Expansion and Inflation

[geordief]

Space between non gravitationaly bound objects such as  galaxies  increases with time.

 

I have read about the consequences of this phenomenon but not so much about the phenomenon itself.

 

It permits objects to recede from one another at speeds higher than c,I think.

 

Is this speed as seen from a third frame of reference or  also from that of one of the objects in question?

 

If the latter is true does that imply that these objects are (never were) not connected in the causative sense? 

 

Also ,is Inflation similar to Expansion (differing in degree and circumstance as it were) or are they completely different animals?

 

[Strange]

41 minutes ago, geordief said:

Space between non gravitationaly bound objects such as  galaxies  increases with time.

I have read about the consequences of this phenomenon but not so much about the phenomenon itself.

It permits objects to recede from one another at speeds higher than c,I think.

That is correct. If you multiply the distance between things by a constant scaling factor, then the speed of separation is proportional to distance. Consider a number of galaxies separated by the same distance (far enough apart that the expansion of space is significant and the same between all of them).

At time 0, they are 1 unit apart:
A.B.C.D.E.F

After some time they are 2 units apart:
A..B..C..D..E..F

After the same time again, they are 3 units apart:
A...B...C...D...E...F

And so on:
A....B....C....D....E....F

Now, if we look at the distance between B and C, for example, it increases by 1 at every time step. But the distance between B and D increases by 2 at every step. So the distance between B and D is increasing twice as fast as the distance between B and C; i.e. the speed of separation is twice as great.

Choose any pairs of galaxies and you will see that apparent the speed of separation is proportional to the distance between them. Take two objects far enough apart and the speed of separation will be greater than the sped of light. 

43 minutes ago, geordief said:

Is this speed as seen from a third frame of reference or  also from that of one of the objects in question?

We can see galaxies that are receding faster than the speed of light. This isn't a problem because the "speed limit" only applies locally (or you can think of it as being a limit within special relativity but not general relativity). We are not in the same (inertial) frame of reference as those distant galaxies.

45 minutes ago, geordief said:

If the latter is true does that imply that these objects are (never were) not connected in the causative sense? 

We are connected causally to galaxies in the observable universe (because we can see them). Some of these are receding faster than c. But we are not causally connected to things beyond the cosmological horizon (outside the observable universe - actually, that isn't exactly the same thing, but near enough for now!)

I'm not familiar enough with inflation to comment on that. My understanding is that, unlike expansion, it would have been driven by some sort of force/field in order to achieve the massive expansion rates hypothesised.

[geordief]

8 minutes ago, Strange said:

 

We can see galaxies that are receding faster than the speed of light. This isn't a problem because the "speed limit" only applies locally (or you can think of it as being a limit within special relativity but not general relativity). We are not in the same (inertial) frame of reference as those distant galaxies.

 

That seems an interesting observation . I am not sure I understand that.  You can't expand ( a tiny bit) on that  can you?

[swansont]

36 minutes ago, geordief said:

That seems an interesting observation . I am not sure I understand that.  You can't expand ( a tiny bit) on that  can you?

Adding space (expansion) doesn't count as a speed. Two objects get further apart, but it is not due to their motion, so the SR limit of moving slower than c does not apply.

[geordief]

2 hours ago, swansont said:

Adding space (expansion) doesn't count as a speed. Two objects get further apart, but it is not due to their motion, so the SR limit of moving slower than c does not apply.

It was Strange's "but not general relativity" that had me intrigued.

[Strange]

2 hours ago, geordief said:

It was Strange's "but not general relativity" that had me intrigued.

Well, it probably wasn't a very accurate statement. Except that SR only deals with local, inertial frames of reference - so no curvature, no change in scale factor (expansion), etc.between the two frames. For those cases you need GR where, as we can see, it is possible for apparent speeds to be greater than c. (But still, locally, the speed limit applies.)

[geordief]

2 minutes ago, Strange said:

Well, it probably wasn't a very accurate statement. Except that SR only deals with local, inertial frames of reference - so no curvature, no change in scale factor (expansion), etc.between the two frames. For those cases you need GR where, as we can see, it is possible for apparent speeds to be greater than c. (But still, locally, the speed limit applies.)

I didn't realize GR  could\did  model the expansion of the Universe.

Are we getting into "Einstein's greatest mistake" territory?

 

[Strange]

1 hour ago, geordief said:

I didn't realize GR  could\did  model the expansion of the Universe.

Oh yes. The Big Bang model is solidly based on GR. The first person to come up with this solution to the equations of GR was Lemaitre. Who then used the observations (later described as Hubble's law) to determine the rate of expansion.

Quote

Are we getting into "Einstein's greatest mistake" territory?

Kinda, yeah. He initially assumed the universe was static (because everyone did, then) and added just the right amount of energy to keep it balanced between expanding and contracting. When Lemaitre published his work, Einstein probably slapped himself on the head!

[Mordred]

Probably and he probably kicked himself with Hubbles findings of expansion even though he knew his model predicted either expansion or contraction.

I have to admit Geordief your starting to make a huge progress in your recent threads well done and keep up the good work. You are asking well thought out questions.

Edited December 31, 2017 by Mordred

[geordief]

53 minutes ago, Mordred said:

Probably and he probably kicked himself with Hubbles findings of expansion even though he knew his model predicted either expansion or contraction.

I have to admit Geordief your starting to make a huge progress in your recent threads well done and keep up the good work. You are asking well thought out questions.

Thanks for that encouragement. And a happy new year to all

[beecee]

On 12/31/2017 at 11:08 PM, swansont said:

Adding space (expansion) doesn't count as a speed. Two objects get further apart, but it is not due to their motion, so the SR limit of moving slower than c does not apply.

 

On 1/1/2018 at 4:21 AM, Strange said:

Well, it probably wasn't a very accurate statement. Except that SR only deals with local, inertial frames of reference - so no curvature, no change in scale factor (expansion), etc.between the two frames. For those cases you need GR where, as we can see, it is possible for apparent speeds to be greater than c. (But still, locally, the speed limit applies.)

 Both answers that are essentially correct, although as a lay person, and answering other lay persons, I generally just say that the universal speed limit, "c" only applies to things with mass...spacetime has no mass.  How many out of ten for that answer? 

[Mordred]

How about 5 out 10 massĺess particles are also limitted to c. Though they equal c lol. Also spacetime curvature requires a mass density distribution even though spacetime itself is just a volume where time is treated with dimensionality of length. After all mass tells spacetime how to curve. Probably the more accurate answer is expansion does not involve kinematic motion. As the universe is roughly uniform in mass distribution there is no net force in any direction to cause a directional motion via f=ma. Though unfortunately that tends to confuse some laymen lol.

  

Edited January 2, 2018 by Mordred

[geordief]

Global Expansion seems like it should have a quantifiable rate .

.Would  this rate of expansion have any relationship  or connection to c?

Was there any value for c (according to the model,I guess) in the inflationary period?

[Mordred]

The dimensionless scale factor " a" or  the Hubble parameter. Both vary at different points of the expansion history. The reason is quite lengthy to explain but as expansion occurs the density of radiation and matter changes as well but at different ratios.

 Expansion is a thermodynamic process, as the matter, and radiation density varies while the cosmological constant stays constant each affects expansion though during different eras in our expansion history one has been more dominant than the other. The sequence is radiation, matter then Lambda dominant eras. (inflation is a radiation dominant phase)

[beecee]

1 hour ago, Mordred said:

How about 5 out 10 massĺess particles are also limitted to c. Though they equal c lol. Also spacetime curvature requires a mass density distribution even though spacetime itself is just a volume where time is treated with dimensionality of length. After all mass tells spacetime how to curve. Probably the more accurate answer is expansion does not involve kinematic motion. As the universe is roughly uniform in mass distribution there is no net force in any direction to cause a directional motion via f=ma. Though unfortunately that tends to confuse some laymen lol.

  

You are essentially saying....

 

https://einstein.stanford.edu/content/relativity/a11332.html

Can space exist by itself without matter or energy around?

No. Experiments continue to show that there is no 'space' that stands apart from space-time itself...no arena in which matter, energy and gravity operate which is not affected by matter, energy and gravity. General relativity tells us that what we call space is just another feature of the gravitational field of the universe, so space and space-time can and do not exist apart from the matter and energy that creates the gravitational field. This is not speculation, but sound observation.

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

The highlighted part was an error which you need to omit. I e-mailed Sten Odenwald on that rather confusing bit..- I wish he would take the time to remedy though!

 

Edited January 2, 2018 by beecee

[Mordred]

No thats not what I stated at all. You've probably seen the expression " spacetime tells mass how to move, mass tells spacetime how to curve". Spacetime is any metric where time is treated as a dimension. Space is simply the volume.

 Whether space can exist apart from spacetime is a seperate topic deserving of its own thread. 

 

 

4 hours ago, beecee said:

 

 , I generally just say that the universal speed limit, "c" only applies to things with mass...spacetime has no mass.  How many out of ten for that answer? 

If spacetime requires a mass distribution to cause curvature how can it have no mass ? The quoted section doesn't make much sense considering the the following formulas (not including critical density

The acceleration equation is given as

[latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex]

This leads to

[latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex]

The evolution of matter, radiation and lambda and how it affects expansion can be seen here

[latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex]

These formulas all involve mass terms in the matter, radiation and Lambda density terms.

(trying to answer two posts at once)

Anyways it is the mass densities of each contributor that defines the rate of expansion. So the quoted section doesn't make much sense.

The reason why they don't cause an inherent direction to expansion to LSS and galaxies is those same contributors have a uniform distribution surrounding the LSS and Galaxies. So in essence via f=ma no structure facing has a greater force than any other facing. The uniform distribution doesn't support a stronger force upon any facing to impart inertia. 

Instead the metric volume itself expands.

Not to mention the greater than c expansion rate is due to a specific formula [math] v=H_0d[/math] the greater the distance the greater the recessive velocity. (its an apparent not a true inertial velocity that depends on the observers distance).

Local to any observer location the rate is identical within the first Mpc roughly 70 km/sec/Mpc. Being the value of time (now) in the past ie at CMB its roughly 22990 times that value. One can calculate that via the last equation.

You can see the column here that applies that equation. The row where S =1.00 and a equals 1.00 is today the last column is rate today the 1090 row is surface of last scattering in the H/H_0 column. 

We chose to use Gly instead of Mpc as many posters better relate to lightyears as opposed to parsecs

[math]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/math] [math]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&H/Ho \\ \hline 0.001&1090.000&0.000373&0.000628&45.331596&0.041589&0.056714&22915.263\\ \hline 0.002&608.566&0.000979&0.001594&44.853035&0.073703&0.100794&9032.833\\ \hline 0.003&339.773&0.002496&0.003956&44.183524&0.130038&0.178562&3639.803\\ \hline 0.005&189.701&0.006228&0.009680&43.263304&0.228060&0.314971&1487.678\\ \hline 0.009&105.913&0.015309&0.023478&42.012463&0.396668&0.552333&613.344\\ \hline 0.017&59.133&0.037266&0.056657&40.323472&0.681908&0.960718&254.163\\ \hline 0.030&33.015&0.090158&0.136321&38.051665&1.152552&1.651928&105.633\\ \hline 0.054&18.433&0.217283&0.327417&35.002842&1.898930&2.793361&43.981\\ \hline 0.097&10.291&0.522342&0.785104&30.917756&3.004225&4.606237&18.342\\ \hline 0.174&5.746&1.252327&1.874042&25.458852&4.430801&7.300157&7.684\\ \hline 0.312&3.208&2.977691&4.373615&18.247534&5.688090&10.827382&3.292\\ \hline 0.558&1.791&6.817286&9.184553&9.242569&5.160286&14.365254&1.568\\ \hline 1.000&1.000&13.787206&14.399932&0.000000&0.000000&16.472274&1.000\\ \hline 1.791&0.558&22.979870&16.668843&6.932899&12.417487&17.112278&0.864\\ \hline 2.961&0.338&31.510659&17.154169&10.671781&31.602098&17.220415&0.839\\ \hline 4.896&0.204&40.170941&17.267296&12.969607&63.498868&17.267296&0.834\\ \hline 8.095&0.124&48.860612&17.292739&14.364429&116.275356&17.292739&0.833\\ \hline 13.383&0.075&57.557046&17.298283&15.208769&203.541746&17.298283&0.832\\ \hline 22.127&0.045&66.254768&17.299620&15.719539&347.823873&17.299620&0.832\\ \hline 36.583&0.027&74.952986&17.299815&16.028491&586.370846&17.299815&0.832\\ \hline 60.484&0.017&83.651102&17.299968&16.215356&980.768127&17.299968&0.832\\ \hline 100.000&0.010&92.349407&17.299900&16.328381&1632.838131&17.299900&0.832\\ \hline \end{array}}[/math]

 

 

Edited January 2, 2018 by Mordred

[beecee]

53 minutes ago, Mordred said:

No thats not what I stated at all. You've probably seen the expression " spacetime tells mass how to move, mass tells spacetime how to curve". Spacetime is any metric where time is treated as a dimension. Space is simply the volume.

Yes. John Wheeler?? from memory. OK, I see the difference, personally I'm in a habit of referring to it all as spacetime.

 

Quote

 Whether space can exist apart from spacetime is a seperate topic deserving of its own thread. 

I'll consider that. 

 

Quote

If spacetime requires a mass distribution to cause curvature how can it have no mass ? The quoted section doesn't make much sense considering the the following formulas (not including critical density

I understand that, but doesn't the universe/spacetime overall have a topology that is very nearly flat?   And isn't there a difference between the mass/energy density IN spacetime, [galaxies, stars planets etc] to the mass/energy density OF spacetime? [possibly the Cosmological Constant or whatever is the impetus of the DE component]? 

Quote

(trying to answer two posts at once)

I have "faith" in your ability.  

 

Quote

Anyways it is the mass densities of each contributor that defines the rate of expansion. So the quoted section doesn't make much sense.

Just as our local group of galaxies, due to mass/energy densities is decoupled from the overall expansion rate? And as other high mass/energy density regions of spacetime are decoupled.

 

Edited January 2, 2018 by beecee

[Mordred]

Yes the overal topology is flat but one must have care on what the term flat vs curve means in this context.

 Its not flat as per a shape but flat as to how the universal field densities affect the worldlines of light paths. Curvature causes parallel light paths to either converge or diverge. A flat field geometry maintains parallel paths. This is how it applies within our observable portion.

21 minutes ago, beecee said:

 

Just as our local group of galaxies, due to mass/energy densities is decoupled from the overall expansion rate? And as other high mass/energy density regions of spacetime are decoupled.

 

Yes but one has to be careful here the infall of matter into LSS formation aids expansion as it concentrates matter into smaller regions while reducing the overall global density. So a matter only universe can expand due to this evolution as the global density decreases gravity on a global scale lessens. While at the locality of an LSS strengthens.

21 minutes ago, beecee said:

 And isn't there a difference between the mass/energy density IN spacetime, [galaxies, stars planets etc] to the mass/energy density OF spacetime? [possibly the Cosmological Constant or whatever is the impetus of the 

 

Yes the mass density of an LSS region is much higher than the average. A side note the cutoff boundary of an LSS is when the mass density becomes less than 100 times the critical density of the universe. It is the local strength of gravity that prevents global expansion via the cosmological constant from affecting within the LSS structure. The coupling strength of an LSS overpowers the Lambda term locally. So yes an LSS is in essence decoupled from expansion.

Edited January 2, 2018 by Mordred

[beecee]

7 minutes ago, Mordred said:

Yes the overal topology is flat but one must have care on what the term flat vs curve means in this context.

 Its not flat as per a shape but flat as to how the universal field densities affect the worldlines of light paths. Curvature causes parallel light paths to either converge or diverge. A flat field geometry maintains parallel paths. This is how it applies within our observable portion.

Yes but one has to be careful here the infall of matter into LSS formation aids expansion as it concentrates matter into smaller regions while reducing the overall global density. So a matter only universe can expand due to this evolution as the global density decreases gravity on a global scale lessens. While at the locality of an LSS strengthens.

OK, I'm getting there, (I think) slowly but inevitably. Thanks. 

[Mordred]

No problem anytime