# Must (Ve) expansion of the universe be C?

1. Jun 14, 2014

### bobie

Is there any experimental, practical reason or aspect of the theory/model that requires that the speed of expansion of the universe be ≥ C?

The Hubble constant, the only experimental datum, comes from a formula Ve/T0*Ve

that allows any possibility. If we considered Ve = C/2 , R would be 7.2 Gly, would that be a problem, since distances are measured according to a model and are not absolute?

That would make inflation, if it really occurred, more plausible , as an increase of speed over a short period wouldn't change sensibly the size of the universe. That would also allow for an increase in the rate of expansion, now, without violating the founding law of the universe

Thanks for your attention.

2. Jun 14, 2014

### Staff: Mentor

What do you mean with "speed of expansion"? There is no unique, meaningful way to express the expansion of the universe as a speed (distance per time).

3. Jun 14, 2014

### marcus

Hi Bobie, I'm always interested by your posts because you seem to be intelligent, but very confused about concepts. You ask questions that are intelligent too, but based on fundamental confusion.

Maybe you could kind of "reboot" your set of conceptions and then it would be easier for you to communicate and get into real discussion of stuff in cosmology. I can try to suggest some conceptual steps, hoping that you will understand it as well-intentioned and not pretentious of me or condescending.

1. We don't know the size of the universe, so we can't say how fast it is expanding, in the normal way you can if you know something's size. So the quantity "Ve" does not exist for us. It is not defined. So your whole post here, because it is about something that is meaningless, is itself meaningless.

2. The pattern of distance expansion IS NOT LIKE ORDINARY MOTION because in Hubble law distance expansion NOBODY GETS ANYWHERE. Nobody approaches any goal, the relative positions of everybody stay the same. Just that everybody gets farther apart.
That kind of distance expansion is allowed by 1915 General Relativity. It is not subject to the 1905 Special Relativity speed limit on ordinary motion.

3. When you say "increase in the rate of expansion, now, without violating the founding law of the universe" you probably are thinking that "the founding law of the universe" is the 1905 Special Relativity speed limit on ordinary motion of one object in another object's frame of reference. Basically the idea that nobody can catch up to, and pass, a flash of light, or if you like "nobody can pass a photon".
But that does not say that DISTANCES cannot increase faster than c, or for that matter HUNDREDS of times faster than c. Distances increasing affects everybody including photons. When distances scale up in all directions between all things, it does not cause anybody to catch up and pass a photon.

4. 1905 SR was about static flat non-expanding geometry. It is very useful because the geometry we live in is only very very slighty curved and only very very slightly expanding. So SR is an excellent approximation
But 1915 GR trumps SR. General Rel is about dynamic (ie. changing) geometry. The effects are almost imperceptible but they are real enough and they show up most clearly over extragalactic distances. We have no right to expect that distances will remain the same. Geometry interacts with matter. Geometry has a kind of "momentum". If it gets started expanding it will tend to continue although the rate may gradually change.

5. In cosmology we have a criterion of being AT REST relative to the background of ancient light. there is the so called CMB the cosmic microwave background that dates back to around year 370,000. It is the soup of ancient glow from the ancient hot gas that filled space at that time. If you move relative to the ancient soup of light, ie. relative to Background, you will detect a doppler hotspot ahead of you and a doppler cold spot behind you.

We know the speed and direction that the solar system is moving, relative to Background.

6. Strictly speaking, the Hubble law expansion of distances is not about any old distance. It is about distances between objects which are at rest with respect to Background---between objects "at CMB rest"---between objects for which the CMB is "isotropic" that is the same temperature in all directions. Normally the individual motions of objects are small---galaxies are pretty much at rest,when you look at the large-scale picture. But strictly speaking you'd have to take account of the fact that they have some small individual motions that aren't part of the Hubble law distance expansion pattern. The current percentage rate of distance growth (between stationary objects) is about 1/144 of one percent, per million years. There is a bit of uncertainty about it. Some people say it is around 1/140 of one percent per million years.

these are just basics (and I'm not an expert, some others here will hopefully correct or clarify as needed). But if you get past the basics there are a lot of fascinating things to learn in cosmology! I hope you stick around and get more into the subject!

Last edited: Jun 14, 2014
4. Jun 15, 2014

### bobie

Hi marcus, it is true that sometime I use imprecise language, I rely on the intelligence of my readers to make little adjustments, but it does not seem to be the case now.

- I just called (for short) Ve what you call recession speed and I specified it means expansion of U. If I made a mistake because Ve implies MOTION, then that's what implies also recession speed and an expanding universe: we are both saying that the distance between us (at the center of the Hubble sphere) and a point/object at distance of a Hubble radius increases by≈C every second

The comoving radius of a Hubble sphere (known as the Hubble radius or the Hubble length) is c/H_0, where c is the speed of light and H_0 is the Hubble constant....
The Hubble length c/H0 is 14 billion light years in the standard cosmological model, somewhat larger than c times the age of the universe, 13.8 billion years. This is because 1/H0 gives the age of the universe by a backward extrapolation which assumes that the recession speed of each galaxy has been constant. However, modern observations indicate recession speeds are increasing slightly due to dark energy, so that 1/H0 is only an approximation to the age of the universe.

You say we don't know the size of the universe,but you know the age of the universe (≈14 Gy)
and that the Hubble radius (U) is ≈C times the age of the universe (14 Gly), well, isn't that the size of the universe? I am using this term as wiki (and everybody) uses that.

- The fact that the size of the Hubble radius is ≈C times the age of U implies that ever since BB the universe has been expanding at ≈C, ergo the average Ve of U is ≈C according to the standard model. Where is the confusion? If the average Ve had been of C/2 the Hubble radius would be ≈7 Gly.
- Moreover, H0 (the only experimental datum about the present), says that 1cm becomes 1cm+2.2*10-17cm every second. Why you derive the size of the present universe dividing C by H0 ? If you consider the present rate equal to the average equal to C/2 (or any other speed) the formula will work: .5 C/H0*.5 C = T0.
Why do you choose C and not C/2, C/4, I asked?

Thanks for you kind words, btw, a friend can never be read as condescending

Last edited: Jun 15, 2014
5. Jun 15, 2014

### Mordred

there is a point your missing, The Hubble sphere is less than the size of the observable universe, considerably less. Though the way your post reads that might be wrong in how I am interpreting your post.
The Hubble radius is more accurately the point at which we observe recessive velocities at c, however at the edge of the observable universe, we observe redshift as at roughly 3c.
so in answer to your question

"You say we don't know the size of the universe,but you know the age of the universe (≈14 Gy)
and that the Hubble radius (U) is ≈C times the age of the universe (14 Gly), well, isn't that the size of the universe? I am using this term as wiki (and everybody) uses that."

this is not the size of the Observable universe, Marcus also referred to the problem that we don't know the size of the entire universe, we only know the size of the observable portion(observable universe, often shortened to just universe many articles don't specify so its best to assume they are referring to the observable universe) Which is larger than the Hubble radius.

using the term moving in regards to expansion should be used carefully (though it is accurate in a sense). The distance is increasing as the volume of space expands, but this imparts no inertia

The term movement though implies momentum which is an inertia term. However as Hubble didn't know why galaxies were receding were stuck with the term recessive velocity (even though there is no velocity involved) in a sense its an apparent velocity rather than an actual velocity.

these two articles will provide some direction in the above
http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell
http://arxiv.org/abs/astro-ph/0310808 :"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies

6. Jun 15, 2014

### bobie

Thanks for your explanation, Mordred. So universe is used both for Hubble sphere and observable universe.
Many think that it is there real size of U, if it is finite ( as you know I assume)
If it were so, then the average Ve is ≈3C.
But then my question remains with a different parameter: since all distances are conventional and model dependent what happens if we set the radius of the Uobservable at 3/2C /H0?

Is it a necessity, bound to some absolute, experimental datum or can be arbitrary?

Last edited: Jun 15, 2014
7. Jun 15, 2014

### Mordred

no your getting this wrong The Hubble radius is the radius at which the recessive velocity becomes greater than c.
it is not referred to as the universe, The observable universe is.
however you need to realize that recessive velocity is a distance dependent relation
Hubble's law states the greater the distance the greater the recessive velocity.

you can't set an average recessive velocity

$$v_{recessive}=H_oD$$

8. Jun 15, 2014

### Mordred

R (Gly) is the Hubble radius, D(par) is the observable universe. Z=000.0 bottom column is the universe today
Z=1089 is the universe when t=0, keep in mind these charts are done in terms of proper distance

the both the R(Gly) and D(par) are non linear you cannot use an average value and get a non linear growth rate

$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&T (Gy)&R (Gly)&D_{par}(Gly) \\ \hline 1089.000&0.0004&0.0006&0.001\\ \hline 767.343&0.0007&0.0011&0.002\\ \hline 540.606&0.0012&0.0019&0.003\\ \hline 380.779&0.0021&0.0033&0.005\\ \hline 268.117&0.0036&0.0057&0.009\\ \hline 188.701&0.0062&0.0097&0.016\\ \hline 132.721&0.0107&0.0165&0.028\\ \hline 93.260&0.0183&0.0280&0.048\\ \hline 65.444&0.0312&0.0475&0.084\\ \hline 45.837&0.0531&0.0805&0.145\\ \hline 32.015&0.0902&0.1363&0.249\\ \hline 22.272&0.1529&0.2307&0.427\\ \hline 15.405&0.2590&0.3901&0.731\\ \hline 10.564&0.4384&0.6592&1.248\\ \hline 7.151&0.7414&1.1130&2.128\\ \hline 4.746&1.2523&1.8740&3.621\\ \hline 3.050&2.1099&3.1334&6.148\\ \hline 1.855&3.5312&5.1412&10.399\\ \hline 1.013&5.8131&8.0532&17.449\\ \hline 0.419&9.2287&11.4928&28.801\\ \hline -0.000&13.7872&14.3999&46.279\\ \hline \end{array}}$$

9. Jun 16, 2014

### Matterwave

I just want to address this one point. The paper gave a lower limit for the size of the universe. There are no upper limits that we know of. So the Universe might be finite but very large, or it might be infinite. We don't know. If the universe is spatially infinite, we can not ever prove this since there is the existence of a Hubble horizon.

10. Jun 16, 2014

### bobie

Read the passage more carefully, Matterwave: it says it may be bigger, that is D> 78 Gly ( in fact many think it is 92) but finite

Last edited: Jun 16, 2014
11. Jun 16, 2014

### bobie

Thanks , marcus, for your resumé of cosmological conceptions. I am and was fully aware of those points, I surely must learn communicate. Let's see if I am able to ask some clear questions:
- which is the 'conception'?

...78 billion light-years :In 2003, Cornish et al. found this lower bound for the diameter of the whole universe (not just the observable part), if we postulate that the universe is finite in size...
,
do you know U is infinite, or not?, if it is finite, which size? Which way should I 'reboot'?
- 'observable' universe (Uo) is a misleading word, as most objects beyond Hubble radius are observed where/as they were in the past, but surely not observable where the stand now, correct?
- is T0 ≈13.8 Gy generally agreed or not? if we change it to, say, 28.8 isit a problem?
- the fact that objects recessing at Ve=c are at 14.4 Gly, whil T0 is 13.8 implies that the average expansion of the edge Ve-av from BB up to now is (14.4/13.8 =) 1.044 c, is this correct?
- H0 is considered the Ve of 1 cm at present time, but, is it possible at all to determine it current value, aren't you determining it sudying distant galaxies? Suppose next minute the expansion stops suddenly (as it began) , when/how could you register that?

The question I asked in the OP is simple :
- if we suppose that Ve-av ,the edge of U has been expanding at ≈.5C, U is finite, its radius would be now(T0*Ve*3.15=) 21.7 Gly (Hubble radius = 14.4 Gly) and the recession speed of Uo= 1.505 C ( below the threshold of relative motion of 2C), what happens? could we rescale the distances of galaxies without problems?, or what problems do arise?
- is the fact that a finite U has an edge a problem?

I hope you have the kindness and patience to address all points, marcus

Last edited: Jun 16, 2014
12. Jun 16, 2014

### Matterwave

How did...how did your original post get under my post?

Anyways, the "finite" part of that passage was a postulate. It's not proven. It is not known currently that the universe is finite.

13. Jun 16, 2014

### bobie

Of course, generally speaking, matterwave, anything in this theory is a postulate, a conjecture: it is infinite, it is finite it is 39, 46, 78, 90..http://en.wikipedia.org/wiki/Observable_universe,

BTW can you address some points so that marcus can solve the more complex ones?
Thanks

I hope someone could restore the post in its proper place.

Last edited: Jun 16, 2014
14. Jun 16, 2014

### Matterwave

The size of the observable universe is not a postulate. It is calculated based on the age of the universe and the theoretical history of the universe's past evolution. However, depending how how the universe expanded in the past, there might be different sizes for the current "observable universe". As we don't have a full and complete history of the universe (although we have some pretty good models) we can't pinpoint perfectly exactly what this size is. However, with better measurements, we should be able to pinpoint this better in the future.

The size of the ACTUAL universe is, by definition, not able to be pinpointed by experiment. This is because obviously if we have an "observable universe" then there is a possibility of an "unobservable universe" which is outside of our Hubble sphere. We can't take measurements of this un-seeable piece of the universe, so we can not say for sure whether it is finite or infinite.

The best we can do is use our current best model of the universe, the FLRW model based on general relativity, and extrapolate its mathematical consequences to the universe at large. The mathematical consequence of this theory is that if the universe is (spatially) FLAT or if the universe's (spatial) curvature is NEGATIVE, then the universe is infinite. If the universe's curvature is POSITIVE, then the universe can be finite. This is a result of the math. If you take the FLRW metric with a positive curvature and integrate over the whole 3-submanifold, you will get a finite answer, whereas if you take the FLRW metric with a flat or negative curvature and integrate over the whole 3-submanifold then the answer diverges.

15. Jun 16, 2014

### bobie

Do you understand they mean this as a postulate or must I rather take it as a basic 'conception' of the theory?

do you get the impression they are saying they do not know?

and what about this:

Last edited: Jun 16, 2014
16. Jun 16, 2014

### Matterwave

I'm not sure what you're asking now.

The theory we use to describe the universe is general relativity. The model that we use is the FLRW model. In this model, a flat universe is infinite as I mentioned in my post above, and your quote says. Current observations is consistent with a flat universe. But flatness is basically a null result. You can't exactly rule out that the universe has SOME curvature but just one much larger scales than we can currently measure.

The above paragraph doesn't tell me the size of the OBSERVABLE universe. The size of the OBSERVABLE universe is something we can go out and make concrete measurements of. But the exact size, since it is dependent on the universe's expansion history, is still dependent on the model.

17. Jun 16, 2014

### bobie

I am asking if a lay reader, like myself, should take both quotes as basic 'conception' of the theory and conclude they do know that the size of U is infinite and that the second quote is conflicting because if T0 is finite (even if enormously greater than the current value) the rate of expansion must be infinite, which is impossible .But, are you hinting that it is known that U is infinite?
What are the parts of the theory that indeed are proven?
it is not exactly like that:
You don't go out there, you use your model to decide the values of the distances. If the model is wrong there is no way to know

Last edited: Jun 16, 2014
18. Jun 16, 2014

### julcab12

......Just a laymen's point of view. T0 is a construction assuming we have a cosmic time/coordinate system that started as 0 (used in slicing spacetime into spacelike sllices). U=Infinite as a postulate is a prediction or limit of the FLRW when approaching time 0 (where density and temperature becomes infinite). We have evidence that our universe is 'statistically' homogeneous and isotropic and not exactly Homogeneous and isotropic due to very very small curve. But since we are dealing with approximation. The model/FLWR best explains this condition. The only natural drawback is when the metric leads to breaking point as it approached 0. It tells us that we need to have a extended mathematical model (QG- String or LQG).

The short answer and key point is that the theory works to a point.

.... Finite part of the picture came from the very small curve (blackbody radiation spectrum). It's the same reason why cosmologist took the mental image of spherically symmetric geometry and use triangle to measure it like how we measure or calculate the circumference of Earth.

19. Jun 16, 2014

### phinds

There is no such thing as "proven" in physics. The best you can do it "fits the data better than anything else and SO FAR has seen no counter-examples". Folks 100 years ago were pretty confident that Newton's Law of Gravity had been "proven" but physicists are more cautious these days

20. Jun 16, 2014

### Matterwave

Nobody can "know" that the size of the universe is infinite. At most, we can use our current mathematical model and show that the model produces an infinite universe given the data. That is all we can say about that. That is all that I ever said.

There are no parts of the theory that are proven. There are postulates of the theory, and then there are parts of the theory that are in accord with data (currently this corresponds to the approximately flat, accelerated expanding, universe).

I mentioned that the size of the observable universe is model dependent. But the size of the observable universe is fundamentally different than the size of the unobservable universe, because BY DEFINITION we can observe the observable universe. In other words, we can make measurements to fit our models. We can refine our models, we can use the observable universe to narrow down those models that give good predictions. We cannot use the unobservable universe to do this.

21. Jun 18, 2014

### bobie

Thanks for your ample discussion of point 1.

Waiting for marcus to answer to the last point (the OP), can you discuss this point?

or give me a link where I can learn in detail how Plancks mission o WMAP determine H0 and T0:
I am not looking for technical details (wiki has plenty ) but for an explanation of the relation between the 2 values:
- which is determined empirically and how , I suppose it's H0,
- if H0 simply 1/ H0, or it can be determined in other ways
- why 1/H0 must be exactly the age of the U

Thanks

22. Jun 18, 2014

### marcus

Hi Bobie, I've been busy lately! This past weekend, our chorus, that I sing in, has given three performances of the long oratorio by Mendelssohn called ELIJAH. Do you know of it? For some reason I assume you are a regular church-goer. If you are, you will quite likely have sung hymns with words set to music by Felix Mendelssohn. You might even be in the choir! I sing bass (either high or low bass depending on what the director needs.)

For the moment I'm at a loss as to how your needs can be met regarding cosmology.

I suspect you need first and foremost to learn to compartmentalize your brain and learn how to think like one of us with part of your mind. You can keep your own private thoughts in another mental "compartment". But whatever your ultimate purposes and interests, you would benefit from assimilating the basic ideas from the point of view of someone who accepts 1915 general relativity as a good approximation.
That is what the current cosmic model is derived from. We use the 1923 Friedman equation which is simplification of the GR equation. (GR is our "Law of Gravity" nowadays, having been repeatedly checked and cross-checked in numerous ways to exquisite degrees of precision.)

In a mathematical science like cosmology there are no final absolute truths. Cosmologists are constantly challenging the 1923 Friedman model and proposing alternatives, and they are constantly challenging the 1915 GR equation that it is derived from. So far these have stood up amazingly well. But I don't know of anyone who thinks they are FINAL. Everybody I know is skeptical in that sense, and expects some proposed alternative to eventually provide a better fit to the data and win out. There are literally MILLIONS of data points that a model must fit, more coming in all the time. Telescopes are automated. So far 1915 GR has stood up, as has its 1923 Friedman simplified version.

There are 3 or 4 basic numbers that need to be plugged in to Friedman equation and adjusted to make the curves fit the data. In that sense many statements (like about age since start of expansion, and about current rate of expansion) are MODEL-DEPENDENT. But keep in mind that these 3 or 4 basic parameters are now rather narrowly constrained. Within a few percent.

You can't make RADICAL changes in either the plug-in parameters or the equation itself without losing a snug fit with the data. So what I would propose is this: whatever your private thoughts may be, you learn the basic language and assumptions of the standard model first, before you try to challenge or find contradictions.

For example suppose your fundamental motivation were to challenge and find contradictions, then by understanding the standard cosmic model you would be able to do so more efficiently! ( Moreover you would be able to better understand current criticism and alternative proposals by professionals---there are professional cosmologists who've devoted their lives to trying to pick holes in the current model and think up alternatives.)

Last edited: Jun 18, 2014
23. Jun 18, 2014

### marcus

One thing to learn is not to assume U has an edge. There is no convincing evidence of an edge. There might be! But without evidence we must remain skeptical and not assume any kind of boundary. (The currently observable region, which is constantly growing as more light comes in from further matter, is of course finite but that is different. The model is of the whole cosmos because so far no indication of boundary.)

There is also no evidence that the U has finite extent. It might be finite and edgeless (analogous to the surface of the earth) or it might be infinite in volume. It is a media lie that expansion started out at a "point". If it is infinite volume now then it was infinite volume at the start of expansion. This cannot be ruled out based on what we know so far, so we have to include it as a possibility.

Go to Lightcone and put this number in for Supper: 0.92956
You will get that with Lightcone's choice of parameters it will be over a billion years before T0 = 1/H0
that coincidence will not happen until year 14.856 billion according to Lightcone.

It is simply not true that T0 = 1/H0 at the present day. Lightcone's figure for the present day is year 13.787 billion. So that particular ephemeral coincidence will not occur for over a billion years. And one should not attribute excessive importance to a temporary coincidence. (The line have to cross some time or other and it just happens the current estimate is they'll cross some time a bit over a billion years from now.)

Last edited: Jun 18, 2014
24. Jun 19, 2014

### bobie

Hi marcus, I am really, sincerely grateful for the time you find for my questions, if you sing low bass you must be quite different from Alfred Newman and more like Pavarotti, quite a great guy !
Please take yor time to reply, just , please, let me know when you've had enough of my whims, don't just drop out.

I hope I'll never think like one of you or luckily like anyone else. I know great scientists refuse to accept GR or other theories. I do not try to pick holes in cosmology: some elementary things puzzle me, and if you answer my question directly I can decide if I was sceptic because I lacked information or rightfully so. I do not hope, or even wish, you to say I was right, after my experience in other threads, but...
Very often physicists are not able to see the wood because of the leaves, so an ignorant schoolboy without microscope-nor-telescope may easily spot it. I pinpoint elementary issues like the fact that if you do not know the size of something, you are never allowed to say it is infinite, if you say something is finite and edgeless, you can refer only to the surface of a sphere, and can never say it is flat. If you forget basic coherence, I scream, if I trespass this boundary you rebuke me.

If you are a great projecting engineer at Ferrari and get in your car from the left, any schoolboy can tell you your car won't go, since you have 2 flat tires on the right side. That does not mean he doesn't appreciate your 'model'.

Now , whenever you have time, please let me know (or tell me where I can learn) a few concrete items not necessarily related to theory:
- if you determine H0 examining galaxies as they were recessing billions of years ago, even if you do it today, that datum refers to U billions of years ago. Probably that galaxy does not exist and U stopped expanding ever since, I asked, " how/when would know if U stopped expanding next minute"
- how you determine T0, and why it is 1/H0, and if it is only determined by H0
- why is it a problem if U has an edge

This is not, I suppose, picking holes, just curiosity.

Last edited: Jun 19, 2014
25. Jun 19, 2014

### Matterwave

You determine the present Hubble constant by looking at galaxies moving away from us. You plot their redshift vs the distance to those galaxies, and you will see a roughly linear pattern. The redshift gives you a recessional velocity, and you define H from the equation: $v=H_0 D$. The Hubble constant is the slope of the best fit line.

When Hubble first discovered this constant, he could only see out to so far and the expansion was always linear. So H was constant as far as Hubble knew. However, the Hubble constant sadly is NOT actually a constant (go figure, what a weird way to name this). This is because if you plotted in your graph out far enough, the data points will no longer be linear. In that case there is no best fit line.

You determine the age of the universe depending on the model of the universe that is used. It is not always 1/H. In fact, the age of the universe is only T=1/H if the universe's expansion was and has always been constant. This is not the case. So the actual age of the universe depends on the model that best fits the expansion history of the universe. It so happens...by coincidence, that the actual age of the universe, using our best current model, IS actually quite close to 1/H. But this is, as far as I know, simply a coincidence of the current best fit model.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook