# Idea for cosmo Basics (minimum to understand meaning of expansion)

1. May 24, 2013

### marcus

If you want, see how this would work as really beginner-level introduction. I'm hearing misconceptions about expansion---not necessarily from the present company, more generally in lay public. People ask what is expanding? how can galaxies recede faster than light? if space is boundaryless then it must be infinite and if it is infinite how can it expand? So if it expands it must have a boundary and there must be "space outside of space", right? You may have heard fallacies like that.
Can you define the key cosmo concepts in a nutshell and do it CONCRETELY enough so beginner has something definite he/she can picture? Some permanent mental images to hang on to?
For concreteness I've included numbers in this thumbnail sketch. So many numbers might be counterproductive, not sure about that. Instead of trying to say what space "IS", I concentrate on the Cosmic Microwave Background. Redbelly once observed that from a certain POV it is the CMB which is expanding. In an operational practical sense, I think. Anyway here it is, feedback welcome. There are seven points:
======

1. We live in a remarkably uniform soup of ancient light.
A cubic meter has about 413 million ancient photons from around year 370,000. A typical wavelength is nowadays about one millimeter. Microwave ripples about as fine now as wrinkles in your skin or the teeth of a comb. When emitted in or around year 370,000, they were much shorter wavelengths: light similar to sunlight but just a bit more orange colored.

2. If you move in some direction at some speed relative to the soup, you will detect a brighter microwave background spot in that direction. The temperature will be fractionally warmer by the fraction which equals your speed divided by the speed of light. That is the doppler effect. Solar system is moving at 1/8 of a percent of speed of light in a certain direction. We see the ancient light just 1/8 of one percent warmer than average in that direction.
For an observer at cosmic rest, not moving relative to this soup of photons, the brightness or temperature of the light is isotropic (meaning: same in all directions). It is the same in all directions to within one part in 100,000---uniform to within one thousandth of one percent.

3. Models of the universe run on cosmic time, as could be clocked by observers at cosmic rest anywhere in space (but not so close to a concentration of mass like a black hole that it would appreciably slow their clocks down.) Given similar clocks and thermometers, stationary observers all over the universe measuring the same temperature of ancient light would estimate the same age of universe--IOW share a common time.

4. Probably the most widely used idea of distance at cosmic scales is proper distance defined at some specified instant of cosmic time. This is simply the distance as it would be conventionally measured if you could freeze things at a particular moment. Of special interest are distances between pairs of stationary or nearly stationary objects (whose individual motions relative to the background of ancient light are small enough to be neglected).

5. The ancient light was emitted (in year 370,000) from matter which was then 42 Mly from what became our galaxy, and which is now 45 Gly from us. Both the distance to that matter and the wavelengths of the light have been enlarged by the same factor (slightly over 1000-fold) while the light has been in transit. The temperature of the light has fallen off by the same factor, as its wavelengths have stretched out.

6. What is meant by expansion is that, at any given moment, distances between stationary observers (i.e.pairs of observers at cosmic rest) and wavelengths of light in transit are growing at the same universe-wide percentage rate. This is estimated to be currently 1/144 % per million years and to be headed for a longterm limiting rate of 1/173% per million years. The two basic things that the standard LCDM cosmic model is about are:
A. the dynamical behavior of this percentage growth rate: how large it has been in past, how rapidly it has declined, what longterm rate (we think 1/173%) it is tending towards, and
B. the curvature of space. We know it is nearly zero, and exactly zero would mean that the radius of curvature (somewhat like a car's turning radius) would be infinite. However the curvature measurements so far are consistent with either infinite radius of curvature, or just very long (on the order of 100 Gly or larger).

7. So far no convincing evidence either that space has any boundary or that the distribution of matter is not approximately uniform throughout. So for simplicity we don't "make up stuff" about some higher dimensional "space outside of space" or empty space beyond some imagined "limit" of matter. The cosmic model, based as it is on GR, would become needlessly complicated if one tried to include such features---and why include them absent solid evidence? Space not having boundary does not imply anything about its volume---the overall volume of a boundaryless space can be either finite or infinite.

Last edited: May 24, 2013
2. May 25, 2013

### timmdeeg

Not necessarily. Note that locally euclidean spaces may be compact as well. The LCDM model isn't about topology and whether or not the universe is infinite, it's about the local geometry of space.

To my opinion the Cosmological Principle, which you mentioned quite indirectly, belongs to the very Basics. Perhaps it would fit into 7.

3. May 25, 2013

### marcus

Thanks for the comment! I agree that locally flat spaces can be compact!
I was referring to the radius of curvature---unless I'm mistaken this is defined locally and can be infinite where the curvature vanishes (whether or not the space is compact.)
That said, point 7 doesn't cut it. Needs to be better thought out. If you have a few sentences you'd be willing to offer as a substitute, I'd welcome seeing them. I was thinking about perennial confusions we see people struggling with and tacked that point on at the end admittedly without a clear idea of what needs to be communicated. For now, unless you or someone else gets inspired and suggests an addition, I will just edit point 7 down:

7. So far no convincing evidence either that space has any boundary or that the distribution of matter is not approximately uniform throughout. So for simplicity we don't "make up stuff" about some higher dimensional "space outside of space" or empty space beyond some imagined "limit" of matter. The cosmic model, based as it is on GR, would become needlessly complicated if one tried to include such features.​

Maybe less is more, in this case. Fewer words could add clarity and make it read better.

Last edited: May 25, 2013
4. May 25, 2013

### timmdeeg

Yes I think so too, infinte radius of local spatial curvature means mandatory exact flatness. What I intended to express was that e.g. the 3-Torus is locally 'exactly' flat. There is no contradiction.

5. May 25, 2013

### marcus

Maybe the 3-torus should actually be mentioned. The "pac-man" idea can communicate how it can be exactly flat. A Euclidean cube with opposite faces identified. Or that could belong in another "chapter". I'm trying to think how to boil down the hard essentials. what does really need to say, in one page, or even one paragraph, about cosmology, to a misconception-ridden newcomer who imagines the big bang as an explosion from a point called "singularity" outwards into empty space. :-)

Last edited: May 25, 2013
6. May 26, 2013

### Jorrie

I found that this start may be a mental barrier to beginners, because we also live in a "soup of ancient starlight", with a lot more oomph! I do not know how to keep it short, but something about the all-encompassing, cooling "particle-photon' soup and its transparency should perhaps be said. What about starting with: "Before there were stars and galaxies, the entire universe consisted of a hot, dense, remarkably uniform soup of particles and photons that were cooling, because the particles were rapidly separating from each other and the wavelengths of the photons increased in step with the lower temperature...", or something similar.

7. May 26, 2013

### marcus

Sounds good to me. I'll try to incorporate those ideas in a revised next draft.

It's clear, as you point out, that to human eyes the starlight is a lot more noticeable! So it may seem strange to beginners not to mention starlight. It would be appropriate, I think, to say something indicating how substantial this CMB "soup" is, even though we don't see or feel it! It takes advanced instruments to detect and map it, even though it represents 96% of the electromagnetic energy in an average cubic kilometer of space.

In case of curiosity about the relative energy density (as a fraction of critical) here is Peeble's energy inventory (2004):
http://arxiv.org/abs/astro-ph/0406095

Compared with the "dark sector" in which he includes dark energy and represents roughly 95% in his accounting, the estimated EM radiation portion is understandably very small. Negative powers of 10 like 10-4 and 10-5---so numbers like 1/10,000 and 1/100,000 of critical.

They give the CMB fraction as 10-4.3

and "post-stellar" radiation, including starlight, as 10-5.7 (These large scale average densities naturally don't reflect local conditions like being near the sun :-D)

From this sees that the CMB currently represents about 96% of all electromagnetic radiation in an average cubic kilometer of space. Starlight and other contributions make up the remaining 4%.

(I just put 10^-4.3 /(10^-4.3 + 10^-5.7) into google calculator for evaluation and it came out slightly over 0.96)

Last edited: May 26, 2013
8. May 26, 2013

### Naty1

Marcus,
If you'd like to see a very interesting 20 minute explanation of 'cosmological expansion' try Leonard Susskind's 'cosmology, Lecture #3.

The full list is here: You can pick out Lecture #3

In the first 20 minutes or so of Lecture #3, he recaps the full detailed explanation and calculations which comprise all of his Lecture #2. The big advantage I see is that Susskind introduces the scale factor a[t] in a rather direct and uncomplicated way...not necessarily intuitive, but darn close to it.

See what you think.

Note: Susskind does not provide any motivation for the cause of expansion; he assumes it and then describes what it means...how we measure it....It seems that's your aim, too.

9. May 26, 2013

### marcus

Timmdeeg and Jorrie, thanks for the responses! I feel I'm out on a limb here, trying to boil down cosmology basics for beginner is something like one or two pages. It may not be possible, or I may be going about it the wrong way. But I want to try. And it certainly helps to have some reaction!

What's on my mind is that you can't really define the time or distance used in cosmology without the idea of cosmic rest or as sometimes said "CMB rest". Expansion itself is not even isotropic except to observers at rest.
So do we tell beginners about this, or do we gloss it over with necessarily vague language?

And then the Hubble law expansion speeds are also dependent on the idea of observer at CMB rest. Hubble law would not hold in a boosted frame, and so on.

So if we take a stab at introducing that right at the start, what do we call it and how describe it?
413 million photons in a cubic meter, 96% of all the electromagnetic radiation loose in the universe, more than 10 times as much as starlight. This ought to make an impression as something real. And very nearly uniform, so you can really tell when you are moving relative to the soup.

At the moment I can't think of much in the way of an alternate introduction to the idea of cosmic rest (and the other things that logically depend on it for their definition.)

10. May 27, 2013

### timmdeeg

Cosmo Basics for Beginners. So, why not start to bring typical beginner questions into the right order? Then a frame including the answers (I wouldn't mention the questions) would be given. E.g. having explained the Cosmological Principle things like edge/center and the like are clarified. Then a few sentences regarding expansion. From this together with the CP the meaning of 'at rest' follows quite easy. Any arbitrary observer at rest will see the galaxies recede the same way. In this respect, I would explain the CMB shortly, because too many details might confuse the beginner. And perhaps then continue to differentiate between observable universe / universe as a whole, and this refering to the big bang era and the following epochs, including some remarks regarding finite / infinite.

But believe me, Marcus, I am well aware that many cooks might spoil the soop.

11. May 27, 2013

### marcus

Just speculating. Tim and Jorrie, that might be a good opening sentence, and then one could bring in the CP idea that Tim was stressing. And then touch on the idea of "cosmic rest" or observers being "at CMB rest". For instance something like:

"Before there were stars and galaxies, the entire universe consisted of a hot, dense, remarkably uniform soup of particles and photons. So far we have not seen evidence that this had a center, or edges. We see no indication of a boundary, of any "space outside of space", or of any major asymmetry: the cloud ancient matter, judging from the most ancient light we can detect, looks approximately the same in all directions---the technical term is "isotropic".

The structured appearance of matter today, and the individual motions of galaxies can be explained by the matter comprising that ancient, nearly uniform cloud having fallen together in clumps and clusters drawn by its own gravitational attraction. If we look at the big picture we still see a universe that is homogeneous and isotropic--and as a reality-based assumption about the cosmos at large scale this is called the Cosmological Principle...."

That could be a way to bridge between Jorrie's opening sentence and Timdeeg's suggestion of basing the development of ideas on the Cosmological Principle. Then one could introduce the idea of isotropic observers---who are at rest relative to ancient matter and ancient light and therefore see the cosmos as essentially the same in all directions (without a big Doppler effect due to their own motion).

Feel welcome to add to, subtract from, or rewrite any of this! Adding to especially: one or more paragraphs of proposed continuation would be great!

12. May 27, 2013

### Mordred

The first paragraph should include homogenous along with isotropic definition. Instead of particles and photons, You might consider radiation.

I would also recommend recessive velocity explanation, and using a 3d graph of coordinates as part of the explanation of expansion.

key points on the graph 1]the coordinates do not change 2]the angles between any set of coordinates do not change. merely the space between coordinates.

13. May 27, 2013

### Ogr8bearded1

Does the lack of asymmetry take into account the latest Planck data? I'm curious because of what I read here from http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe specifically the following "Another is an asymmetry in the average temperatures on opposite hemispheres of the sky. This runs counter to the prediction made by the standard model that the Universe should be broadly similar in any direction we look.

Furthermore, a cold spot extends over a patch of sky that is much larger than expected.

The asymmetry and the cold spot had already been hinted at with Planck’s predecessor, NASA’s WMAP mission, but were largely ignored because of lingering doubts about their cosmic origin.

“The fact that Planck has made such a significant detection of these anomalies erases any doubts about their reality; it can no longer be said that they are artefacts of the measurements. They are real and we have to look for a credible explanation,” says Paolo Natoli of the University of Ferrara, Italy."

14. May 27, 2013

### marcus

the cold spot and the hemispheric anisotropy are (to me at least) interesting and, as you mention, they were detected by WMAP. I recall a fair amount of discussion. However we still have approximate uniformity to one thousandth of one percent. This is the first thing to realize--the amazing evenness.

Then once you realize that, temperature variation only one part in a hundred thousand, you can lay over that an awareness of these very interesting slight departures from the basic underlying uniformity. That's my PoV anyway.

The things you mention were discussed in the March official Planck report (the scholarly technical journal type one, e.g. in the conclusions section at the end. You might like to read the way they presented those findings in the official report---the language is carefully measured, kind of hype-less compared to what I've seen in public media and press-release writing about the same topics.

You may have seen this:
http://arxiv.org/abs/1303.5076

conclusions on pages 53 and 54. Actually your pubic outreach article may be more comprehensible :big grin: Thanks for the link.

Last edited: May 27, 2013
15. May 28, 2013

### timmdeeg

I agree with all you are saying but does it belong to Basics, stuff for beginners? Asymmetry and cold spot might still be explainable as being due to fluctuations!

16. May 28, 2013

### Naty1

Marcus:
Seems like you kind of assume people know the universe is expanding in your early points.

suggest putting something upfront [#1] about a most basic characteristic of the universe: It is expanding..... ever since about 13.7B years when it first appeared in space and time.

I'd also be inclined to mention that when the CMBR was emitted at your 370,000 years of age the universe was close to 3,000 K and today it is about 2.7K.....and is expected to continue to cool more, get bigger while CMBR is expected to continue getting weaker....

Of course, if you use everybody's ideas you'll have a book instead of a few pages!!

You also posted sometime ago how expansion affects the number of observable galaxies....that's a concept beginners could find 'concrete relative to their own visual observations.

17. May 28, 2013

### Ogr8bearded1

Would this be a good visual of how the expansion is working? Imagine an escalator going up and you are walking down. One step down equals one light year travelled. For every x steps you take, another step appears at the bottom of the escalator. You have to travel every step that was between you and the bottom and also the new steps that appear in order to reach the bottom. The Hubble Constant determines how fast the escalator is going. If the 'speed' of the escalator adding new steps is faster than your speed you never reach the bottom. If it is slower, you will reach the bottom, but had to travel further than if had been on a standard staircase.

18. May 28, 2013

### marcus

Timdeeg, Jorrie, Mordy, Ogr8, Naty thanks for all the comments and suggestions! Maybe everyone who isn't too busy could try writing a couple of opening paragraphs, or an entire page. We could see how different openers read.

I looked up Wikipedia on "Cosmological Principle" and found that it seems to be said different ways by different people, often rather abstractly. And I couldn't find any reference to cosmic rest!

They were saying "looks the same in all directions, to all observers" but that is not true. If you are moving some direction relative to the universe it looks different in that direction from what it does in other directions. The CMB is hotter in the direction you are going.

So I hesitate to launch a basic spiel for beginners with a statement of the Cosmo Principle because its so abstract and there is no one unambiguous statement of it (judging from Wikip).

But one or more of you others might pull it off and it might be better than what I have in mind. I'd urge you to try.

I'm leaning towards an approach where you say as quickly as you can what cosmic rest means, and base that on very concrete experience.

Because all the other definitions (including expansion if you want to be really clear about it) depend on having a clear idea of cosmic rest---of what it means to be an observer who is stationary relative to soup of ancient light.

I think that also means, as far as we can tell, stationary relative to the ancient matter---the hot cloud--which we in effect SEE at a distance of 45 billion ly, because the light is the hot 3000 Kelvin glow that was shining from that cloud, and finally after all those years is getting to us.

So being a stationary object or observer is a very concrete real thing. That's how I'm thinking I would begin (rather than on an abstract level).

But it would be great to see some alternative opening paragraphs, for comparison. and in fact they might give us ideas of getting the best of both approaches, or they might simply be better.

19. May 28, 2013

### marcus

That's a good dynamic image but you know that most of the galaxies we are seeing today emitted the light we are getting when they were receding faster than light, so the light was initially losing ground. In other words there are some complications and subtleties that an escalator or moving sidewalk doesn't get. For example the SPEED of distance growth is proportional to the size of the distance. A feature that the escalator doesn't have. But there's a place for such analogies, or, say, a swimmer or a boat trying to go upriver.

There's a good visual illustration of a photon or flash of light getting swept back at first and loosing ground, and then holding its own, and then gradually making progress and eventually getting there! What this does is show the track. Getting farther away at first. The distance from us rising at first, leveling off, and then sloping down and getting less and less as it approaches us.

This is how to get the picture. It's easy to graph curves, good skill to pick up. Basically 3 clicks.
Open http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
Click on "chart" and "set sample chart range"
Click on "column definition and selection" and UNCHECK everything except Time and Dthen
Press "calculate"

Dthen is the distance from us back THEN (at the indicated time) of a photon which is eventually going to get to us and will arrive today. So you can see it increase at first. And then get smaller and hit zero at present-day which is year 13.8 billion.

After that, the curve tells the story of a photon or flash of light that we send out today, so you can see it getting farther and farther, actually helped by expansion (rather than being hindered as the incoming light was.)

Last edited: May 29, 2013
20. May 28, 2013

### Mordred

If you want short this don't qualify lol. Naty1 has it right covering all the key points in expansion leads to an ever expanding article lol.
Anyways heres what I have thus far.

The subject of Expansion is a major factor in understanding Cosmology. As a key factor in our understanding of the large scale properties and development of the observable universe, it is of crucial importants. A useful analogy to visualize expansion is to make use of a 3d graph. With each (x,y,z) line crossing representing a coordinate. The rate of expansion in accordance to the cosmological principle, which
can be defined as "no preferred location" or homogeneous (one region is the same as another) and "no preferred direction " or isotrophy (one direction is the same as another). In cosmology this applies at extremely large scales roughly 100 Mpc.
As expansion occurs the distances between all coordinates (x,y,z) in a uniform and even manner (at large scales). The angles between any two coordinates, nor the coordinates themself change. The amount of space between the coordinates have simply increased in a uniform distribution. 3) the increase in space imparts no inertia or momentum to any mass.
As gravity pulls matter and therefore energy together. Some other force must be driving expansion. As energy-mass per volume (energy mass density) is equivelent to pressure, expansion energy/force can be defined as negative pressure. Or more classically "vacuum energy" or "dark energy". Represented by the greek symbol lambda. The source of the vacuum energy is still not understand however its key properties is. 1) It is constant thoughout the universes history. 2) It is of uniform distribution.

The historical development into our understanding the nature of expansion occured primarily since the Early 1900's. Notable advances occured with Hubble's measurements of receeding galaxies which developed into "Hubble's law": " The greater the distance the greater the recessive velocity" . This means that at large enough distances the recessive velocity is greater than the speed of light. However this does not violate the speed of light barrier as expansion imparts no inertia. In truth Hubbles kaw is an "observer dependant scalar value.
Another key research is Einsteins field equations, which inlcude general and special relativity.
These developments as well as others. Combined with the uniform nature of the universe allowed the development of an important mathematical modelling of the universe called the FLRW metric. Or Freidmann-Lemaitre Robertson Walker
metric. In which the rate of
expansion at a given slice of time
is represented with "a". " the
cosmological constant with
lambda.

Last edited: May 28, 2013
21. May 29, 2013

### marcus

Thanks for contributing your ideas Mordy. I'm still concentrating on what Ogr8 (Ogreat :-) said about the progress of a photon thru expanding space. I want to show in a simple way how it sometimes it gets swept back but can still make it later.
So I followed the "3 click" recipe I described above, with one difference, that I did not uncheck the Hubble radius. The size distance that at any given time is expanding at speed c. Including that curve gives us a handle on how the expansion rate changes over time. So here's the picture. You can see the photon is dragged back at first, then at a certain point its forward motion is exactly canceled and the slope is zero (neither gaining nor losing ground). And then it begins to close the distance to its destination (us.) It arrives in year 13.8 billion, at which time you can see the Hubble radius is about 14.4 billion ly.

The red curve is the photon's proper distance from us. The blue curve is the Hubble radius. They cross where the photon is making zero progress because its distance is increasing at speed c, just canceling. The swimmer is swimming exactly the same speed as the current setting him back.

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22. May 29, 2013

### Naty1

One approach might be to divide your discussion into a few general parts such as

General Concepts,

What is Cosmology
What is the universe
What is the most used model of the universe
What are the basic assumptions in that model
The universe is expanding
The expansion is accelerating
Time and Distance in cosmology
What can we observe in the Universe

Observations and Characteristics
Tools
How are scale factor, redshift, and Hubble parameter related
CMBR characteristics
Balloon analogy
etc,etc,etc
scale factor
expansion factor z
superluminal expansion

23. May 29, 2013

### timmdeeg

They (Wikip) neglect peculiar velocities and I think that's ok in a cosmological context.

It's funny, I would argue vice versa. Having introduced the concept of isotropic expansion, then the concept of 'being at rest' follows quite naturally. Observers at rest would recede isotropically away from each other. This includes the CMB, because the atoms emitting this radiation are at rest too.
In other words, firstly one would introduce the expanding balloon and then mark the dots on it.

24. May 29, 2013

### marcus

Hi I just got back after doing some chores and was glad to see your comment. I'd especially like to see what you would come up with by way of a one or two page introduction to cosmology. How would you introduce the concept of isotropic expansion?

It seems like an elegant approach. The concepts of cosmic rest, cosmic time, proper distance, and stationary observers getting farther apart (including at speeds > c) DO seem to follow from it, unless they have been already introduced in order to say what "isotropic expansion" is.

I should say what got me thinking about this. I have been exposed (not at PF, somewhere else) to a bunch of stubborn expansion-denialists and people with the deep-rooted preconception of matter exploding from a center outwards into pre-existing empty space. Some do not seem prepared to imagine space with anything besides Euclidean ℝ3 geometry, so no finite volume boundaryless geometry is conceivable. Almost any ABSTRACT language will be misconstrued. So I've gotten around to considering what might be possible by way of a very concrete experiential introduction, where the concepts are clearly defined at each step (to minimize the chance of misconstruction.)

This does not mean that you or anybody else should be urged to write for that audience! I'd really like to see what you would come up with for a different audience, say more like yourself (e.g. able to handle abstractions and imagine experiencing curved/changing geometry), that just happens to include newcomers to the subject. Or whatever readers you have in mind.

I'm curious to see how you would introduce the idea of isotropic expansion as an opening gambit (understand the blank balloon first and then paint galaxies on it, as you said.)

25. May 29, 2013

### Mordred

LOL glad you mentioned that I tend to jump right in on writing articles for that matter currently working on 5 of them on different subjects