Lambda-CDM theory - Woo or not?

[Tim Thompson]

Galaxies, Cosmology and Science by Press Release Fails Again

One of the topics introduced by Mozina in an attempt to discredit standard LCDM cosmology is the appearance of "mature" or "old looking" galaxies at high redshifts, when the universe was very young. The allegation is that the universe is so young that there has not been time for galaxies to form, thus falsifying LCDM cosmology. Of course, as usual, Mozina does not quantify this claim. He never specifies how long he thinks it should take for a galaxy to form, nor does he provide any non faith-based reason for believing that the real universe should be unable to form galaxies so quickly.

But, as we can pretty confidently predict, not once have you read, and understood, any of the relevant papers (published in relevant, peer-reviewed journals, etc) on galaxy evolution, especially any which contains theoretical models.
So, fair question, how would you know?

A fair question indeed, which Mozina has never answered. Naturally, one assumes he is very deficient in relevant knowledge by which he might be expected to know. In other words, he's making it all up.

Why are you guys always "surprised"?
http://www.spacedaily.com/reports/M..._Eight_Times_More_Massive_Than_Milky_Way.html
So which paper predicted all this stuff DRD?
http://www.spaceref.com/news/viewpr.html?pid=14524

I have already addressed both of these in detail here: Science by Press Release Failure. The first is now known to be a lower redshift galaxy mistaken for a high redshift galaxy, and the second a paper which reports that 2/3 of massive galaxies form after the universe is 3,000,000,000 years old. See my previous post for details & references to the appropriate research papers.

So which paper if I only "properly" understood it, "predicted" this observation:
http://www.spaceref.com/news/viewpr.html?pid=30822

Let us begin to examine this one by comparing the language of the press release with the language found in the associated research paper.

However, it's not the size nor the age of the cluster that amazes the team of researchers led by Dr. Casey Papovich, an assistant professor in the Texas A&M Department of Physics and Astronomy and member of the George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy. Rather, it's the surprisingly modern appearance of CLG J02182-05102 that has them baffled -- a huge, red collection of galaxies typical of only present-day galaxies.
Spaceref.Com Press Release 14 May 2010
​

The photometric redshift probability distributions for the red galaxies are strongly peaked at z=1.62, coincident with the spectroscopically confirmed galaxies. The rest frame (U-B) color and scatter of galaxies on the red sequence are consistent with a mean luminosity weighted age of 1.2 +/- 0.1 Gyr, yielding a formation redshift, z_f = 2.35 +/- 0.10, and corresponding to the last significant star formation period in these galaxies.
Abstract, A Spitzer Selected Galaxy Cluster at z = 1.62, Papovich, et al., 2010; Astrophysical Journal, in press.
​

Now, you read the press release and you think people are falling all over themselves in surprise at such a thing. And note the part where they say, " ... typical of only present-day galaxies.". Yet when we read the abstract of the research paper, things are quite a bit different. Not only is there no hint of surprise, but we see that the galaxies are seen at an age of 1,200,000,000 years. But the stellar disk of our Milky Way is about 9,000,000,000 years old, and globular cluster stars are nearly 13,000,000,000 years old. These galaxies do not in fact look like modern day galaxies because they are extremely young by our local standard; there are no galaxies that young anywhere near the Milky Way. The press release is certainly attention getting, but it's also just plain wrong.

Seen sitting at redshift 1.62, these galaxies are sitting in a universe that is 4,046,000,000 years old. And if they formed at redshift 2.35, they formed when the universe was 2,844,000,000 years old (the difference being roughly 1,200,000,000 years). Is there some non faith-based reason, by which we are supposed to be "surprised" that galaxies did not form until the universe was 2,844,000,000 years old? Exactly what needed to be "predicted" as Mozina asks? Meanwhile, the authors estimate a dynamic mass of about 4x10¹⁴ solar masses for the cluster, and a mass estimate from the X-ray emission of about 1x10¹⁴ solar masses. But the masses are highly uncertain; although the authors do not quantify the uncertainty, they do say that both of these estimates (differing by a factor of 4) are "within the large error budget". That mass at redshift 1.62 should come forward in time as a rich galaxy cluster comparable to the Coma cluster. I don't see a problem here.

We can dismiss the alleged problems brought up by Mozina thus far as either not really problems, or in one case being a mistake (which he might have known had he followed the science literature instead of the press releases). Another failure for "science by press release".

In reality however, that hasn't been born out by the observations. We find very old clusters of galaxies less than 4 billion years from the event, every bit as massive as those we find in our own neighborhood today.

Factually false. No, we do not find "old" galaxies and clusters (old is 10 billion years, not 1 billion years). No, we do not find galaxies "every bit as massive as those we find in our own neighborhood today", if we are talking about high-mass galaxies. Our own Local Group of galaxies is dominated by the Milky Way and M31, both roughly 10¹² solar masses each. Number 3 in the group is M33, a satellite of M31, and weighing in at roughly 10¹⁰ solar masses, a mere 1% of the mass of the Milky Way or M31. All the rest of the 60 some odd galaxies in our local group range from about 10⁹ solar masses and down. Galaxies that small can form very quickly after the big bang, so finding galaxies at high redshift that are comparable to the mass of smaller galaxies in our local group is hardly a problem. It is in fact what we would expect. The few high mass (like 10¹¹ solar masses) galaxies we see at high redshift occur when the universe is already several billion years old. There is certainly no reason to believe that massive galaxies cannot form given several billion years to pull it off. And remember, the universe was much smaller and more densely packed at high redshift, so you expect hierarchical formation of large galaxies by the accretion of smaller galaxies to work efficiently (and indeed that is the leading hypothesis for galaxy formation in LCDM cosmology, e.g., Baugh, 2006 and citations thereto).

We "should" see some sort of progression from "simple" to complex at time marches on. In reality however, that hasn't been born out by the observations.

In reality, however, that is exactly what the observations do show us. Some of the best examples come to us from the Hubble Space Telescope. See, for instance ...

• Hubble Reaches the "Undiscovered Country" of Primeval Galaxies (5 Jan 2010).
  The new Wide Field Camera 3 looked at the old Hubble Ultra Deep Field to accomplish the deepest astronomical near infrared image yet made. They find galaxies in the universe when it was somewhat younger than a billion years. The galaxies they find are what you would naturally expect to find; they are very blue (in rest frame color) and very small (about 10⁹ solar masses and about 2200 light years across compared to 10¹² solar masses and 100,000 light years for the Milky Way). See, e.g. Bouwens, et al., 2010, Gonzalez, et al., 2010, Oesch, et al., 2010, Bouwens, et al., 2009 and citations to the papers.
  
• Barred Spiral Galaxies are Latecomers to the Universe (29 Jul 2008).
  A census of 2157 spiral galaxies shows that barred spiral galaxies become more common as the universe ages. The implication is that the central bar is a sign of maturity for galaxies (the Milky Way is a barred spiral galaxy). See Sheth, et al., 2008.
  
• Compact Galaxies in the Early Universe Pack a Big Punch (29 Apr 2008).
  Galaxies seen when the universe was lass than 3,000,000,000 years old; about 2x10⁸ solar masses and 5,000 light years across. See van Dokkum, et al., 2008.
  
• Hubble and Spitzer Space Telescopes Find "Lego-Block" Galaxies in Early Universe (6 Sep 2007).
  Some of the smallest, faintest and most compact galaxies yet seen (in 2007), from 100 to 1000 times smaller than the Milky Way. Exactly what we expect in an expanding universe cosmology; small galaxies form first and build bigger galaxies by merging. See Pirzkal, et al., 2007.

Just a few examples of what we actually do see, as opposed to what Mozina wishes we saw.

We find very old clusters of galaxies less than 4 billion years from the event, every bit as massive as those we find in our own neighborhood today.

In a few cases, we do see massive clusters, as large as 10¹⁴ solar masses, as noted above. However, we see them in a multi-billion year old universe. How do you know that clusters that massive can't form in a few billion years, in an environment more compact and crowded than we have today? How is this supposed to be a problem for LCDM cosmology?

And as for "old", galaxies evolve because the stars in them evolve. Galaxies look "old" because the stars in them look "old", and the evolution of stars is very mass dependent. As I pointed out in Science by Press Release Failure ...

The main sequence lifetime for the sun is about 10¹⁰ years. But the main sequence lifetimes fall fast with increasing mass because the proton-proton and CNO fusion cycles are very sensitive to the increased central temperature that comes with increased mass. So, for a stellar mass in solar masses, a good approximation is t_star/t_solar = (M_star/M_solar)^-2.5 where t_star is the stellar main sequence lifetime and M_star is the stellar mass. So a 3 solar mass star has a main sequence lifetime of about 640,000,000 years. So if a "massive" galaxy in the early universe has a lot of massive stars, they will look red & old pretty quickly, on astronomical time scales. Plenty of time to look "old" in a billion years, even less. I don't see how the formation of a "massive" galaxy in anything over a billion years is any problem at all, let alone a problem that "blows away" every prediction.

It's easy to make a galaxy "look old" (i.e., red) by simply giving it some massive stars. Even if low mass stars outnumber high mass stars by a factor of 10, the high mass stars could easily outshine the low mass stars by considerably more than a factor of 10. The red color of a "few" high mass stars that have evolved quickly could easily mask the low mass stars (which are cooler and likely to be redder in color anyway just because of their temperature). So, you can look at a galaxy, see the red color, and call it "old" even if it is only 1,200,000,000 years old. There is a significant difference between a galaxy that looks old and a galaxy that really is old, and it's not so easy to tell just by looking at a picture or even a simple color. It takes more work than that to figure out what the galaxy is made of before you decide between "looks" and "is". And of course, if all you ever do is read press releases and newspaper articles, it's an iron clad guarantee that you will never know.

Bottom line to take away from this post: There is no reliable evidence of any critical problem with hypotheses of galaxy formation in an LCDM cosmology, as compared to the observational characteristics of galaxies in the early universe.

 

[Reality Check]

Any constant term must vanish at the Newtonian limit. Since non-zero constant terms don't actually vanish, the correspondence with Newtonian physics imposes an upper bound on lambda: It must be too small to make a difference at scales for which the Newtonian approximation is appropriate.

The logic that Einstein used derived his field equations ended up with normalization to fit the Newtonian limit and no lambda. I seen this process in a couple of places, e.g. Sean Carroll: Lecture Notes on General Relativity and Leonard Susskind's 12 lecture videos on GR (over 24 hours of viewing!).

What I remember happening is that mathematically there is no effect on the GR dynamics by adding a lambda term (a constant times the metric) to the field equations because the dynamical equations all involve double differentiation of the field equations. Thus the lambda term vanishes.

As you know, the lambda term does have a effect in cosmological models.

 

[D'rok]

Another excellent post by Tim.

Keep up the good work Michael. Your fractal wrongness produces value for us lurkers as long as Tim stays engaged.

 

[W.D.Clinger]

What I remember happening is that mathematically there is no effect on the GR dynamics by adding a lambda term (a constant times the metric) to the field equations because the dynamical equations all involve double differentiation of the field equations. Thus the lambda term vanishes.

Ah! Thanks for explaining.

As you know, the lambda term does have a effect in cosmological models.

Responding to MM, I oversimplified that effect so I'll correct myself now. Without the lambda term, the Einstein field equations have no exact solution that obeys local causality, contains matter, and is

1. static
2. spatially homogeneous
3. isotropic

Einstein wanted a solution with all three properties. Flat (Minkowski) space-time has those properties, but lacks matter. The Robertson-Walker (Friedmann) solutions have properties 2 and 3.

A handout by Michel Janssen, one of the editors for volumes 7 and 8 of the Einstein Papers Project, describes the historical origin of the lambda term:

[Willem de Sitter] argued that Einstein’s distant masses would have to be outside the visible part of the universe, and that an explanation of the origin of inertia invoking such invisible masses was no more satisfactory than one invoking Newton’s absolute space and time.

Einstein came to accept De Sitter’s criticism and abandoned the proposal. As he wrote to De Sitter on February 2, 1917: “I have completely abandoned my views, rightfully contested by you, on the degeneration of the g_μν. I am curious to hear what you will have to say about the somewhat crazy idea I am considering now.” In his famous paper “Cosmological Considerations on the General Theory of Relativity” (...) published later that month, he circumvented the problem of boundary conditions at infinity simply by abolishing infinity! That is to say, he introduced a spatially closed model of the universe. A new term involving the so-called cosmological constant had to be added to the field equations to allow this model as a solution. As he emphasized in the final paragraph of the paper, however, the new term is needed not so much to allow for a closed universe as to allow for a closed static universe...

I look forward to Michael Mozina's explanation of how Einstein “used "gravity" to explain his lambda!”, and of how “We can drop an object and justify Einstein's lambda.”

 

[sol invictus]

The logic that Einstein used derived his field equations ended up with normalization to fit the Newtonian limit and no lambda. I seen this process in a couple of places, e.g. Sean Carroll: Lecture Notes on General Relativity and Leonard Susskind's 12 lecture videos on GR (over 24 hours of viewing!).

What I remember happening is that mathematically there is no effect on the GR dynamics by adding a lambda term (a constant times the metric) to the field equations because the dynamical equations all involve double differentiation of the field equations. Thus the lambda term vanishes.

As you know, the lambda term does have a effect in cosmological models.

The effect of lambda is to contribute a constant piece to the curvature of spacetime. Physically that means that the universe on the length scale set by the magnitude of lambda (which is proportional to its inverse square root) will certainly not look Newtonian. If the sign of lambda is positive, there will be event horizons, a quantum temperature, and objects will fall away from each other. On the other hand if its sign is negative objects will fall towards each other, and the universe itself will crunch.

If lambda is small, the length and time scale it sets is long. Local (small scale) experiments will have a tough time detecting its effects, although of course they can do so if they are sufficiently sensitive. That's why the easiest way to detect lambda today is with cosmology, and the hardest way is with earth-based lab experiments.

 

[W.D.Clinger]

The effect of lambda is to contribute a constant piece to the curvature of spacetime. Physically that means that the universe on the length scale set by the magnitude of lambda (which is proportional to its inverse square root) will certainly not look Newtonian. If the sign of lambda is positive, there will be event horizons, a quantum temperature, and objects will fall away from each other. On the other hand if its sign is negative objects will fall towards each other, and the universe itself will crunch.

To forestall possible confusion, "objects will fall away from each other" means geodesics will separate. It does not mean gravity will become repulsive.

If lambda is small, the length and time scale it sets is long. Local (small scale) experiments will have a tough time detecting its effects, although of course they can do so if they are sufficiently sensitive. That's why the easiest way to detect lambda today is with cosmology, and the hardest way is with earth-based lab experiments.

So how come Michael Mozina says it's easy to justify (or is it "qualify"?) lambda by dropping an object?

 

[sol invictus]

To forestall possible confusion, "objects will fall away from each other" means geodesics will separate. It does not mean gravity will become repulsive.

What's the difference?

Probably what you have in mind is the fact that ordinary massive objects do still attract each other in the presence of lambda, perhaps with enough strength to overcome their tendency to fall away from each other or perhaps not (depending on their masses, the magnitude of lambda, and the distance between them).

But it's the case that a large object - with sufficiently small mass that we can ignore its self-gravity - would feel a "stretching" strain (i.e. a force trying to expand it in all directions) if lambda>0. Is that "repulsive gravity"? That's probably not the best term, but I wouldn't go so far as to say it's wrong.

 

[W.D.Clinger]

Probably what you have in mind is the fact that ordinary massive objects do still attract each other in the presence of lambda, perhaps with enough strength to overcome their tendency to fall away from each other or perhaps not (depending on their masses, the magnitude of lambda, and the distance between them).

That's exactly what I meant.

But it's the case that a large object - with sufficiently small mass that we can ignore its self-gravity - would feel a "stretching" strain (i.e. a force trying to expand it in all directions) if lambda>0. Is that "repulsive gravity"? That's probably not the best term, but I wouldn't go so far as to say it's wrong.

The problem with that phrase is we have been trained to assume the force of gravitational attraction is proportional to the product of two objects' masses. Curvature arising from a non-zero lambda (positive or negative) does not have that property.

 

[sol invictus]

The problem with that phrase is we have been trained to assume the force of gravitational attraction is proportional to the product of two objects' masses. Curvature arising from a non-zero lambda (positive or negative) does not have that property.

In a way it does.

To see how, first recall that the analog of the "m"s in the Newtonian formula for the gravitational force between two objects Gm₁ m₂/r² is not just mass. It's (rho+3*P/c²)*volume, where rho is mass density and P is pressure.

Normally - for everyday non-relativistic materials - that pressure term is negligible (because c is so big), leaving you with rho*V=m. That's why the pressure term didn't appear in Newtonian gravity - it was too small for Newton to notice. But for lambda, P=-rho c² (the sign is easy to understand from the definition of pressure as the derivative of energy with respect to volume), so that combination is negative for positive lambda (positive lambda means positive energy/mass density, but negative pressure). The pressure term is big because lambda is an inherently relativistic thing - it's completely invariant under Lorentz transformations, unlike any other form of energy (or any other thing for that matter).

Now, for a spherical test mass, the energy and pressure due to lambda in the volume outside the mass isn't relevant, because by symmetry it doesn't induce any net force (if you want to be formal that follows from Gauss' law and/or Birkhoff's theorem).

So - what's the force due to lambda on our spherical test mass? Assuming it's an ordinary chunk of stuff with too little mass to have a strong self-gravity, it's just the product of its mass "m₁" with (rho_lambda+3P_lambda)V, where V is the volume of the mass, because that's the total contribution of lambda to the effective "m₂". Since m₂<0 the force is repulsive, which means it tries to push the mass away from the origin (i.e. stretch it).

(If you find the direction of the force confusing, it might help to think of a spherical test shell, or a spherically symmetric arrangement of point test masses.)

Caveat: I haven't bothered to check that this argument gives the correct numerical coefficient for the force, but I'll bet it does.

 

[Michael Mozina]

Michael, there is no difference between what Einstein did.....

Oh yes there are some important and fundamental differences sol. FYI, I really liked your explanation to Mr. Spock about how positive and negative lambda work. That was quite clear, but I would make one small adjustment.

Einstein used a "small" positive lambda, to attempt to explain a "static" and stable universe. A small positive lambda need not "necessarily" lead to an event horizon as you seem to believe, or at least that isn't what Einstein attempted to do with his positive lambda. (Maybe that's a better way to phrase it).

What you're doing with Lambda is in fact fundamentally different than what Einstein attempted to do in two significant ways. First of all, he did not otherwise violate any known laws of physics by suggesting a "static" universe. Your theory however presupposes "faster than light speed expansion". That's a fundamental difference between your lambda and Einstein's use of lambda.

The second fundamental difference is your selection of invisible friends rather than known forces of nature to provide that lambda. Einstein's lambda was presumably "caused" by simply gravity. Gravity did not ever become "repulsive" in his lambda, rather it was consistently "attractive". By interjecting your duo of metaphysical entities, you're trying to now justify "repulsive gravity". Nothing like that happens which is why you can't jump off the planet.

You didn't simply select a "known force of nature" to insert into lambda as Einstein did. You selected metaphysical woo to stuff into lambda, and thereby created a "faster than light speed expansion creation story" with a "beginning" date and everything.

You'll have to at least cop to the two fundamental differences between your use of lambda and Einstein's use of lambda before we can meaningfully proceed. You aren't using a known force of nature to insert into lambda. A positive lambda does not automatically equate to "repulsive gravity'. Both of these are "assumptions" on your part that are without empirical merit.

 

[sol invictus]

Einstein used a "small" positive curvature, to attempt to explain a "static" and stable universe.

The magnitude of the lambda he added is comparable to the one observed, actually.

A small positive lambda need not "necessarily" lead to an event horizon as you seem to believe

False.

or at least that isn't what Einstein attempted to do with his positive lambda. (Maybe that's a better way to phrase it).

Einstein made a technical mistake. He didn't notice a crucial characteristic of his solution (that it's unstable, which means it cannot exist physically).

What you're doing with Lambda is in fact fundamentally different than what Einstein attempted to do in two significant ways. First of all, he did not otherwise violate any known laws of physics by suggesting a "static" universe. Your theory however presupposes "faster than light speed expansion". That's a fundamental difference between your lambda and Einstein's use of lambda.

Nonsense - there is no law of physics that forbids faster than light expansion of the universe.

Think for a second, Michael. This is relativity we're talking about. It's the theory from which the limit on the speed of light is derived. How can it possibly violate its own rules? It can't and it doesn't.

The second fundamental difference is your selection of invisible friends rather than known forces of nature to provide that lambda. Einstein's lambda was presumably "caused" by simply gravity. Gravity did not ever become "repulsive" in his lambda, rather it was consistently "attractive".

Absolutely wrong. Einstein added exactly the same term with exactly the same effect as the term modern cosmologists believe is responsible for the current acceleration. The difference is that Einstein made a mistake (and he also needed positive spatial curvature, which at least so far has not been observed).

Einstein's lambda of course did cause a repulsive force; that's precisely why he added it. He needed something to balance the attractive gravity of ordinary mass.

 

[r-j]

Can somebody explain, in very simple terms, what happens to both light and gravity when spacetime expands? I checked Wikipedia, but it's way over my head.

It looks like light is redshifted. Light is also redshifted when something is moving away. And also due to expansion.

What happens to gravity?

Now that I asked that, I guess blueshift also happens when something is moving towards us.

What happens to gravity? I read it is limited by the speed of light. Does that mean it is redshifted? And what would that mean for gravity?

And if it isn't effected, what does that mean?

Remember, in simple terms if possible. I can't follow the math at all.

 

[DeiRenDopa]

Oh yes there are some important and fundamental differences sol. FYI, I really liked your explanation to Mr. Spock about how positive and negative lambda work. That was quite clear, but I would make one small adjustment.

Einstein used a "small" positive curvature, to attempt to explain a "static" and stable universe. A small positive lambda need not "necessarily" lead to an event horizon as you seem to believe, or at least that isn't what Einstein attempted to do with his positive lambda. (Maybe that's a better way to phrase it).

What you're doing with Lambda is in fact fundamentally different than what Einstein attempted to do in two significant ways. First of all, he did not otherwise violate any known laws of physics by suggesting a "static" universe. Your theory however presupposes "faster than light speed expansion". That's a fundamental difference between your lambda and Einstein's use of lambda.

The second fundamental difference is your selection of invisible friends rather than known forces of nature to provide that lambda. Einstein's lambda was presumably "caused" by simply gravity. Gravity did not ever become "repulsive" in his lambda, rather it was consistently "attractive". By interjecting your duo of metaphysical entities, you're trying to now justify "repulsive gravity". Nothing like that happens which is why you can't jump off the planet.

You didn't simply select a "known force of nature" to insert into lambda as Einstein did. You selected metaphysical woo to stuff into lambda, and thereby created a "faster than light speed expansion creation story" with a "beginning" date and everything.

You'll have to at least cop to the two fundamental differences between your use of lambda and Einstein's use of lambda before we can meaningfully proceed. You aren't using a known force of nature to insert into lambda. A positive lambda does not automatically equate to "repulsive gravity'. Both of these are "assumptions" on your part that are without empirical merit.

(bold added)

So tell us all, MM, how do you - using your own, oft-stated framework - decide what a "known force of nature" (or ""known force of nature"") is? Please be as clear and precise as you can.

Also, how do you - using your own, oft-stated framework - decide what a "known law of physics" is? Please be as clear and precise as you can.

Finally, what is "empirical merit"? I note that you seem to rather, shall we say, vague on what this is. In particular, your notions seem to be (almost entirely) subjective, and certainly not independently verifiable.

In what way is being subjective, and not independently verifiable, scientific?

 

[Michael Mozina]

MM wants to use statements like "you only have evidence for lambda" because he thinks they'll win this argument for him. But they're not very clear or unambiguous statements---I think he expects to need to weasel out of them later.

Michael, can you make an explicit and un-weasel-able statement for a change? Do you or do you not think that the evidence supports the presence of a constant-curvature term in the gravitational evolution of the Universe?

I do personally believe that the evidence does actually favor an expanding and accelerating universe, yes. I personally lack belief that inflation and/or dark energies have anything to do with it.

 

[Michael Mozina]

Can somebody explain, in very simple terms, what happens to both light and gravity when spacetime expands? I checked Wikipedia, but it's way over my head.

Be careful with the terms "spacetime" and "space" when it comes to expansion. "Spacetime" can only "Expand" as the objects that makeup spacetime move away from each other. The analogy that comes to mind here is objects in motion stay in motion, and that motion of mass away from each other eventually stretches 'spacetime'. When they talk about "space" expansion, it's a metaphysical horse of a different color. The example in Einstein's use of lambda shows that "space" isn't really expanding with his positive lambda. It simply kept "spacetime" from collapsing. What they're proposing is something completely unrelated to the expansion of 'spacetime" (mass objects in motion say in motion), but it's a metaphysical sort of 'space" expansion, where 'space' is physically undefined and unrelated to Einstein's use of lambda or his use of "general relativity theory" proper.

 

[sol invictus]

What happens to gravity?

Gravitational fields generally get weaker as the universe expands, except in cases where they're produced by a local concentration of mass that stays constant or increases (like in the solar system, or even inside a galaxy).

Gravity waves redshift with expansion/recession (or blueshift for an object moving towards us) exactly the same way light waves do.

 

[Michael Mozina]

The magnitude of the lambda he added is comparable to the one observed, actually.

It was never the observation I objected to, always the "explanation" you've been trying to sell.

False.

Einstein made a technical mistake. He didn't notice a crucial characteristic of his solution (that it's unstable, which means it cannot exist physically).

Well, you burned me with that before, so you'll notice I laid that problem at Einstein's feet It actually would depend on the nature of lambda. You're probably correct that gravity alone may not suffice. I don't really know how that might play out in an eternal, infinite universe.

Nonsense - there is no law of physics that forbids faster than light expansion of the universe.

Except GR theory as Einstein consistently used it. Even if we assume he made a mistake, at no time did he ever try to claim that "space" (physically undefined) somehow "expands". Never! You're peddling a whole different sort of cosmology theory sol, and a whole different sort of 'expansion'. Einstein's positive lambda did not cause "space" to expand. It simply prevented spacetime from collapsing into itself (at least according to him).

Think for a second, Michael. This is relativity we're talking about. It's the theory from which the limit on the speed of light is derived. How can it possibly violate its own rules? It can't and it doesn't.

Your "interpretation" is a violation of the "faster than light" speed rule that applies to all objects of mass sol! You're trying to do something fundamentally different with lambda than Einstein ever tried to do with lambda. Even if you're going to claim some kind of acceleration applies, how can you be so sure it involves 'faster than light expansion'?

http://arxiv.org/abs/astro-ph/0601171
http://arxiv.org/find/astro-ph/1/au:+Chodorowski_M/0/1/0/all/0/1

 

[ben m]

I do personally believe that the evidence does actually favor an expanding and accelerating universe, yes. I personally lack belief that inflation and/or dark energies have anything to do with it.

That's not what I asked. If you read what I said you would know the difference.

I asked: Do you think the acceleration is due to a curvature of spacetime (i.e. like gravity)? Or are you holding out for acceleration due to EM forces?

 

[ben m]

Except GR theory as Einstein consistently used it. Even if we assume he made a mistake, at no time did he ever try to claim that "space" (physically undefined) somehow "expands". Never! You're peddling a whole different sort of cosmology theory sol, and a whole different sort of 'expansion'. Einstein's positive lambda did not cause "space" to expand. It simply prevented spacetime from collapsing into itself (at least according to him)

Baloney, in every possible way. The whole reason that Einstein discarded the cosmological constant was that he realized that this constant caused the universe to expand. He tried to make a static Universe but failed because (as he saw later) the lambda term---according to the rules of his own GR---inevitably caused EITHER accelerating expansion OR contraction. On realizing this, he discarded the term.

Your objection is complete and utter nonsense even as historical trivia, and even worse nonsense as a statement about gravity. Have you no shame?

Of course you don't. I'm sure you can make something ELSE up that allows you to pretend GR is wrong. Then you'll forget about this and re-assert the "Einstein never said that" baloney in the next thread.

 

[W.D.Clinger]

So - what's the force due to lambda on our spherical test mass? Assuming it's an ordinary chunk of stuff with too little mass to have a strong self-gravity, it's just the product of its mass "m₁" with (rho_lambda+3P_lambda)V, where V is the volume of the mass, because that's the total contribution of lambda to the effective "m₂". Since m₂<0 the force is repulsive, which means it tries to push the mass away from the origin (i.e. stretch it).

Caveat: I haven't bothered to check that this argument gives the correct numerical coefficient for the force, but I'll bet it does.

If it's off, it's probably off by some product of 4π, the gravitational constant, and c², depending on your units.

To see how, first recall that the analog of the "m"s in the Newtonian formula for the gravitational force between two objects Gm1 m2/r2 is not just mass. It's (rho+3*P/c²)*volume, where rho is mass density and P is pressure.

Normally - for everyday non-relativistic materials - that pressure term is negligible (because c is so big), leaving you with rho*V=m. That's why the pressure term didn't appear in Newtonian gravity - it was too small for Newton to notice. But for lambda, P=-rho c² (the sign is easy to understand from the definition of pressure as the derivative of energy with respect to volume), so that combination is negative for positive lambda (positive lambda means positive energy/mass density, but negative pressure).

So rho+3*P/c²=-2*rho, which is negative when rho is positive.

That may explain something that has been bothering me. I understood why positive vacuum energy implies negative pressure, but I hadn't understood why positive vacuum energy affects curvature as though it were a negative mass density. If I understand you correctly, the equation I just stated says the negative contribution from the pressure overcomes the positive contribution from the mass equivalent of the vacuum energy.

For example: Misner, Thorne, and Wheeler's Gravitation §17.3, equation (17.13) is in cosmological units:

[latex]$$\rho^{\hbox{\tiny (VAC)}} = T^{\hbox{\tiny (VAC)}}_{\hat{0}\hat{0}} = + \frac{\Lambda}{8\pi}$$[/latex]

The other three components along the diagonal involve (the negative of) pressure, which is presumably where the 3 came from in (rho + 3P).

Equation (17.13) above was derived by subtracting the lambda term from the stress-energy tensor. So long as we're content with analogies, however, it might be possible to avoid pressure while demonstrating that a positive lambda's contribution to the gravitational potential is analogous to that of a constant negative mass density. In Hawking and Ellis, The Large Scale Structure of Space-Time, the motivation for the field equations in §3.4 includes an application of Stokes's Theorem to equation (3.14), but inexplicably omits lambda. Putting lambda back in, the lambda behaves (in their units) like a (negative) mass density of -Λ/(4π) or a (negative) pressure of -Λ/(12π).