've been trying to write up some perl scripts to pull the data out of each piece, getting the magnitude, the redshift, right-ascension, type and declination of each supernova in the list.

Here's a sample line: Supernova 2006sj, with it's discovery date, right ascension, declination, magnitude, redshift, and type
#2006sj# &Nov. 14& *2 10 22.418* ^- 3 33 09.32^ $23.0$ |0.7| ?Ia?

This is a pretty high redshift and high (dim) magnitude for a supernova in 2006. I'll have to get further into the data before I know whether by 2014 they were discovering much dimmer and more distant ones.

From what I've been led to understand, is that the nearby objects are receding at 74 km/s per MPc and the statistical fit is nearly perfect, and objects further away than about 6Gly are receding at less than 74 km/s per MPc, and there is a great deal of statistical "noise" beyond that point. Now whether this "noise" is due to actual differences, or measured differences, I don't know. Beyond 6 billion light years, you're getting into magnitudes well above (fainter) than 20, so the data might be difficult to get accurately.

Also, I'm not sure whether the redshift is calculated based on emission lines from the supernova itself, or the galaxy in which it is embedded. The issue of trying to use the supernova itself would be that it is light coming from exploding material that may be flying toward you at a significant speed. The issue of getting it from a galaxy is that the supernova might not actually be in that galaxy.

Also, I'm not sure what maximum brightness can be expected from the different types of supenova, (type Ia, Ib, Ic, II, etc). I think there would be a different magnitude-to-distance calculation for each type.

My impression, though, is that the best large-scale measurement of distance in cosmology is the magnitudes of these one-time explosions. In particular, the type I supernova which represent a very specific chain of events--matter accumulating on a white dwarf until it reaches a critical mass and converts into a neutron star.

The fact that we can see anything beyond 7 billion light years means that the big bang (everything starting from a point 13.7 billion years ago and moving outward at constant speed) cannot be right. But I usually find the explanations of "accelerating expansion" to be too vague in their relationship to the actual observed quantities.

 

[phinds]

The fact that we can see anything beyond 7 billion light years means that the big bang (everything starting from a point 13.7 billion years ago and moving outward at constant speed) cannot be right.

I don't follow your logic on that. What's special about 7 billion light years?

 

[JDoolin]

I don't follow your logic on that. What's special about 7 billion light years?

If the unmodified "Big Bang Theory" were correct, and everything in the universe came from a point 13.7 billion years ago and didn't accelerate, then the fastest it could be moving away is the speed of light, and the fastest it could return is the speed of light. So the furthest we could actually see is 13.7/2 = 6.85 billion light years.

6.85 billion years for the object to get to where we see it, and 6.85 billion years for the light to get to us.

 

[Bandersnatch]

Last summer I subscribed to the International Astronomical Union long enough to download a whole bunch of CBET###.txt files from Harvard's database. This summer I've been trying to write up some perl scripts to pull the data out of each piece, getting the magnitude, the redshift, right-ascension, type and declination of each supernova in the list.

Here's a sample line: Supernova 2006sj, with it's discovery date, right ascension, declination, magnitude, redshift, and type
#2006sj# &Nov. 14& *2 10 22.418* ^- 3 33 09.32^ $23.0$ |0.7| ?Ia?

You know, you can do such queries from publicly-available databases. Like Simbad:
http://simbad.u-strasbg.fr/simbad/sim-fid
e.g. use 'SN 2006' to display all supernovae in 2006; you may want to adjust output options first.
Here's a sample:

Spoiler

It's easy to find what you need there.

The issue of trying to use the supernova itself would be that it is light coming from exploding material that may be flying toward you at a significant speed.

That's not an issue. A light curve from any standard candle supernova looks the same - all such supernovae have the same proportion of material coming directly at you and traveling perpendicular to your line of sight, with the same associated broadening of the spectral lines. You then get this standard light curve and measure the redshift of the whole thing.

Also, I'm not sure what maximum brightness can be expected from the different types of supenova, (type Ia, Ib, Ic, II, etc). I think there would be a different magnitude-to-distance calculation for each type.

Supernovae of other types than Ia are not used as standard candles, since their light curves vary depending on progenitor star mass and composition. There's nothing standard about those, unlike Ia.

The fact that we can see anything beyond 7 billion light years means that the big bang (everything starting from a point 13.7 billion years ago and moving outward at constant speed) cannot be right. But I usually find the explanations of "accelerating expansion" to be too vague in their relationship to the actual observed quantities.

If the unmodified "Big Bang Theory" were correct, and everything in the universe came from a point 13.7 billion years ago and didn't accelerate, then the fastest it could be moving away is the speed of light, and the fastest it could return is the speed of light. So the furthest we could actually see is 13.7/2 = 6.85 billion light years.

6.85 billion years for the object to get to where we see it, and 6.85 billion years for the light to get to us.

It's true that 'everything starting from a point' cannot be right. But that is not what the Big Bang theory is! That's just a common misconception. The material you see at 6Gly did not need to 'go there' at the speed of light before sending you its signal.
What have you read so far about the theory? We could link you some reading material, but I don't want to send you stuff that's below your level.

 

[phinds]

If the unmodified "Big Bang Theory" were correct, and everything in the universe came from a point 13.7 billion years ago and didn't accelerate, then the fastest it could be moving away is the speed of light, and the fastest it could return is the speed of light. So the furthest we could actually see is 13.7/2 = 6.85 billion light years.

6.85 billion years for the object to get to where we see it, and 6.85 billion years for the light to get to us.

Ah. Got it. Thanks.

 

[marcus]

Bandersnatch post #40, right before this brief one of Phinds, is really informative over a wide range of issues including the standard candle SNe data base which is online and publicly available. Also at the end Bander has a response to JDoolin's idea about "6.85 billion years for the object to get there" that Phinds quoted just now. It's concise and potentially enlightening:
==quote Bander==
It's true that 'everything starting from a point' cannot be right. But that is not what the Big Bang theory is! That's just a common misconception. The material you see at 6Gly did not need to 'go there' at the speed of light before sending you its signal.
What have you read so far about the theory? We could link you some reading material, but I don't want to send you stuff that's below your level.
==endquote==
don't want to lose sight of that merely because we turned a page just now.

 

[JDoolin]

That Simbad thing is cool.

I was looking here at http://www.cbat.eps.harvard.edu/lists/RecentSupernovae.html about a year ago, and sent an email to somebody in charge there asking where I could access the redshifts. He said "in the individual CBETs". So I started downloading all the CBET's. Might have the same information as Simbad. But the CBET's do have more information... What kind of telescope; multiple observations of the supernova over time, magnitudes through different colored filters.

A light curve from any standard candle supernova looks the same - all such supernovae have the same proportion of material coming directly at you and traveling perpendicular to your line of sight, with the same associated broadening of the spectral lines. You then get this standard light curve and measure the redshift of the whole thing.

Thanks for that. I was momentarily under the impression that redshift couldn't be determined directly from the light of the supernova itself. But I see I was mistaken.

Here: https://en.wikipedia.org/wiki/Type_Ia_supernova#/media/File:SN1998aq_max_spectra.svg is the spectrum of a Type 1a supernova (taken in 1998). We could (perhaps) identify this pattern by the double-peak in the spectrum around 4000 angstroms. (Do you see the double-peak I'm talking about?)

So if that supernova happens something like a billion light years away, with a redshift of 0.7, then the double-peak would happen at somewhere around 4000*1.7=6800 angstroms. You would identify the redshift of 0.7 by the fact that the double-peak was around 6800 angstroms and solving the equation (1+z)4000=6800. Right?

Then by determining how "bright" the double-peak was--that is, what the intensity of the light through a spectrometer in the region of the double-peak, you would determine the magnitude of the supernova, right?

Now, how standard is this methodology for reporting supernova data, though? Does every astronomer reporting their data use compatible methodology so that everybody is measuring redshift and magnitude of the same features, and on the same scale?

 

[JDoolin]

I think it is an interesting thing to note, what Valenmur calls "constant expansion" is in some ways exponential.
After one period of time the distance from green to blue doubles. After another equal period, that distance doubles again.

The same can be said for the distance from green to purple, and for the distance from green to red.

Is that a standard description of what is meant by constant expansion?

I would probably represent that as dr/dt = k r.
dr/r = k dt
ln r = k t
r = e ^(kt)

r = r_0 * 2^t

 

[Bandersnatch]

But the CBET's do have more information... What kind of telescope; multiple observations of the supernova over time, magnitudes through different colored filters.

I'm pretty sure all those data are accessible from Simbad or the other interfaces listed in the top toolbar on that site. Have a look through the 'output options' and/or display detailed view of an object and explore the links therein.
But perhaps it's easier for you to pull data from your files - I wouldn't know. Just mentioning that there are other options.
By the way, this catalogue:
http://cds.aanda.org/component/article?access=bibcode&bibcode=2012A%2526A...538A.120L
combines CBAT and two others, with some refinement. It's also viewable from Simbad and VizieR on the CDA site. The paper has some links and good discussion of the parameters used - it might be of interest to you.

Here: https://en.wikipedia.org/wiki/Type_Ia_supernova#/media/File:SN1998aq_max_spectra.svg is the spectrum of a Type 1a supernova (taken in 1998). We could (perhaps) identify this pattern by the double-peak in the spectrum around 4000 angstroms. (Do you see the double-peak I'm talking about?)

So if that supernova happens something like a billion light years away, with a redshift of 0.7, then the double-peak would happen at somewhere around 4000*1.7=6800 angstroms. You would identify the redshift of 0.7 by the fact that the double-peak was around 6800 angstroms and solving the equation (1+z)4000=6800. Right?

That's pretty much it, as far as I understand it. You can do a similar analysis with black body spectrum of the CMBR, by the way.
The only issue in what you wrote is tangential to the question: z=0.7 corresponds to about 5 Gly at the time of emission, and about 8.5 Gly now, not 1 Gly.

Then by determining how "bright" the double-peak was--that is, what the intensity of the light through a spectrometer in the region of the double-peak, you would determine the magnitude of the supernova, right?

If you mean apparent magnitude in that band, then yes, it would do. Absolute magnitude ordinarily needs knowledge of distance to calculate. For SN Ia absolute magnitude is always the same (in the sense of e.g. peak magnitude; of course it varies in time for each explosion, but in the same way).

Now, how standard is this methodology for reporting supernova data, though? Does every astronomer reporting their data use compatible methodology so that everybody is measuring redshift and magnitude of the same features, and on the same scale?

I can't help you here. Those are the basics behind the observations. What a typical observation and analysis consists of I do not know, but I'd imagine them to be pretty standardized, considering for how long they've been made.
For something more informative on methodology you'd need to ask somebody who actually does this for a living. Or, what you could do is follow the bibliography Simbad lists for each object and check the methodology in those papers. If it's at all listed, that is. It might be considered trivial.

I think it is an interesting thing to note, what Valenmur calls "constant expansion" is in some ways exponential.
After one period of time the distance from green to blue doubles. After another equal period, that distance doubles again.

The same can be said for the distance from green to purple, and for the distance from green to red.

Is that a standard description of what is meant by constant expansion?

Yes. It means that the first derivative of the scale factor is constant.
By analogy, this is the same as saying that your savings account is growing at constant rate of X% of compound interest, even as the actual amount of money grows exponentially.
Similarly, accelerated expansion means that the first derivative of a(t) increases over time. These are the meanings of acceleration/constancy/deceleration of expansion used in cosmology - not the change in velocities of individual galaxies.
By focusing on a single point in Valenmur's graphs and its motion with respect to the origin over the history of expansion, you may observe accelerated motion even as the expansion is decelerating.

 

[JDoolin]

This is a question for clarification and verification. Valenmur presented three different models

(1) If we had the "constant expansion" universe, the governing differential equation would be $\frac{dr}{dt}=a(t) r$, and a(t) is constant in time. It simplifies to $\frac{dr}{dt}=k r$

(3) If we were to describe that model where everything in the universe starts at a point, and moves outward from that point at constant speed, then the equation for that would be $distance = velocity * time$ or in differential form: $\frac{dr}{dt}=\frac{r}{t}$. This is what shows up in valenmur's diagram as a "decelerating expansion". Or to use the $\frac{dr}{dt}=a(t) r$ description, you could define a scale factor $a(t)\equiv \frac{1}{t}$.

(3) If we have an "accelerating expansion" universe, the governing differential equation would be the same, ($\frac{dr}{dt}=a(t) r$), but a(t) would be increasing over time. For instance, one example might be $\frac{dr}{dt}=k t r$I am surprised by this, because I would have thought of (2) as being "constant expansion" whereas (1) is exponentially increasing expansion, and (3) is, perhaps "hyperexponential" expansion.

 

[Egregious]

I have a very brief layman's question. Thank you everyone for the lively discussion that is mostly over my head.

Q) Based on red-shift, do we know/speculate/theorize that the acceleration of the universe is increasing or decreasing?

There are more technical ways to ask this question. Note that I do understand the difference between acceleration and deceleration. That is not my question. I want to know if there is a contemporary belief about the changing nature of the acceleration of the expanding universe over time. (i.e.: What is happening to the rate of acceleration?) Feel free to be blunt in your replies - I can take it. e.g. I realize that it may be well beyond our collective capacity to measure this with precision over the course of time that we have observed the red shift phenomenon. I have no idea whether this question asks the impossible, or not. I have been wondering this for a while, and unfortunately, the keywords are too common for me to locate an answer.

Thank you kindly.

 

[marcus]

It could help to be clearer what the expansion history looks like and what the acceleration looks like, and think about how you'd assign an amount to it. How you'd quantify it so you could gauge how it was increasing.
In this graph the blue curve shows the size of a generic distance. 0.8 is the present moment in time.
The curve tracks a distance which is set to ONE at the present. For example it could be a distance that is one billion light years at present---and we can look back and see its past history as it grew. And its projected growth in the future.

Think of the the scale on the horizontal axis measuring time in units of 17.3 billion years.
The changeover from deceleration to acceleration happened between time 0.4 and 0.5 when the distance was about level 0.6 on the vertical scale. When it was about 60% of its present-day size.
The deceleration (until around time 0.44 or 0.45) is fairly subtle but we can still see it by eye, in the curve of distance growth. The acceleration is very gentle at first, barely visible. But it gradually builds up.

I'll pause here in case you want to think about this, ask questions. Maybe other people want to respond too, or will explain more stuff. How the model is fitted to observational data. How the model is based on our best theory of the way gravity works: General Relativity as written down in 1917. The equation underlying the curve is derived from the GR equation. GR has been challenged and tested many ways over the years and is supported by a a large amount of data. The standard cosmic model is derived from GR and is in its turn the best fit to a large amount of astronomical data. It does not require the existence of any mysterious "dark energy" , it simply posits a cosmological curvature constant Lambda which governs the longterm fractional growth rate of distance which is expected to level out at around 1/173 of one percent per million years. (The fractional growth rate of distance is the gold curve in the picture, you can see it has been declining and has started to level off.) "Dark energy" was made up as one speculative way to explain Lambda but so far there is no evidence that the curvature constant is anything but that, a constant curvature. Other people may want to discuss this. My main aim here is just to show the expansion history curve and point out the slight deceleration and acceleration in it, to give an idea of what we are actually talking about.

 

[Egregious]

It could help to be clearer what the expansion history looks like and what the acceleration looks like, and think about how you'd assign an amount to it. How you'd quantify it so you could gauge how it was increasing.

I believe that this was in response to my inquiry. Thank you, Marcus for your kind reply and for everything you do for this community.

Again, I am not a physicist. I am merely attempting to resolve a logical conflict in my own mind. Briefly, I agree that a richer understanding of expansion history, but I do not have the requisite tools to begin to understand what happened early in the history of the universe with inflation theory and such (I am 44 years old at the onset of my own quest of self-learning). I do have a cursory understanding of red-shift and the the expanding universe idea. Specifically, images used by Professor Krauss and others have fostered my understanding of the present expansion and why there is no 'center' of the universe. I get this:

https://s16-us2.ixquick.com/cgi-bin/serveimage?url=http%3A%2F%2Fts2.mm.bing.net%2Fth%3Fid%3DJN.GTToVI6o%252fk6J4ZSftGq3bw%26pid%3D15.1%26f%3D1&sp=e79792a08764088e95042fb134e03448​

The logical problem I am confronting goes like so:

1. Nothing can travel faster than the speed of light.
2. Every celestial body is moving away from my planet [i.e. relative to me; i.e the universe is expanding (with a few anomalous exceptions)].
3. This expansion is accelerating.

[edited to merge identical concepts]

My question is whether #3 is also increasing. If I understand your diagram correctly, this appears to be the case (I need to revisit my calculus education). If so, or even if the acceleration is constant, wouldn't there be a a time that #1 is violated relative to earth. This is troubling.

I realize that there may be many esoteric details that I am not prepared to understand. I am embarking on my learning journey from the starting point now to hopefully one day understand more complex questions such as my immediate inquiry. Again, kindly feel free to be blunt: "You are not there yet" is a perfectly acceptable response.

Many kind thanks and warmest regards.

 

[Bandersnatch]

If so, or even if the acceleration is constant, wouldn't there be a a time that #1 is violated relative to earth. This is troubling.

See this FAQ entry:
https://www.physicsforums.com/threads/at-what-velocity-does-the-universe-expand-can-it-be-faster-than-light.508610/

 

[marcus]

Egregious, Bander's suggestion is good. distance expansion is not like ordinary motion, nobody gets anywhere by it, everybody just becomes farther apart. no goal is approached by anybody, relative positions (e.g. longitude and latitude on the balloon if you like that metaphor) do not change. So the general pattern of geometry change---of distance expansion---is not like motion thru space we are used to, and not subject to same rules.

Distance expansion is not limited by the speed limit we have for local motion thru space. nobody is zooming past anybody or outracing a photon of light. But the distances to most galaxies we can see with telescope are increasing faster than light. (so if they sent us a message TODAY it might never get here, but that doesn't matter because they already sent us years and years worth of light which is on its way and will be arriving for billions of years to come so we can observe them they are part of our universe and we are part of theirs.)

 

[PeterDonis]

if we could look further to the time of the Big Bang (which we can not cause the universe becomes opaque to light at a certain point), those two regions would actually be at the same location

No, they wouldn't, because the "Big Bang" singularity is not part of spacetime, and our current models do not even include it as a limit. Instead, there are various speculations about how inflation got started, none of which involve explosive expansion from a single point.

In the idealized FRW spacetimes, there is an initial singularity, but it is still not actually part of the spacetime; it's only present as a limit. But even in these models, two distinct "comoving" worldlines emerging from the initial singularity are causally disconnected until some finite amount of cosmological time has elapsed--how much time must elapse depends on how "separate" the two worldlines are (how much their spatial coordinates differ in the standard FRW coordinate chart). To really see how this works, you need to look at a conformal diagram, which makes causal relationships clearest; Ned Wright's cosmology tutorial contains a good one (see the "Horizon Problem" section at the bottom of the page).

(In fact, the term "Big Bang" should not even be used to refer to the initial singularity; it is properly used to refer to the hot, dense, rapidly expanding state that existed at the end of inflation.)

at one time they were very close together, in the same general location, effectively contiguous

"In the same general location" does not guarantee "causally connected", which is the relevant concept. See above.

 

[Berenices]

Okay can I clean up one topic.
Say you had two distant galaxies just the right distance away from each other that the effects of gravitational acceleration and dark energy were essentially the same.
I am fairly certain that dark energy does not effect the actual velocity of objects but only the distance from each other that two coordinates are observed to be over time. As gravity has an exponential acceleration over time, would the two galaxies eventually get to the point in which their speeds towards each-other overcome the stretching of the space in between them?

 

[valenumr]

I think it is an interesting thing to note, what Valenmur calls "constant expansion" is in some ways exponential.
After one period of time the distance from green to blue doubles. After another equal period, that distance doubles again.

The same can be said for the distance from green to purple, and for the distance from green to red.

Is that a standard description of what is meant by constant expansion?

I would probably represent that as dr/dt = k r.
dr/r = k dt
ln r = k t
r = e ^(kt)

r = r_0 * 2^t

That is what I meant by constant expansion in this context, and your interpretation is exactly correct. By constant in this example, I mean space is expanding at a constant rate for all time, i.e. one (arbitrary) unit of space becomes two after one (arbitrary) unit of time. Because the expansion is a continuous process, this looks like an exponential. At the same time, you should also see that the recession rates are linear with respect to distance. So in this case, the redshift / distance graph would be a perfectly straight line.

So good question, because it really highlights all the key points I wanted to get across.