# F-L-R-W metric

1. Mar 9, 2014

### bobie

I am trying to self-study FLRW and I hope someone cares to answer a simple question regarding this explanation:http://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric#Newtonian_interpretation
If I got it right the expanding matter is contrasted by the force of gravity, now if at the big bang all the matter exploded at the same moment, there was nothing or very little left, where does the G pull come from?

2. Mar 9, 2014

### Bandersnatch

Hi bobie,
Try not to think of BB as an explosion like that of a dynamite, but the beginning of a continuous increase in distances between "stuff". After BB the total amount of matter(and energy) was the same as it is today. It just became more diffused as space expanded.

3. Mar 9, 2014

### Staff: Mentor

To add to Bandersnatch's post, note that right after the big bang, at the point where our calculations can predict things instead of giving us infinities, the universe was VERY hot and VERY dense. The energy in the universe consisted of matter and antimatter particles along with extremely high energy EM radiation. Conditions were so extreme that the radiation itself interacted and created particle-antiparticle pairs, which then annihilated with each other to produce high energy radiation. This cycle of creation and annihilation would have continued forever had the universe not been expanding. Fortunately for us, the universe does expand, and this expansion reduced the average temperature of the universe to around 3 kelvin instead of 3 trillion kelvin or more.

In GR gravity comes from the stress-energy tensor, and mass contributes to the energy part of that tensor. So gravity in the early universe came from the mass of the existing particles, their kinetic energy, and the energy in the form of EM radiation.

4. Mar 10, 2014

### bobie

That is what I am thinking of, Marcus's balloon analogy. Matter is getting more distant from the origin and diffusing itself in a wider sphere, so the Sun and the earth and galaxies and black holes ets exert a pull in a direction norma to the the radial expansion of the universe whose radius is a in the formula.

If it is not so can you give a better explanation/interpretation of the formula?
One more question, (k) c^2/2 is kinetic energy? if so it implies that the speed of expansion is C?

5. Mar 10, 2014

### Bandersnatch

What I think you're doing, is misinterpreting the analogy. The balloon analogy requires you to think only of the surface of the balloon as the universe. There is no radial component to the universe confined to the surface. The third spatial dimension in which the surface is embedded has got no physical meaning. That's why there is no point of origin, and there is no empty void surrounded by a shell of matter anywhere in the universe.

So, matter is not getting more distant from the point of origin(there is none! the BB happened everywhere at once!), it's only getting more distant from other matter. For all intents and purposes one could think of the Milky Way as occupying roughly the same region of space that it has occupied since it had formed.

We can think of the radius of the curvature of the universe, to describe how much space is curved globally(i.e., open, close or flat universe), but this does not imply the existence of a fourth spatial dimension. It's just a way to describe the geometry of space.

In the equation cited, the kinetic energy is on the leftmost side of the equation. But I don't feel confident enough to discuss it in detail. Maybe somebody else will.

6. Mar 10, 2014

### bobie

so , this is wrong?http://en.wikipedia.org/wiki/File:Universe_expansion2.png
if the universe is just the top layer of the picture, where is to origin from where to calculate the values here:
The second equation says that the kinetic energy (seen from the origin) of a particle of unit mass moving with the expansion plus its (negative) gravitational potential energy (relative to the mass contained in the sphere of matter closer to the origin) is equal to a constant related to the curvature of the universe. In other words, the energy (relative to the origin) of a co-moving particle in free-fall is conserved.
How do you delimitate the sphere 4/3πa3 ?
Lastly, if the top layer is not a sphere (the surface of Marcus's balloon) all CMB would be long lost, don't you think?

Last edited: Mar 10, 2014
7. Mar 10, 2014

### Bandersnatch

In the picture you linked to, there third axis is not spatial but temporal(it's t not z).

The origin in the wikipedia description of the Newtonian interpretation of Friedmann equations is not the origin of the universe(there is none!), but an arbitrarily chosen point from which you measure e.g., the potential energy of a particle.

I don't understand what you mean by delimitating the sphere.

The CBM wold be long lost if the universe was a sphere of matter receeding from some point of origin. You've got it backwards.

8. Mar 10, 2014

### bobie

Thanks, probably I was misled by the balloon analogy.
Let's start all over from the beginning, if you are willing to follow me patiently:

At the origin of time t0 at the bottom of the picture there was a cube od dense matter/energy, then everywhere inside this cube there was at the same time there where a great number of "explosions" which are not explosion like with dynamite, but of mysterious origin.
Am I right so far?
- the laws of physics are valid everywhere and at any time since then, so , according to the third law of motion, the expansion should take place in every direction, while in the picture it develops only on the xy plane, why so?
The side of the cube is a in the formula and a with one dot is velocity and with two dots is acceleration,is that right? if so could you please explain the formula in details?
a^2/2 is KE of a unit mass near the origin (where mass was at t0) this is contasted by the G-pull in a sphere with radius a divided by the radius itself multiplied by ρ (the curvature of the plane xy ) and the difference is a konstant k multiplied by C^2/2 ?

Is the speed of each unit-mass the same and is it C?
If the "explosions" take place everywhere , don't the particles overlap, clash and the espansion is not isotropic in conclusion.

9. Mar 11, 2014

### Bandersnatch

Just to make sure you understand what the "cube" is(I can't tell from the paragraph):
It has got nothing to do with the physical shape of the early universe. The cube is an arbitrarily chosen volume of possibly infinite space, used to derive the first pair of the two equations that you can find on the wiki page under "Newtonian interpretation". The cube is used simply because it makes it easier to calculate how much 'stuff' is leaving through each of the six rectangular sides.
Similarly, the second equation(the one you linked to in post #4) uses a sphere to describe an arbitrary volume of expanding space, simply because it makes it easier to write down the gravitational potential for a unit mass sitting on the sphere's outer edge.
Neither describes the shape of the universe, and both are valid descriptions for ALL space, at ALL times.(keeping in mind that Newtonian interpretation is not actually valid but an approximation)

Also, it's best to completely forget about explosions, and just think of distances increasing. Imagine a cartesian grid floating in space in an early universe. You could give 'stuff' back then coordinate positons. All the BB is about, is that these coordinates ALL increase by the same factor.
This factor is called the "scale factor", and is what $a$ is in the Friedmann equations. $a$ is a function of time, so it's actually $a(t)$, which means that we can talk about the rate of change $\dot{a}$ and the rate of change of the rate of change(i.e., acceleration) $\ddot{a}$.
The scale factor is understood in mathematical terms to be $r=a(t)x$, where $r$ is the "proper distance", i.e., the distance between e.g., two galaxies(or anyting) you could measure with a measuring stick at some particular moment if you stopped the expansion for the duration of the measurement. $x$ is the "comoving distance", which is the distance the grid floating in the early universe(or at any time we defined beforehand) that I mentioned before would show. Comoving distance is the distance that 'moves with the Hubble flow', i.e., it doesn't change as the time passes.

A planar representation of the universe is usually used to allow visualisation of four-dimensional effects. It's impossible to imagine a 3d space curved in the fourth dimension, but it's quite easy to visualise a 2d space curved in third. That's what the balloon analogy does. In the case of the wiki picture, one could arguably draw a 3d shape and show how it expands as time progresses, but I think the picture simply wants to tie in with the balloon analogy representation of the universe as a 2d surface.
The important part: it's just an analogy. We live in spatially 3d, expanding universe. Not on 2d plane.

The $\dot{a}$ was explained earlier when talking about the scale factor.
The c in the equations is not a speed, but a constant(or a conversion factor). It doesn't mean anything is moving at c any more than c in $E=mc^2$ does.
There is no clashing or overlapping, since the equations are NOT describing explosions. They describe metric expansion of space. That is, all distances in all of space(possibly infinite) increase equally(by the same factor). If this is true, then you can't get an overlap, as that would mean some distances decreased. This is exactly what the balloon analogy aims to show: each and every distance increasing.

As I said, I'm not feeling too comfortable explaining the details of the equation, as I don't understand it all that well.

Why won't you try reading some earlier threads on the forum like this one:
the OP appears to have a similar conundrum to yours.

You can also type into google "newtonian interpretation of friedmann equations" and read through many lecture notes and simialar resources you'll find there.

There are also university lectures on youtube that can help you understand the prerequisite ideas of the scale factor, Hubble parametre etc. (look for introduction to cosmology. I think Leonard Suskind has got a number of those)

10. Mar 11, 2014

### bobie

You have done a wonderful job, Bandersnatch, thank you!, I'll try to digest that and get back.

In the meanwhile, please, check if I got the main scheme right:

There was some matter (1053 Kg) in a region of space (unknown volume), at t0 (BB: 13.8 billion years ago = 4.3*1017 sec) space starts expanding and drags along matter in it. The radius of the universe now is estimated 4.3 *1028 cm.. Curvature is 0
Can we conclude that the rate/speed of expansion is close to C?

One simple question, if you know:
If there is no "explosion" where does KE come from? Can empty space, or a metaphysical entity such as a "metric" move matter?
Thanks again

Last edited: Mar 11, 2014
11. Mar 11, 2014

### Bandersnatch

I can see from the numbers that you're talking about the observable universe specifically. We can calculate what size the volume that is now 46 billion ly across was during the recombination(when CMBR was emitted). It was 1090 times smaller.

The curvature is not necessarily 0, but it does look like it might be.

You can't conclude that the expansion speed is globally c, or any other velocity for that matter, because it is distance dependent.
Remember Hubble's law? The expansion speed is defined as $v=H_0D$. As you can see, the speed depends on the distance, so you can find two points in the universe that will be sufficiently far away from each other, that after multiplying by the Hubble parametre $H_0=~67.8 km/s/Mpc$ will net you whatever speeds you want, including c and over c(breaking c around 14.5 billion ly). But any points close to each other receeded at correspondingly lower speeds.
Just look at the balloon analogy again - the points close by expand proportionally slower than points farther away.

But if the whole point of asking was to find out whether the expansion can break the speed of light, then yes it can. Despite that, nothing can ever overtake light on its way, so it is not in conflict with relativity.

I've no idea where it comes from. I don't even know if it's a sensible question to ask, given that it's just a newtonian interpretation. Again, I don't have a thorough enough understanding of the subject.

As for moving matter, the whole point of expansion is that it's not really 'moving' anything(hence no problem with breaking the speed of light). Everything stays where it was(comoving distance remains the same). It's only that (proper) distances increase. Which I know is a weird thing to wrap one's head around.

12. Mar 11, 2014

### Staff: Mentor

According to my understanding, there is no KE. The expansion is not matter "moving through" space, but the geometry of space changing in a way that causes distances to increase without requiring any acceleration of any matter.

13. Mar 12, 2014

### bobie

I think nothing is weird as long as it is rational and does not violate the fundamental laws of physics, but "metric" is just measure of space, which is empty, has no energy, no force, no powers what made it swell: dark energy? Still more pregnant is the fact that it was not an exceptional, unique event, but it is happening in this very moment.
But the main point is : suppose it is true, and it can indeed reproduce itself and expand ad lib, how can it make increase the distance between two massive bodies?

What I do not understand is : if , as also Drakkith says, there is no KE involved bodies do not move, then the only force in play is G, which, (as distance always increases), becomes weaker and weaker so, what is the sense of the second equation?

Another thing which is not clear is: how can CMB survive since the universe is unbouded in every direction and CMB can escapes and be irretrievably lost?,
if universe were really spherical like a balloon it would circulate indefinitely. You said the reverse is true, can you explain why?

One last simple question:
what prevents the hypotesis that matter was in one place and exploded like a huge hypernova? That would have scientifical basis, concrete evidence, consistency with known regular observable phenomena and solve most of the problems

Last edited: Mar 12, 2014
14. Mar 12, 2014

### Bandersnatch

Ugh. This is a typical case of the blind leading the blind.
I refuse to continue this discussion for the fear of sowing even more confusion.
All I can say is that there most certainly is a term for KE in the equation(find the derivation on the net) and that it's just a newtonian interpretation and so it is grossly incomplete(e.g., lacks 94% of energy in the universe).
Seriously, get a proper book with derivations and discussion.

I did not say that, or at leats did not mean to say that. I think we're still not on the same page regarding the balloon analogy.
If all there is to the universe is the analogue of the balloon's surface, and the CMBR is also confined to that surface(there's no third dimension), then it is indeed possible to imagine it circulating indefinitely(but it won't, due to the expansion of space having the ability of being faster than the speed of CMBR propagation).
I thought you meant to say, back when I was correcting you on this, that an explosion happened in the centre of the balloon, and what we see as CMBR is the radiation emitted therein passing the surface - which would happen only once and we would never see it again.
Is that more clear now?

Eh, you keep saying that but you never mean it
You need to think about what you mean when you say that. What does it mean it has got "scientific basis"? What concrete evidence is there to support it? Is there any that disproves it? Why should it need to be similar to some other phenomena?(if we like to think of the Big Dipper as a dipper, is it ok to say it must be a real dipper?) What problems would it solve?(apart from being easier to imagine)

The point being, it's the expansion of space that fits the observations(homogenity and isotropy, Hubble law, CMBR), has got scientific basis(General Relativity), solves most of the problems(why it looks like we're in the centre of the universe? why is CMBR so uniform?). It even is consistent with a known regular observable phenomenon of balloons expanding, if you care for that kind of thing.

You can find all there is to know about why it is thought that there was no localised explosion on the net, starting with our own FAQ:
this page has got a thorough treatment of the evidence for the layman:
http://www.talkorigins.org/faqs/astronomy/bigbang.html

Last edited by a moderator: May 6, 2017
15. Mar 12, 2014

### bobie

Thanks, Bandersnatch, you have been very kind and helpful, I knewe those links, the point is that I do believe there was BB, I am only trying to learn what forces make it happen. Maths, derivation and formulas only describe quantitavely how it works, do not explain what is behind.

If you care, I'll tell you what I meant:
If you consider the universe as the rubber part of a deflated balloon (not 2-D but ly-s thick) and inflate it blowing it by KE, you get all the phenomena Hubble describes, and also numerical values are consistent T =2 r, the distance increases according to observations the radiations (CMB included) circulate indefinitely , space-time is curved, and the universe keeps it itself like a soap bubble thanks to surface tension provided by G. Is there need to imagine constants or dark matter/energy?,
why can't the universe be a 3-D sphere?
I hope someone is able to answer this question?

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

### Staff: Mentor

The metric is not a measure of empty space. Per wiki:

The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past.

The metric is used to describe spacetime at ALL locations, from the supervoids of intergalactic space, to the inside of black holes.

There is no reproduction. Empty space is not a "thing". The expansion does not create empty space, it simply makes distances between objects increase over time.

The part of the CMB that reaches us was radiated from sections of space further away from us 380,000 years after the big bang at the time of recombination than the part of the CMB that reached us yesterday or the day before. The current radius of the observable universe is about 45 billion light years. That means that the part of the universe that radiated the CMB that we see now is currently 45 billion light years away. At the time of recombination, that part of the universe was only millions of light years away, not billions. Due to expansion, it has taken the current CMB almost 13.7 billion years to reach us.

In simpler terms, the CMB we see today was created shortly after the big bang and has simply taken all this time to reach us. But what we are seeing now is only a very, very small part of the CMB. The rest of the CMB was radiated in a different direction and will never reach us, just like most of the light from the Sun is radiated into space, not onto the Earth.

What? The evidence we have is entirely against such an explosion. The very fact that we can look in every direction and see large scale homogeneity in the CMB and galaxy distribution is strong evidence against the idea of an explosion of matter in one location.

The fact that it is X light-years thick goes against the very idea that the big bang was an explosion of matter at one point in space. It also doesn't fit observations since a balloon's material gets thinner as you blow it up, which would be the opposite of what we observe.

17. Mar 12, 2014

### Bandersnatch

@bobie:
It can't be like that because then there would be a preferred direction. I.e., the universe would not look isotropic. The expansion radially would not look the same as the expansion tangentially(the radial expansion velocity would not be proportional to distance as Hubble law shows - it would not be accelerating). There would be no homogenity, as there would be voids of space in all but tangential directions. The CMBR would not be homogenous either, as the radiation coming from the radial direction would have a finite thickness to travel through, and would not experience redshifting equally from all directions. You could even identify the direction of origin, and it would not look like it's where you're standing(what we observe).

18. Mar 12, 2014

### bobie

Thanks a lot folks, for your help, I hope I can get back when I have digested all that

Last edited: Mar 12, 2014