When Will the Big Crunch Happen According to Current Models?

[Devils]

I've looked up various sources & none gives a time for the big crunch. We know the universe is accelerating, which I presume gives us a quadratic equation that can be solved. So when will the big crunch happen using current models?

And no I'm not after an answer like '9am on a Saturday!", an answer to the closest billion years would suffice.

 

[phinds]

According to current theory, there will not be a big crunch. Why do you think there would be?

 

[Devils]

Well I see Big Rip (increase in dark energy density), Big Freeze (heat death), and Big Crunch as possible scenarios in what's I've read.

Can you point me to why the Big Crunch is excluded.

 

[phinds]

The Big Rip is not an increase in dark energy, it is the result of one hypothesis as to whether or not dark energy can ever have any effect on small scales. The current consenus is that it cannot, thus no big rip. If it CAN, then current theory leads to the Big Rip

Heat Death is the end result of current theory.

Big Crunch would require something to overcome dark energy and stop the expansion, allow it to reverse into collapes and at present there is not even a hypothesis as to what that might/could be.

 

[Mordred]

Along with Phinds answer. With current measures were headed toward heat death. However no standard theory has a timeline. As say standard theory in that their have been some articles describing heat death around 14billion years from now. However that is only a single model proposol. Not a universally accepted timeline. There is no universally agreed upon timeline.

 

[cepheid]

Well I see Big Rip (increase in dark energy density), Big Freeze (heat death), and Big Crunch as possible scenarios in what's I've read.

Can you point me to why the Big Crunch is excluded.

To add to what others have said, current observations show that expansion of the universe is accelerating (speeding up). This should automatically tell you that if this trend continues unchanged, the universe will expand forever. A Big Crunch would require the expansion to slow down, stop, and reverse itself, becoming a contraction. This is ruled out by current observations, which favour a universe in which the distance between any two points in space vs. time looks something like the solid bold line in this figure:

http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

Notice that this plot shows that this distance continues to increase without bound, and it does so not just linearly, but at an ever increasing rate.

The Big Rip is not an increase in dark energy, it is the result of one hypothesis as to whether or not dark energy can ever have any effect on small scales.

To be fair, I'm pretty sure that a Big Rip scenario requires a dark energy whose density increases with time, as opposed to remaining constant, as is the case for dark energy in the form of a standard cosmological constant.

 

[phinds]

To be fair, I'm pretty sure that a Big Rip scenario requires a dark energy whose density increases with time, as opposed to remaining constant, as is the case for dark energy in the form of a standard cosmological constant.

I think I've heard it both ways as far as gravity is concerned, but on thinking about it, it DOES seem to me that if the big rip is to go all the way down to the level of atoms then it would require an increase in dark energy's power to break the strong force.

 

[cepheid]

I think I've heard it both ways as far as gravity is concerned, but on thinking about it, it DOES seem to me that if the big rip is to go all the way down to the level of atoms then it would require an increase in dark energy's power to break the strong force.

The dark energy is usually described by its equation of state parameter, w, which is ratio of its pressure to its energy density. For more details, see the second paragraph of this paper here:

http://arxiv.org/pdf/astro-ph/0302506v1.pdf

or just read the whole thing. It's short (just a letter) and I found it to be great fun. As you can see from the equation at the end of that second paragraph, w = -1 corresponds to a dark energy density that is constant with time (or with scale factor 'a', as a proxy for time), and w < -1 (which is required for a Big Rip) corresponds to a dark energy density that increases with time.

Of course, that was 8 years ago, and current constraints on w are perfectly consistent with w = -1. For instance, temperature anisotropy data from Planck, combined with WMAP polarization data, data from another CMB experiment with higher angular resolution (ACT), and BAO data sets constrain w = -1.13^+0.23_-0.25. I think the "Big Rip" scenario has more or less been ruled out.

 

[marcus]

...
Of course, that was 8 years ago,... I think the "Big Rip" scenario has more or less been ruled out.

That's the impression I get too. The paper you cited is 10 years old.

 

[cepheid]

That's the impression I get too. The paper you cited is 10 years old.

In my mind I wish it was still 2011

 

[marcus]

I've looked up various sources & none gives a time for the big crunch. We know the universe is accelerating, which I presume gives us a quadratic equation that can be solved. So when will the big crunch happen using current models?

And no I'm not after an answer like '9am on a Saturday!", an answer to the closest billion years would suffice.

I agree with Cepheid's answer to this. He already responded, but I will add some additional comment.

You are asking about the current consensus model that most cosmologists use and continues to be increasingly supported as more and more data comes in. It is called LCDM model. It does not involve any "big rip" or "big crunch".

Those dramatic fantasies were discussed quite a bit 10 years ago, or longer. But in the past 10 years we've seen a wonderful abundance of data. Observational data just pours in! and it keeps confirming LCDM.

So now there is not much talk about exotic speculative things that were getting attention 10 years or more ago, like "big rip and big crunch". That might change of course! Future data might hold some surprises! but for now, I would urge you to learn about the cosmic model that is considered most reliable and is in general use by professionals.

What "universe is accelerating" means, in the standard LCDM context, is that if we use the latest Planck mission data that was just reported this month distances between stationary observers are increasing at a rate of 1/146 percent per million years.

And this percentage rate of distance growth is due to decrease in the future and eventually level off at an estimated 1/176 % per million years.

It is this leveling off of the decline in percentage growth rate which is meant by the attention-getting words "accelerating expansion". The decline levels off at a positive rate, instead of going all the way down to zero-percent growth.

So in standard cosmology there is no "crunch" and structures like Milky or solar system or you and me are not "ripped" apart. And "accelerating" just means that the percentage rate of distance growth continues to decline, but doesn't go all the way down to zero.

It's more like classical music and less like Wagner, or the Doors (if you know what I mean
but it's still beautiful! Find out about standard LCDM cosmology! You'll love it!

 

[Devils]

To add to what others have said, current observations show that expansion of the universe is accelerating (speeding up). This should automatically tell you that if this trend continues unchanged, the universe will expand forever.

When you throw a ball up in the air it constantly accelerates (due to gravity), but eventually returns to ground, its starting point ie we solve a quadratic equation. The same logic applied to the big bang means the universe at some point will start contracting, leading to the big crunch.

What "universe is accelerating" means, in the standard LCDM context, is that if we use the latest Planck mission data that was just reported this month distances between stationary observers are increasing at a rate of 1/146 percent per million years.

And this percentage rate of distance growth is due to decrease in the future and eventually level off at an estimated 1/176 % per million years.

It is this leveling off of the decline in percentage growth rate which is meant by the attention-getting words "accelerating expansion". The decline levels off at a positive rate, instead of going all the way down to zero-percent growth.

So in standard cosmology there is no "crunch" and structures like Milky or solar system or you and me are not "ripped" apart. And "accelerating" just means that the percentage rate of distance growth continues to decline, but doesn't go all the way down to zero.

It's more like classical music and less like Wagner, or the Doors (if you know what I mean
but it's still beautiful! Find out about standard LCDM cosmology! You'll love it!

So, is what you are saying, the size of the universe is best modeled by a 3rd or 4th degree polynomial, that eventually just slows down growth. I'll do some reseatch on LCDM.

 

[cepheid]

When you throw a ball up in the air it constantly accelerates (due to gravity), but eventually returns to ground, its starting point ie we solve a quadratic equation. The same logic applied to the big bang means the universe at some point will start contracting, leading to the big crunch.

NO. That's what physicists thought prior to 1999. That the universe is expanding, but that the expansion should be slowing, because of the mutual gravitational attraction of all the matter within it. What was discovered was that the expansion is NOT slowing. It is getting quicker. The acceleration is positive, not negative. That's what's so crazy about dark energy: it has a repulsive, anti-gravitational effect. It's like throwing a ball up and having it keep going. Not only that, but it goes faster and faster and faster! Did you even read my first post and look at the plot I linked to there? If you had, you would have seen this.

 

[Devils]

Well that's totally crazy, as crazy as quantum mechanics.

 

[Passionflower]

The current consensus is that it cannot, thus no big rip.

When the evolution of physics is guided by the popular vote then watch out.

Feel free to show mathematically why FRW dust solutions would work differently at the small scales until then the popular vote is just as important as who wins the local juggling contest.

I mean who needs crackpots when we have 'scientist' claiming with a straight face that nebulae in expanding FRW universes do not expand because they are gravitationally bound?

 

[cepheid]

Well that's totally crazy, as crazy as quantum mechanics.

"Crazy" is a subjective notion. When I said "crazy" in my previous post, I merely meant "counterintuitive," or, "contrary to expectation." In the end this (an accelerating universe) is what the data support, and that is what's ultimately important in science. The same is true of quantum mechanics. We hold on to it as a theoretical framework because of its predictive power and the stunning degree to which it has withstood experimental test so far. Or, to put that another way, the degree to which it has been supported by experimental evidence. We don't just cling to it because physicists are perverse and like to promote "crazy" ideas. You, of course, are free to think of it as being crazy if you like.

When the evolution of physics is guided by the popular vote then watch out.

Feel free to show mathematically why FRW dust solutions would work differently at the small scales until then the popular vote is just as important as who wins the local juggling contest.

I mean who needs crackpots when we have 'scientist' claiming with a straight face that nebulae in expanding FRW universes do not expand because they are gravitationally bound?

Actually, it IS shown mathematically in the paper I linked to above (Caldwell, Kamionkowski, and Weinberg), that if w >= -1, then systems that are presently gravitationally bound will remain so forever, whereas if w < -1, all gravitationally bound systems will eventually be ripped apart. This is because, in the latter case, the dark energy density continues to increase with time, until it eventually becomes dominant even on small distance scales, whereas in the former case, the dark energy density remains constant or decreases with time. I'm sorry that this doesn't accord with your intuition, but's not really anyone's problem but your own.

You seem to have an axe to grind, and are resorting to semantics in order to do so. Phinds did not mean to suggest that physics was done by popular vote. In the context of a scientific result, when someone says, "the consensus is <blah>", he or she means that the current best interpretation of the observational data is <blah>, and therefore the majority of scientists conclude <blah>. If you just want to pick a fight by resorting to strawman arguments like this, then I suggest you do so elsewhere.

 

[Passionflower]

Actually, it IS shown mathematically in the paper I linked to above (Caldwell, Kamionkowski, and Weinberg), that if w >= -1, then systems that are presently gravitationally bound will remain so forever, whereas if w < -1, all gravitationally bound systems will eventually be ripped apart. This is because, in the latter case, the dark energy density continues to increase with time, until it eventually becomes dominant even on small distance scales, whereas in the former case, the dark energy density remains constant or decreases with time.

I am not disagreeing with that. I am disagreeing with saying "well at large it is ripped but not locally because it is gravitationally bound" there is zero mathematical proof for that or feel free to show observational data that indicates the proposition true.

 

[cepheid]

I am not disagreeing with that. I am disagreeing with saying "well at large it is ripped but not locally because it is gravitationally bound" there is zero mathematical proof for that or feel free to show observational data that indicates the proposition true.

I don't get it. It seems like you are saying, "I'm not disagreeing with this, I'm just saying something that is totally contrary to it." Can you perhaps clarify your position?

Independently of dark energy and "ripping" (let's say there was no dark energy), if you're wondering why the universe as a whole expands, but gravitationally-bound structures (a single galaxy, our solar system, or an atom, which is bound by electromagnetic forces) do not expand, the answer is even simpler. At that point, you're not dealing with an FRW solution anymore! Recall that FRW solutions are solutions to the Friedmann equations, which are a simplification of the Einstein Field Equations (EFEs) that are true in the case of isotropy and homogeneity. On the largest scales, the universe is homogeneous, and so an FRW solution accurately describes the global dynamics of the universe (as a whole). However, on small scales, the distribution of matter in the universe is highly inhomogeneous. You have a galaxy "over here" and absolutely nothing "over there." The simplifying assumptions that lead to the Friedman equations and FRW solutions are not longer valid. So, the solution to the EFEs locally is totally different than it is globally. For one thing, it's a non-expanding solution.

Even earlier in the universe's history, when things were more homogeneous, this idea still applied. For example, suppose you had a flat universe, with a mean density approximately equal to the critical density. Now, suppose, at some point in space you have a matter over-density, a region where the density locally is higher than the mean. Within this over-dense region, the density is higher than critical, and you can show that this region acts like its own little closed pocket FRW universe, within the flat FRW background. The perturbation does not expand at the same rate as the background, but behaves somewhat independently of it. Also, the amount of over-density actually grows linearly with time. However, this is within the context of linear perturbation theory, which is valid when δρ/ρ < 1. Eventually, things go non-linear, and this overdense region collapses into a gravitationally-bound structure (a dark matter halo). At this point its physical size remains fixed, independent of the expanding background. This is how gravitationally-bound structures arise within the LCDM paradigm in the first place.

 

[Passionflower]

So, the solution to the EFEs locally is totally different than it is globally. For one thing, it's a non-expanding solution.

Do you know that GR is a non linear theory? Do you agree that that implies you cannot simply add local solutions to global solutions?

Do you disagree with that?

Also an FRW solution is a fluid (of dust if you think that sounds fancier) solution, there is no single piece of vacuum in this solution, it is all matter. I suppose you fail to see the irony in claiming that 'it does not apply to everything that is not vacuum' when the model is used as an approximation for our own universe, which is mostly empty space with heavy localized clusters of matter?

Now, suppose, at some point in space you have a matter over-density, a region where the density locally is higher than the mean. Within this over-dense region, the density is higher than critical, and you can show that this region acts like its own little closed pocket FRW universe, within the flat FRW background.

I am sure you would not object to show me how to mathematically include, as you call it, pocket solutions into larger solutions?

 

[marcus]

...
What "universe is accelerating" means, in the standard LCDM context, is that if we use the latest Planck mission data that was just reported this month distances between stationary observers are increasing at a rate of 1/146 percent per million years.

And this percentage rate of distance growth is due to decrease in the future and eventually level off at an estimated 1/176 % per million years.

It is this leveling off of the decline in percentage growth rate which is meant by the attention-getting words "accelerating expansion". The decline levels off at a positive rate, instead of going all the way down to zero-percent growth.

So in standard cosmology there is no "crunch" and structures like Milky or solar system or you and me are not "ripped" apart. And "accelerating" just means that the percentage rate of distance growth continues to decline, but doesn't go all the way down to zero.

It's more like classical music and less like Wagner, or the Doors (if you know what I mean
but it's still beautiful! Find out about standard LCDM cosmology! You'll love it!

So, is what you are saying, the size of the universe is best modeled by a 3rd or 4th degree polynomial, that eventually just slows down growth. I'll do some research on LCDM.

I'm glad you're going to learn about the LCDM (Lambda Cold Dark Matter) model. It's what nearly everybody uses and it fits the data remarkably well. It is derived from the usual GR equation with cosmological constant Lambda, by assuming large-scale uniformity.

Instead of tracking the actual "size of the universe" the model tells us the size of a generic distance that is arbitrarily set to equal one unit at the present day, where the unit is some large distance like a billion lightyears. We don't know the size of the universe so we keep track of the size of a generic distance a(t) arbitrarily normalized to equal one at present.

Here's a recent plot of a(t)
https://www.physicsforums.com/showthread.php?p=4319385#post4319385
or rather this plots t as a function of a! So it actually graphs t(a). Well, picture that graph flipped on a 45 degree line so that time runs on the horizontal axis instead of vertical.

You wouldn't probably want to try fitting a 3rd or 4th degree polynomial. But I can see you are curious to know the shape of the expansion history.

I have a link to an older plot that has time on the horizontal axis.
http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

Jorrie's calculator embodies the LCDM model, with the latest (Planck mission) parameters. The calculator (TabCosmo) makes tables so you get to see the whole history. The second column is the number "a" I was talking about, the third column is time.

The logic of putting time after is that when you get some light from a galaxy you can immediately tell what "a" was when the light was emitted, by how much the waves have been stretched! But you have to use the model to calculate the time the light was emitted. the model will have been fitted to a whole bunch of previous data, so its parameters are what give the best fit, so far. but still the time is calculated from the observed stretch. So one tends to use the stretch factor as a handle on everything. I think that's why it comes first in the table. And that's why the expansion history graph looks like it has been flipped on the 45 degree axis.

 

[marcus]

...
So, is what you are saying, the size of the universe is best modeled ...
... I'll do some research on LCDM.

Devils, I was very encouraged by your interest in learning about the standard cosmic model LCDM.
It's definitely a quantitative (not verbal) thing and you have to play around with the model some to get used to it. Mathematically it comes right from the 1915 Einstein equation with two gravitational constants, G and Lambda. To make things tractable you assume approximate uniformity of matter and you get a simplified version of the GR equation.

One thing you MIGHT find helpful is learning to use the TabCosmo calculator that gives you histories of the universe in the form of tables, once you know how to use it and how to interpret some of the columns of numbers. Here is an example. I hope it doesn't put you off, it's really easy to use and interpret once you catch on.

Here's the online device used to produce the expansion history table:
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html

In this case I set it to start sometime in the past (in year 56 million, when distances were 1/45 what they are now) and go to sometime in the future (in year 69 billion, when distances will be 25 times what they are now). As you can see, the present is year 13.83 billion when distances are, of course, exactly what the are today (i.e. S = a = 1).
The "Hubble time" denoted T_Hub is the key to the percentage distance expansion rate I was talking about. So the table is telling you the history of the expansion and also it is telling you how the rate of distance expansion has changed, and will change, over time. Ask questions if you are curious. Several people here can help anyone learn how to interpret the model.

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&amp;a=1/S&amp;T (Gy)&amp;T_{Hub}(Gy)&amp;D (Gly)&amp;D_{then}(Gly)&amp;D_{hor}(Gly)&amp;D_{par}(Gly)\\ \hline45.000&amp;0.022&amp;0.056&amp;0.085&amp;39.362&amp;0.875&amp;1.247&amp;0.153\\ \hline37.201&amp;0.027&amp;0.075&amp;0.114&amp;38.595&amp;1.037&amp;1.488&amp;0.206\\ \hline30.753&amp;0.033&amp;0.100&amp;0.151&amp;37.750&amp;1.228&amp;1.772&amp;0.277\\ \hline25.423&amp;0.039&amp;0.133&amp;0.201&amp;36.821&amp;1.448&amp;2.107&amp;0.372\\ \hline21.017&amp;0.048&amp;0.178&amp;0.268&amp;35.798&amp;1.703&amp;2.500&amp;0.498\\ \hline17.374&amp;0.058&amp;0.237&amp;0.357&amp;34.672&amp;1.996&amp;2.959&amp;0.667\\ \hline14.363&amp;0.070&amp;0.316&amp;0.475&amp;33.434&amp;2.328&amp;3.494&amp;0.893\\ \hline11.874&amp;0.084&amp;0.420&amp;0.632&amp;32.071&amp;2.701&amp;4.111&amp;1.196\\ \hline9.816&amp;0.102&amp;0.559&amp;0.841&amp;30.573&amp;3.115&amp;4.821&amp;1.599\\ \hline8.115&amp;0.123&amp;0.745&amp;1.118&amp;28.926&amp;3.565&amp;5.628&amp;2.137\\ \hline6.708&amp;0.149&amp;0.991&amp;1.485&amp;27.115&amp;4.042&amp;6.538&amp;2.855\\ \hline5.546&amp;0.180&amp;1.317&amp;1.971&amp;25.129&amp;4.531&amp;7.551&amp;3.812\\ \hline4.584&amp;0.218&amp;1.751&amp;2.610&amp;22.951&amp;5.006&amp;8.659&amp;5.086\\ \hline3.790&amp;0.264&amp;2.323&amp;3.443&amp;20.571&amp;5.428&amp;9.846&amp;6.780\\ \hline3.133&amp;0.319&amp;3.076&amp;4.516&amp;17.982&amp;5.740&amp;11.084&amp;9.028\\ \hline2.590&amp;0.386&amp;4.060&amp;5.861&amp;15.189&amp;5.865&amp;12.330&amp;11.999\\ \hline2.141&amp;0.467&amp;5.325&amp;7.485&amp;12.215&amp;5.705&amp;13.526&amp;15.903\\ \hline1.770&amp;0.565&amp;6.923&amp;9.331&amp;9.111&amp;5.148&amp;14.608&amp;20.991\\ \hline1.463&amp;0.683&amp;8.883&amp;11.256&amp;5.963&amp;4.075&amp;15.518&amp;27.544\\ \hline1.210&amp;0.827&amp;11.200&amp;13.059&amp;2.882&amp;2.382&amp;16.225&amp;35.865\\ \hline1.000&amp;1.000&amp;13.834&amp;14.560&amp;0.000&amp;0.000&amp;16.730&amp;46.281\\ \hline0.851&amp;1.175&amp;16.259&amp;15.529&amp;-2.253&amp;-2.646&amp;17.023&amp;56.991\\ \hline0.725&amp;1.380&amp;18.819&amp;16.232&amp;-4.264&amp;-5.883&amp;17.220&amp;69.718\\ \hline0.617&amp;1.621&amp;21.473&amp;16.718&amp;-6.040&amp;-9.789&amp;17.348&amp;84.771\\ \hline0.525&amp;1.904&amp;24.191&amp;17.040&amp;-7.589&amp;-14.446&amp;17.429&amp;102.522\\ \hline0.447&amp;2.236&amp;26.951&amp;17.248&amp;-8.928&amp;-19.964&amp;17.478&amp;123.419\\ \hline0.381&amp;2.627&amp;29.739&amp;17.380&amp;-10.079&amp;-26.473&amp;17.507&amp;147.994\\ \hline0.324&amp;3.085&amp;32.543&amp;17.463&amp;-11.065&amp;-34.139&amp;17.521&amp;176.879\\ \hline0.276&amp;3.624&amp;35.358&amp;17.515&amp;-11.908&amp;-43.154&amp;17.526&amp;210.819\\ \hline0.235&amp;4.257&amp;38.180&amp;17.548&amp;-12.627&amp;-53.751&amp;17.548&amp;250.694\\ \hline0.200&amp;5.000&amp;41.006&amp;17.568&amp;-13.241&amp;-66.203&amp;17.568&amp;297.535\\ \hline0.170&amp;5.873&amp;43.834&amp;17.580&amp;-13.763&amp;-80.832&amp;17.580&amp;352.560\\ \hline0.145&amp;6.899&amp;46.664&amp;17.588&amp;-14.208&amp;-98.017&amp;17.588&amp;417.194\\ \hline0.123&amp;8.103&amp;49.495&amp;17.592&amp;-14.587&amp;-118.205&amp;17.592&amp;493.115\\ \hline0.105&amp;9.518&amp;52.327&amp;17.595&amp;-14.910&amp;-141.917&amp;17.595&amp;582.294\\ \hline0.089&amp;11.180&amp;55.159&amp;17.597&amp;-15.185&amp;-169.772&amp;17.597&amp;687.047\\ \hline0.076&amp;13.133&amp;57.991&amp;17.598&amp;-15.419&amp;-202.490&amp;17.598&amp;810.091\\ \hline0.065&amp;15.426&amp;60.823&amp;17.599&amp;-15.618&amp;-240.921&amp;17.599&amp;954.621\\ \hline0.055&amp;18.119&amp;63.656&amp;17.599&amp;-15.788&amp;-286.064&amp;17.599&amp;1124.389\\ \hline0.047&amp;21.283&amp;66.488&amp;17.600&amp;-15.932&amp;-339.089&amp;17.600&amp;1323.801\\ \hline0.040&amp;25.000&amp;69.321&amp;17.600&amp;-16.055&amp;-401.373&amp;17.600&amp;1558.036\\ \hline\end{array}}
Time now (at S=1) or present age in billion years:13.834

 

[Passionflower]

It is derived from the usual GR equation with cosmological constant Lambda, by assuming large-scale uniformity.

I think that is somewhat of a stretch:

Take Weyl's postulate + a perfect fluid that does not dissipate, is isotropic and homogeneous, plug in some time evolution from Einstein, make it fit with some constant and voila we claim it is derived from Einstein.

 

[cepheid]

Do you know that GR is a non linear theory? Do you agree that that implies you cannot simply add local solutions to global solutions?

Do you disagree with that?

If you are such an expert on GR, why don't you use it to show that everything has to expand away from everything else, even on the smallest spatial scales, and even in the absence of homogeneity, since that seems to be what you are claiming? Once you've done that, perhaps you'd care to explain why something like the Milky Way Galaxy still exists as a bound system when it as been around for the better part of 13 billion years? Even better, perhaps you'd care to explain just how the hell it formed in the first place?

Also an FRW solution is a fluid (of dust if you think that sounds fancier) solution, there is no single piece of vacuum in this solution, it is all matter. I suppose you fail to see the irony in claiming that 'it does not apply to everything that is not vacuum' when the model is used as an approximation for our own universe, which is mostly empty space with heavy localized clusters of matter?

I don't understand what you're saying here. I didn't claim what you said that I claimed above.

I am sure you would not object to show me how to mathematically include, as you call it, pocket solutions into larger solutions?

I was thinking of something like section 11.4.2 Perturbing the Friedmann Solutions in Galaxy Formation by Malcolm Longair.

 

[Passionflower]

If you are such an expert on GR, why don't you use it to show that everything has to expand away from everything else, even on the smallest spatial scales...

That is exactly what expanding FRW solutions do.

, and even in the absence of homogeneity, since that seems to be what you are claiming?

I claim that in the absence of (perfect) homogeneity we simply do not know. We certainly can make educated guesses and verify these guesses with experimental data but then we should not claim it is derived from an FRW like solution.

What bothers me is continuous claims that an FRW solution is a good estimate for our universe and that it is used to explain things that absolutely cannot be derived from this model, for instance the so-called non-expansion of gravitationally bound systems.

You really think I have no point at all here?

 

[skydivephil]

A universe that will re collapse seems inconsistent with the data if we assume that dark energy is a cosmological constant or simply a constant. But given we know very little about dark energy should we not keep open the possibility that is dynamical? According to LCDM the universe already won't through a period of accelerated expansion and that was caused by a field (the inflation) that decayed away. So isn't it possible the same will happen with dark energy? I am not saying this is likely or supported by data, but is it not a possbility we hsould be open to or...?

 

[marcus]

A universe that will re collapse seems inconsistent with the data if we assume that dark energy is a cosmological constant or simply a constant. But given we know very little about dark energy should we not keep open the possibility that is dynamical? According to LCDM the universe already won't through a period of accelerated expansion and that was caused by a field (the inflation) that decayed away. So isn't it possible the same will happen with dark energy? I am not saying this is likely or supported by data, but is it not a possbility we should be open to or...?

Definitely! It seems to me that the professional cosmology community has a culture that is pretty open to individualism, non-conformity, and sounding the alert when you see something in data that might pose a challenge to the standard model. We can follow their example in open-mindedness.

We can be selective though. There are what I would call "stale" challenges that haven't gone anywhere and that people now tune out. I guess there are fashions, maybe you could even call them "fads", as to what kinds of challenges to standard model get experts' attention.

As you know I'm just an interested bystander. What I think we most often encounter here at PF are people asking about standard LCDM cosmology. They want to understand it better. They have some misconception about it. They want something clarified. That's our main topic. And from time to time, in the middle of some discussion, I try to interject a caveat like "And the standard model might be wrong!"

Also as you know perhaps better than anyone there is a huge amount of data coming in and it has been running in favor of LCDM. Lambda seems to be getting more sure of being just the naturally occurring constant. I.e. with equationofstate w = -1, although they regularly try fitting data with w allowed to vary. And cold dark matter seems to be getting realer and realer as supporting evidence piles up.
But we should periodically observe that "future data may contain surprises!"

 

[Mordred]

Pasionflower the homogeneous statement used by cosmologists apply only on the correct measutement scales. Everyone knows that galaxy clusters are inhomogeneous. Thats as obvious as the finger nail on your hand.
The correct application of the homogenous usage applies at large scales above 100 Mpc. Not below. That value was chosen as its larger than most galaxy clusters. Although some recent discoveries such as the Quasar clusters may cause us to increase that value. In regards to expansion being homogeneous and isotropic consider the cause of expansion, as vacuum energy as described in the inflationary model. There is no evidence of variations in the vacuum energy. The vacuum energy is also homogenous and isotropic. As this energy is constant, homogenous and isotropic and the rate of expansion requires the cosmological constant. That would mean expansion is also homogenous and isotropic, the difference in expansion rates is a sum of energy densities. However the vacuum energy density in all areas in space remain the same.

Take for example the De-Sitter universe. this is a universe where matter is removed.

the rate of expansion is defined as h\propto\sqrtλ

this shows that its homogenous and isotropic. Even on gravitationally bound regions. The key differents is the gravitational energy density is greater than the energy density caused by expansion. However that same vacuum energy density is homogeneous and isotropic. However as I've shown to calculate the rate of expansion one must account for any energy densities in a given region.

 

[Nabeshin]

What bothers me is continuous claims that an FRW solution is a good estimate for our universe and that it is used to explain things that absolutely cannot be derived from this model, for instance the so-called non-expansion of gravitationally bound systems.

You really think I have no point at all here?

Well there do exist solutions such as Schwarzschild-deSitter (or just a schwarzschild in a general FRW background) in which you can effectively see the effects of the large-scale expansion of the universe on the local geodesics around the black hole, i.e. on orbits of bodies. Perturbatively, it just shows up as a small extra force which serves to slightly enlarge the orbits.

 

[Mordred]

I would be interested in some of the solutions you just mentioned. I have been looking for some good examples for an article I am writing on this forum. under the thread Redshift development FAQ. The last revision is on page 7. It was politely pointed out the article is more an essay than a FAQ. So I plan on breaking it down to two or three separate FAQs

 

[Nabeshin]

Here's McVittie's solution which is essentially a schwarzschild black hole in an FRW background (dates back to 1933!):
http://adsabs.harvard.edu/full/1933MNRAS..93..325M

 

[Mordred]

Thanks for the link. I'm going to need to examine it in more detail later on. Easter dinner and all with the family

 

[Passionflower]

Well there do exist solutions such as Schwarzschild-deSitter (or just a schwarzschild in a general FRW background) in which you can effectively see the effects of the large-scale expansion of the universe on the local geodesics around the black hole, i.e. on orbits of bodies. Perturbatively, it just shows up as a small extra force which serves to slightly enlarge the orbits.

Indeed.

To me it seems logical that if there is an expansion it must apply to all scales.

 

[Mordred]

Well expansion does apply at all scales. If you were to work out the amount of vacuum or dark energy. You will quickly realize that per cubic meter the amount of energy is extremely small. A rough estimate is 6*10-10. joules sorry for the long hand on my phone atm.

This low energy density is easily countered by gravity. the statement that expansion does not apply in graviationally bound regions is somewhat misleading. The cosmological constant applies everywhere.

however gravity can over power the low energy density of the cosmolical constant.
However in the example above it does have small influences even in gravitationally bound regions.

 

[Passionflower]

the statement that expansion does not apply in graviationally bound regions is somewhat misleading.

I would say it is simply wrong.

however gravity can over power the low energy density of the cosmolical constant.

I think the result will be a non-linear combination of gravity and a little bit of expansion, but the effect will not be zero.

 

[Mordred]

Correct there is always some influence

 

[Jorrie]

I think the result will be a non-linear combination of gravity and a little bit of expansion, but the effect will not be zero.

But I do not think there is 'expansion' per se inside the gravitationally bound structures - just a small constant effect of the cosmological constant that subtracts from the overall binding effect of gravity. Hence slightly larger orbits, but not 'expanding' orbits caused by cosmic expansion. Or do I have it wrong?

I read something along these lines in Carrera and Giulini, http://arxiv.org/abs/gr-qc/0602098

 

[Mordred]

Thats a good article. I've never seen any research to suggest expansion inside gravitationally bound regions other than orbital effects.

 

[Jorrie]

I read something along these lines in Carrera and Giulini, http://arxiv.org/abs/gr-qc/0602098

According to their eq. 86, appendix A.1, the approximate dynamic effect of cosmic expansion \ddot{r}=\frac{\ddot{a}}{a}r depends on the acceleration and not on the rate of expansion. So in early times (decelerating expansion), the dynamic effect on structures would have been in the direction to the structure center, like gravity, i.e. marginally assisting clustering. During the second half of cosmic history it must have been against gravity, gradually growing to a constant positive value in the future.

If taken at face value, \ddot{r} must still be marginally increasing today and hence there must be a very small expansion effect on clusters (or at least on superclusters) going on. Only of academic interest, I guess.