B Is Scale Invariance the Key to Understanding the Expansion of the Universe?

[wolram]

https://www.sciencedaily.com/releases/2017/11/171122113013.htm

A University of Geneva researcher has recently shown that the accelerating expansion of the universe and the movement of the stars in the galaxies can be explained without drawing on the concepts of dark matter and dark energy… which might not actually exist.

What is this scale invariance?

 

[jerromyjon]

What is this scale invariance?

Off the top of my head with only reading the heading it is referring to empty space. (a vacuum solution of GR equations) The paper is paywalled so I can't read it but modified Newtonian dynamics theories aren't new and they have their own problems. IMHO, If it were as simple as a fixed scale with or without fixed time there wouldn't be any problem solving this cosmic conundrum.

 

[PeterDonis]

The paper is on arxiv.org here:

https://arxiv.org/abs/1710.11425

 

[jerromyjon]

https://arxiv.org/abs/1710.11425

"In addition to the general covariance of tensor analysis used in GR, cotensor analysis also admits the possibility of scale invariance of the form:
ds'= λ(x ^μ ) ds"
I wish I truly understood how to interpret this first equation. I guess I should just shut up and read the entire paper first.

 

[strangerep]

ds'= λ(x ^μ ) ds"
I wish I truly understood how to interpret this first equation.

A position-dependent scale-change of the metric.

I guess I should just shut up and read the entire paper first.

Anyone with a surplus of space time should probably start with his "Paper I",
i.e., An alternative to the LCDM model: the case of scale invariance

YMMV. Treat with caution.

 

[jerromyjon]

A position-dependent scale-change of the metric.

Easy for you to say.

YMMV. Treat with caution.

The link color showed I've viewed it before but I don't remember it, I'll read it tomorrow and see what comes back to me...

 

[jerromyjon]

the accelerating expansion of the universe and the movement of the stars in the galaxies can be explained without drawing on the concepts of dark matter and dark energy…

This is just another version of "It can mathematically be done" (within approximate fit to data) but it doesn't lead to any new insights of why expansion and galactic velocities may be related.
I did find an interesting table on top of page 14 in the latest paper, showing the rotation curve evolution of the milky way galaxy. Food for thought!

 

[strangerep]

Uh-oh. Andre Maeder just received some stern discipline, down in Madam Lash's Dungeon.

 

[jerromyjon]

Uh-oh. Andre Maeder just received some stern discipline, down in Madam Lash's Dungeon.

That just killed this thread, similar to what the author stated in the abstract of the "Paper I":
"The presence of even tiny amounts of matter in the Universe tends to kill scale invariance. The point is that for Omega_m = 0.3 the effect is not yet completely killed."
I'm left scratching my head. I would think scale inversion a more appropriate modification. Any chance there are any other suicidal authors toying with a concept like that?
A little more detail... I think Ω_m means mass density, right? So what is special about that? In relation to the scale invariance, it is what makes it work, so, might we have learned from that simple tidbit? Is it useless?

 

[kimbyd]

Uh-oh. Andre Maeder just received some stern discipline, down in Madam Lash's Dungeon.

My take-away from this blog post:
Maeder tried to do something tricky with General Relativity. GR is very, very difficult to get right. Maeder made some mistakes that are really apparent to those who are familiar with such modifications.

Slightly more in-depth: Maeder's attempt amounts to a change of coordinates. Such a change in coordinates should have no dynamical effects. Maeder apparently made some mistakes in deriving some dynamical effects (to mimic dark matter/energy). Done right, his change should exactly cancel in the final equations.

At least, that's how I understand it.

 

[jerromyjon]

Done right, his change should exactly cancel in the final equations.

Then why when it's done wrong does it work? Still scratching.

 

[kimbyd]

Then why when it's done wrong does it work? Still scratching.

My naive guess is it's a matter of publication bias. He likely tried a number of different ways of massaging the equations, happened on one that kinda-sorta works, and published that without properly verifying the math was actually correct. It's much easier to make this mistake than you might think.

 

[ohwilleke]

The core of the criticism at Backreaction is as follows:

Since he doesn’t have a dynamical equation for the extra field, my best guess is that this effectively amounts to choosing a weird time coordinate in standard cosmology. If you don’t want to interpret it as a gauge, then an equation is missing. Either way the claims which follow are wrong. I can’t tell which is the case because the equations themselves just appear from nowhere. Neither of the papers contain a Lagrangian, so it remains unclear what is a degree of freedom and what isn’t. (The model is also of course not scale invariant, so somewhat of a misnomer.)

Maeder later also uses the same de Sitter prefactor for galactic solutions, which makes even less sense. You shouldn’t be surprised that he can fit some observations when you put in the scale of the cosmological constant to galactic models, because we have known this link since the 1980s. If there is something new to learn here, it didn’t become clear to me what.

As I see it, really this is first and foremost a criticism of lack of transparency. There are critical steps in the analysis that aren't spelled out or justified. But, it strikes me as something short of a demonstration that this or something along the same lines isn't possible.

MOND uses gravitational field strength relative to a single constant as its trigger for gravity modification in the weak field, and while this doesn't correctly handle GR effects, the TeVeS generalization by Bekenstein did. This approach uses local matter-energy density relative to a single constant as the trigger for its modification. It strikes me that there is no obvious reason that a local matter-energy density trigger couldn't be included in a more rigorously formulated and reasoned modification of gravity with a similar phenomenological outcome.

 

[ohwilleke]

This is just another version of "It can mathematically be done" (within approximate fit to data) but it doesn't lead to any new insights of why expansion and galactic velocities may be related.

I did find an interesting table on top of page 14 in the latest paper, showing the rotation curve evolution of the milky way galaxy. Food for thought!

FWIW, I think proof of concept, even if a particular model doesn't work, is pretty important at this stage of dark matter phenomena theory. The mere possibility that something can be reduced to simple equations that it is very hard to arrive at with a particle dark matter theory is in and of itself significant.

 

[PeterDonis]

As I see it, really this is first and foremost a criticism of lack of transparency.

No, it's a criticism that there is no possible way to get a consistent model out of what the paper is saying. Note that the passage you quoted says specifically: "Either way the claims which follow are wrong." In other words, it's not clear which of two possible mistakes the author is making, but it's clear that he's making a mistake. That's a more serious criticism than just "lack of transparency".

it strikes me as something short of a demonstration that this or something along the same lines isn't possible.

You're right, it isn't; it's just a demonstration that this paper does not do what it claims to do. It makes no general claim that there is no possible way to do what the paper claims to do (in the general sense of "find some consistent model that doesn't require assuming dark matter").

proof of concept,

The paper is not a "proof of concept" of anything because there is no way to get a consistent model from it.

 

[George Jones]

The core of the criticism at Backreaction is as follows: ...

As I see it, really this is first and foremost a criticism of lack of transparency. There are critical steps in the analysis that aren't spelled out or justified. But, it strikes me as something short of a demonstration that this or something along the same lines isn't possible.

Did you see the comment by John Baez on the blog?

 

[ohwilleke]

Did you see the comment by John Baez on the blog?

Nope. It is interesting. (Not sure, given time zones and comment permissions that it was even there when I read it.)

 

[jerromyjon]

The conformal or scale factor must be a function of time only, for reason of homogeneity and isotropy. A supplemental inverse value for time allows one to apply the Minkowski metric in scale invariance.

I'm left scratching my head. I would think scale inversion a more appropriate modification. Any chance there are any other suicidal authors toying with a concept like that?

Or is it one and the same...