SWAB: True or false: Does gravitational lensing reveal dark matter’s nature?

[SkyHiker]

Ethan sweeps the floor with the recent article about axions being the most likely source of dark matter, https://bigthink.com/starts-with-a-bang ... rk-matter/ .

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As suspected and hence my little bit of a subtle attempt at scepticism at the article, clearly subtle enough to be missed lol

It turns out that Axion DM halos more closely represent what we see...in this model, of this system.

As always, an excellent article by Ethan. Thanks for the post, Henk.

[SkyHiker]

As suspected and hence my little bit of a subtle attempt at scepticism at the article, clearly subtle enough to be missed lol

It turns out that Axion DM halos more closely represent what we see...in this model, of this system.

Very subtle, true! So long as our estimates continue to be off by crazy factors, I am not holding my breath for a grand unified theory based on dark matter and energy. For instance, only two years ago the estimated number of galaxies was scaled down by a factor 10 by New Horizon's UV observations. The research is interesting, but it may take centuries of data and theory to weed out the litany of models that are proposed.

[Gmetric]

As suspected and hence my little bit of a subtle attempt at scepticism at the article, clearly subtle enough to be missed lol

It turns out that Axion DM halos more closely represent what we see...in this model, of this system.

Very subtle, true! So long as our estimates continue to be off by crazy factors, I am not holding my breath for a grand unified theory based on dark matter and energy. For instance, only two years ago the estimated number of galaxies was scaled down by a factor 10 by New Horizon's UV observations. The research is interesting, but it may take centuries of data and theory to weed out the litany of models that are proposed.

Yes, a subtle, but healthy degree of scepticism. Unlike your clear scepticism of dark energy and dark matter, one would almost believe you to err on the side of MOND, I am joking, of course

I know, there are more cosmological models than one can shake a stick at. I have untold new proposals or modifications to existing ideas and theories filling my email box every week. Nevertheless, in the face of the evidence (direct or indirect), and the current state of observational and experimental understanding, we must work with what we have and the current strongest theoretical frameworks all preside in the paradigm of ΛCDM or some form of cosmological inflationary model which include DM & DE, whatever they are. ΛCDM isn't without its problems, though. It has many, with more recent observations that seem to be cracking its foundations https://en.wikipedia.org/wiki/Lambda-CDM_model

A GUT, I suspect, will be more relevant to the SM as it is known to be an incomplete theory and doesn't explain gravity, DM, DE, neutrino mass and the matter-antimatter asymmetry, which will, in turn, bear some fruit on cosmology models. https://en.wikipedia.org/wiki/Physics_b ... dard_Model

As you quite rightly allude to, it is clear that there is still a lot up for debate and as we know from history, paradigms do shift, so let's remain pragmatic and open to the potential for change while remaining steadfast to what nature tells us and keeping our feet on the ground.

[SkyHiker]

As suspected and hence my little bit of a subtle attempt at scepticism at the article, clearly subtle enough to be missed lol

Very subtle, true! So long as our estimates continue to be off by crazy factors, I am not holding my breath for a grand unified theory based on dark matter and energy. For instance, only two years ago the estimated number of galaxies was scaled down by a factor 10 by New Horizon's UV observations. The research is interesting, but it may take centuries of data and theory to weed out the litany of models that are proposed.

Yes, a subtle, but healthy degree of scepticism. Unlike your clear scepticism of dark energy and dark matter, one would almost believe you to err on the side of MOND, I am joking, of course

To me MOND is an ad-hoc kludge that works for one case, fails elsewhere and has a shaky foundation to say the least. Yet also, GR is still up for debate. The EFE are a 2nd rank tensor equality that is compatible with the tests so far (that's only 3, mainly: precession of perihelia, gravity probe B, and light bending). We don't know if higher rank tensor equalities exist that lead to different solutions.

Aside from that, GR is not relative in the sense that SR is. One would expect that inertia depends on the mass distribution of the universe, just so that we can justify "absolute" space as publicized in various GR use cases. Sciama derived alternative gravitation based on that idea (in his early work, nobody picked it up). Until inertia is explained rather than postulated, I am not convinced that GR is complete. This debate that started out as Mach's principle has been going on since the beginning of GR and is still open ended.

Something I find puzzling about cosmology, the RW equations that are the main constituent of the cosmological model are not based on GR but on symmetric spaces theory. That theory does not care about physics yet explains curvature in our observable universe as part of the curvature of the entire universe, including the parts outside the event horizon from where gravitational waves cannot reach us. That is odd to me. In the end all curvature is due to the distribution of matter and energy, and both static and dynamic gravity (curvature) should be bounded by the speed of light. Something doesn't fit, or maybe it's just me.

Dark energy could just be a local curvature quirk due to imperfect homogeneity in the larger universe that we can't see. Dark matter (and dark energy) does not fit in the standard model. If the originator of the SM does not believe in dark matter, why would anyone? It seems to me that the standard model would have to be updated first. It's almost like believing in MOND, finding something that fits a particular problem and concluding that therefore it is true.

Lots of questions, I don't believe we know the complete answer yet even just GR without the dark stuff.

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To me MOND is an ad-hoc kludge that works for one case, fails elsewhere and has a shaky foundation to say the least

Me too

Yet also, GR is still up for debate. The EFE are a 2nd rank tensor equality that is compatible with the tests so far (that's only 3, mainly: precession of perihelia, gravity probe B, and light bending)

Debate? Well, it may be fraying around the edges; it's a bit of a 'stretch' to say it's up for debate. Andrea Ghez's work, which was one of the most comprehensive studies ever on BHs and GR, proved Einstein with unparalleled accuracy. However, I would agree that GR isn't complete and, in that sense, needs further work.

One would expect that inertia depends on the mass distribution of the universe, just so that we can justify "absolute" space as publicized in various GR use cases.

Machivanians may think so Newton defined absolutes in his bucket experiment, in which Newton ascribed an absolute reference frame to the accelerated motion of his bucket. Mach suggested the reference frame was given by the distribution of bodies in the universe by some action at a distance. However, by 1954, Einstein had abandoned Mach for a more mature approach to the problem in which the distribution of bodies contributes to the shape of space and time itself. The bucket experiences accelerated motion not because of the bodies in the universe directly but because it exists in a spacetime that has been formed by all the matter and energy fields in the observable universe. Which I believe to be a more pragmatic approach as opposed to the whole 'the buck is still, and the universe is spinning' rubbish.

RW equations that are the main constituent of the cosmological model are not based on GR but on symmetric spaces theory.

Perhaps a misunderstanding? "The Friedmann–Lemaître–Robertson–Walker metric (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) is a metric based on the exact solution of the Einstein field equations of general relativity." https://en.wikipedia.org/wiki/Friedmann ... ker_metric

Furthermore, in 1922 and 1924, Friedmann published two important papers that had the effect of showing that the cosmological models of Einstein and de Sitter were special cases of a much broader class of expanding or contracting models, all of which were consistent with the field equations of general relativity and the cosmological principle. He died in 1925 and thus could not capitalise on his findings. Robertson and Walker found improved ways of describing these models resulting in a general mathematical framework still used today when discussing relativistic cosmological models of a homogenous and isotropic universe.

That theory does not care about physics yet explains curvature in our observable universe as part of the curvature of the entire universe

Hmmmm. The Friedmann equation is of the utmost importance in the process of cosmological modelling. The Friedmann equation determines the form R(t), which represents the rate of change of the scale factor R which is directly related to the matter density ρ. It is worth pointing out that on the basis of Newtonian physics, the Friedmann equation can be derived by considering the total energy of an expanding spherical distribution of galaxies. In such a derivation, kc^2 is related to the total energy of the sphere, R^2 is related to the kinetic energy of the sphere, and G is the gravitational potential energy of the sphere. And so, the Friedmann equation is also referred to as the 'energy equation' of the universe. I'd say it is dependent on physics.

including the parts outside the event horizon from where gravitational waves cannot reach us. That is odd to me. In the end all curvature is due to the distribution of matter and energy, and both static and dynamic gravity (curvature) should be bounded by the speed of light. Something doesn't fit, or maybe it's just me.

I can understand what you are saying here, and it's an interesting question. The FLRW metric is dependent on the universe being homogenous and Isotropic, and on the basis that, for the most part, it is, one can use comoving coordinates coupled with the scale factor to speak of the observable universe as the entire universe. The assumption being that scale factors remain appropriate beyond the cosmic horizon, and unless physics changes beyond the cosmic horizon, they should be.

Dark energy could just be a local curvature quirk due to imperfect homogeneity in the larger universe that we can't see

Possibly but think about comoving coordinates, the scale factor R(t), cosmological redshifts and the Hubble parameter, and yet the cosmological constant remains, well, constantish ...maybe ...which says something about the energy density and the density parameter for dark energy ...These all point to the expansion of space itself.

If the originator of the SM does not believe in dark matter, why would anyone?

Indeed, but many do. And whatever it is, It must fit on the SM, or the SM must be modified to include it or link with it in some way. Not forgetting that when one uses the SM to calculate DE we get a 120 order of magnitude error.

Needless to say, after all this, there are cracks in the standard model of cosmology; that much is true , and I'm looking forward to seeing how it evolves over time.

[SkyHiker]

One would expect that inertia depends on the mass distribution of the universe, just so that we can justify "absolute" space as publicized in various GR use cases.

Machivanians may think so Newton defined absolutes in his bucket experiment, in which Newton ascribed an absolute reference frame to the accelerated motion of his bucket. Mach suggested the reference frame was given by the distribution of bodies in the universe by some action at a distance.

Weinberg argues that inertial frames in outer space (sufficiently far away from massive bodies) cannot accelerate or rotate relative to the (average motion of the) galaxies. This is based on applying Birkhoff's theorem inside out to a small enough empty vacuum sphere. Since you have a PDF copy of Weinberg, check the ends of sections 11.7 and 15.1 for this. This is the only reference I know of that explains why Newton's absolute space is affixed to the galaxies in the universe. More precisely, affixed to the standard cosmological model of the universe.

However, by 1954, Einstein had abandoned Mach for a more mature approach to the problem in which the distribution of bodies contributes to the shape of space and time itself. The bucket experiences accelerated motion not because of the bodies in the universe directly but because it exists in a spacetime that has been formed by all the matter and energy fields in the observable universe. Which I believe to be a more pragmatic approach as opposed to the whole 'the buck is still, and the universe is spinning' rubbish.

Newton's bucket is the original idea, but we progressed a bit and we need a definition of Mach's principle in a differential geometric context. To me, Weinberg's aforementioned conclusion about inertial frames relative to the universe is one half of it. I am curious if our sense of time and space, which are determined by the metric of the universe, depend on its mass density. If they do, will this result in a different value of the gravitational constant? Lots of Machians are still playing around with these ideas but I don't think there is an answer yet. Weinberg seems to take Mach's principle seriously since he references it quite a few times in his book.

RW equations that are the main constituent of the cosmological model are not based on GR but on symmetric spaces theory.

Perhaps a misunderstanding? "The Friedmann–Lemaître–Robertson–Walker metric (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) is a metric based on the exact solution of the Einstein field equations of general relativity." https://en.wikipedia.org/wiki/Friedmann ... ker_metric

No, not a misunderstanding. I mentioned RW not FLRW. Weinberg contains a derivation of the RW equations in section 13.5 based purely on the cosmological principle using the theory of symmetric spaces. It uses the same type of differential geometric objects as in GR, but GR is not used in this derivation. The FLRW equations have the EFE mixed in through Friedmann's equations, but the RW equations are independent of them. The RW equations just use R(t), Friedmann's equations just fill in that part.

That theory does not care about physics yet explains curvature in our observable universe as part of the curvature of the entire universe

Hmmmm. The Friedmann equation is of the utmost importance in the process of cosmological modelling. The Friedmann equation determines the form R(t), which represents the rate of change of the scale factor R which is directly related to the matter density ρ. It is worth pointing out that on the basis of Newtonian physics, the Friedmann equation can be derived by considering the total energy of an expanding spherical distribution of galaxies. In such a derivation, kc^2 is related to the total energy of the sphere, R^2 is related to the kinetic energy of the sphere, and G is the gravitational potential energy of the sphere. And so, the Friedmann equation is also referred to as the 'energy equation' of the universe. I'd say it is dependent on physics.

Friedmann, yes, Robertson-Walker, no, for the same reasons above.

I don't have anything sensible to add about the rest and hope that some genius will come along to give us the answers. Thanks for your feedback, much appreciated!

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Hey Henk thanks for your response too. When I’m done at work I’ll have a look at the pages you recommended. Chat back soon

[Gmetric]

check the ends of sections 11.7 and 15.1 for this. This is the only reference I know of that explains why Newton's absolute space is affixed to the galaxies in the universe. More precisely, affixed to the standard cosmological model of the universe.

Okay, cheers for the reference. I'll check it out. ( i have)

we need a definition of Mach's principle in a differential geometric context.

Don't you find nFA's arguments convincing enough in this thread https://theskysearchers.com/viewtopic.p ... SK#p224651 ?

RW equations that are the main constituent of the cosmological model are not based on GR but on symmetric spaces theory.
Perhaps a misunderstanding? "The Friedmann–Lemaître–Robertson–Walker metric (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) is a metric based on the exact solution of the Einstein field equations of general relativity." https://en.wikipedia.org/wiki/Friedmann ... ker_metric
No, not a misunderstanding. I mentioned RW not FLRW

Ah, I see; when you said, "RW equations that are the main constituent of cosmology are not based on GR but on symmetric space", You didn't mean generally but by virtue of the fact that Weinberg used symmetric spaces to construct a framework from which to expand on RWs work with four-dimensional space and three-dimensional maximally symmetric subspaces. From this, Weinberg formulates the cosmological principle and works through RW. Okay, I see where you are coming from.

The books I have here, which include the history of cosmology, all state that, and I quote, "Alexander Friedmann was born and educated in St Petersburg and returned there in 1920 to work at the Academy of Sciences. Known for his work on theoretical metrology, Friedmann became interested in general relativity and used his mathematical talents to undertake a highly original exploration of the cosmological consequences of the theory leading to the Friedmann equations. Howard Percy Robertson was an American mathematical physicist specialising in applying general relativity to practical simulations. In 1929, using general arguments that did not depend on specific assumptions about the properties of matter, Robertson deduced the general expression for the separation of events in space-time of any universe that is spatially homogenous and isotropic at all times. Arthur Geoffrey Walker spent most of his academic career at the University of Liverpool, initially as a lecturer and later as a Professor of Mathematics. His expression for the separation of events in a homogenous and isotropic universe was published in 1936. It was based on a somewhat different approach from the earlier work of Robertson."

So it is true to say that the original format of RW motivated in the 1930s was based on GR. However, it is also true to say that Weinberg states on page 408 that his method will use only the cosmological principle and the principle of equivalence from GR, which goes back to chapter 13 and Symmetric spaces to construct his model of the universe. LOL, I think we are both barking up the same tree Good, I'll need a little more reading time to digest it fully.

Therefore, Friedmann, yes, Robertson-Walker, YES, surely?

Right, i best get to bed but thanks for the headache LMAO

[SkyHiker]

Don't you find nFA's arguments convincing enough in this thread https://theskysearchers.com/viewtopic.p ... SK#p224651 ?

No. Regarding his reference to the standard model of particle physics, IMHO we need to wait until this has been integrated with GR. With all the talk about gravitons, there is just more of a gap between these areas than I am comfortable with.

That also applies to his reference to Sciama's paper "The Physical Structure of General Relativity" in my humble opinion. I have spent weeks trying to understand it. At first, especially looking at the introduction, I thought the torsion component of the ECSK metric would explain Mach. In the end it is all about spinors trying to connect with the standard model of particle physics. I don't know much about that, but my understanding is that the Cartan geometry is relevant only inside matter while it reduces to Riemannian geometry outside. I am not comfortable with using Cartan geometry in a world that is clearly Riemannian at the macroscopic level. So that paper seems more like one of the many GUT attempts that have failed so far. Sciama's earlier paper "On the origin of inertia" is very inspiring but incomplete, and I was unable to find out where his promised part 2 was. I thought it was the former paper but now I think it was never written. After that paper I read a lot of articles about the weak field equations (because basically that's what Sciama does with his Maxwell-like equations) that are eventually useful for understanding the Gravity probe B analysis, but they don't not address Mach's principle; well, some do but not convincingly at all.

RW equations that are the main constituent of the cosmological model are not based on GR but on symmetric spaces theory.
Perhaps a misunderstanding? "The Friedmann–Lemaître–Robertson–Walker metric (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) is a metric based on the exact solution of the Einstein field equations of general relativity." https://en.wikipedia.org/wiki/Friedmann ... ker_metric
No, not a misunderstanding. I mentioned RW not FLRW

Ah, I see; when you said, "RW equations that are the main constituent of cosmology are not based on GR but on symmetric space", You didn't mean generally but by virtue of the fact that Weinberg used symmetric spaces to construct a framework from which to expand on RWs work with four-dimensional space and three-dimensional maximally symmetric subspaces. From this, Weinberg formulates the cosmological principle and works through RW. Okay, I see where you are coming from.

Looking at the Wikipedia link for this, it is stated right at the top "Einstein's field equations are not used in deriving the general form for the metric: it follows from the geometric properties of homogeneity and isotropy.". I only just now noticed this; I based my comments on Weinberg's book but this makes it clear I think.

The books I have here, which include the history of cosmology, all state that, and I quote, "Alexander Friedmann was born and educated in St Petersburg and returned there in 1920 to work at the Academy of Sciences. Known for his work on theoretical metrology, Friedmann became interested in general relativity and used his mathematical talents to undertake a highly original exploration of the cosmological consequences of the theory leading to the Friedmann equations. Howard Percy Robertson was an American mathematical physicist specialising in applying general relativity to practical simulations. In 1929, using general arguments that did not depend on specific assumptions about the properties of matter, Robertson deduced the general expression for the separation of events in space-time of any universe that is spatially homogenous and isotropic at all times. Arthur Geoffrey Walker spent most of his academic career at the University of Liverpool, initially as a lecturer and later as a Professor of Mathematics. His expression for the separation of events in a homogenous and isotropic universe was published in 1936. It was based on a somewhat different approach from the earlier work of Robertson."

Now that's interesting, looking at the timeline I see that Friedmann derived his equations in 1922 while Robertson and Walker published their results much later on, in 1929 and 1936.

So it is true to say that the original format of RW motivated in the 1930s was based on GR. However, it is also true to say that Weinberg states on page 408 that his method will use only the cosmological principle and the principle of equivalence from GR, which goes back to chapter 13 and Symmetric spaces to construct his model of the universe. LOL, I think we are both barking up the same tree Good, I'll need a little more reading time to digest it fully.

I stand corrected about the timeline. Regardless, the RW equations are not based on GR or any kind of physics, just symmetric spaces and differential geometry. That's the way in which Weinberg presents it, not how it was discovered historically. BTW Weinberg's chapter on symmetric spaces is not for the faint hearted, and he calls it only an introduction. No wonder it was discovered later on. Once you have the RW equations, the Friedmann equations are a breeze.

Therefore, Friedmann, yes, Robertson-Walker, YES, surely?

Reading back, I hardly understand what I meant to express there. I meant to say that the RW part is based on symmetric spaces/no physics, whereas Friedmann throws in the EFE.

Right, i best get to bed but thanks for the headache LMAO

Welcome to the club!

[SkyHiker]

Speaking about GR being incomplete, Einstein believed that the speed of light is only constant in regions of constant gravitational potential. A constant speed of light is incompatible with the equivalence principle, which is fundamental to GR. These statements can be found in the Princeton collection of Einstein papers, in this case here. He maintained this position at least through 1920, well after completing the current GR. So, there is work to be done.

BTW one interesting paper in the context of Mach's principle is this one. He represents the universe as a spherical shell. If you put a point mass at the center, its mass (inertia) is affected by the mass of the shell. He also shows that a force is enacted by the shell on the point mass if the shell accelerates. The Wikipedia entry for Mach's principle shows that term in refence to work by Sciama (inertial induction). Einstein was very enthused about this and wrote a letter to Mach that you can find in Misner Thorne Wheeler with the same illustration as in that paper.

These ideas about Mach's principle and the variable speed of light were not talked about much later on, in fact Einstein seemed to have abandoned the idea. I have no idea why, but it makes me think that I should not believe everything I read (such as standard and well accepted GR texts).

[SkyHiker]

These ideas about Mach's principle and the variable speed of light were not talked about much later on, in fact Einstein seemed to have abandoned the idea. I have no idea why, but it makes me think that I should not believe everything I read (such as standard and well accepted GR texts).

I just found a great video by Unzicker who discusses GR based on the variable speed of light vs GR based on differential geometry. He claims that Einstein's initial scalar / non-geometric approach is equivalent to the standard GR, and that this fact got lost in history. It is a fun video to watch that also discusses GR approaches by Dicke and Schroedinger. Browsing around, some people have controversial thoughts about Unzicker. He certainly has some thought-provoking videos that should be big news if true. Curious what you all think about this.