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Supernova’s messy birth casts doubt on reliability of astronomical yardstick (nature.com)
60 points by okket on Aug 20, 2017 | hide | past | favorite | 18 comments



The headline here is a bit of an overstatement. Nothing in the original paper is casting doubt on Type Ia supernovae as reliable standard candles. It is definitely an embarrassment that we still don't know the mechanism by which Sne Ia occur, but empirically their luminosities can be calibrated well enough that the accelerating expansion of the universe is not in doubt. However, to determine the nature of dark energy (specifically, its equation of state), it may be necessary to calibrate SN Ia luminosities better, and that will probably require understanding exactly what they are.

There are two major SN Ia models: the double degenerate, which involves two white dwarfs colliding, and the single degenerate, which involves one white dwarf accreting matter from a regular star. There have been two approaches to distinguishing between the two models. One is to look for hydrogen in the spectrum a long time after the supernova. In the single degenerate model the supernova shock will strip hydrogen from the companion star's atmosphere, but in the double degenerate model, there will be no hydrogen to strip.

The other method is to look at the very early light curve of the supernova, as this paper did. The early light is expected to rise in a straight line as the surface area of the shock expands. A deviation from this straight line, particularly in the blue bands, then could indicate some interaction between the shock and a companion. This paper found such a "blue bump" in the early light curve of a recent supernova. (There has been at least one earlier paper that also found a blue bump in another supernova.)

I'm out of the field now, so my knowledge isn't quite up to date, but my impression is that the observational evidence may be pointing to a mix between the two mechanisms. For anyone interested, I wrote a little bit about this problem here:

https://joe-antognini.github.io/astronomy/typeia-progenitors


How would you explain, to a layman, why standard candles--phenomena we must measure from great distances--are trusted to be as consistent as well believe them to be?


It's essentially built up of a chain or ladder. From parallax measurements to cepheid variables to supernova. This might give a good introduction http://www.iop.org/resources/topic/archive/cosmic/


I always hate it when an article drops that we've "proven the existence of dark matter". We've done no such thing. Usually that sentence describes some of the proof of the fact that our matter and energy predictions are off by an order of magnitude... Proof of the problem that dark matter/energy theories attempt to resolve. I know it's a nitpick, but it drives me nuts.


> we've "proven the existence of dark matter"

The article says we've proven the existence of dark energy, not dark matter. They're not the same thing.

That said, if it does turn out that the SN1a "standard candle" scale has to be revised, that might impact the finding of accelerated expansion on which the dark energy model is based. It will be interesting to see how other cosmologists respond to this paper.


Do cosmologists allow for the doping of the matter involved in these interaction due to stella aging? It seems to me that more distant supernovas must act differently from the closer ones because they are much younger and therefore undoped by earlier supernova debris.


As I understand it, the assumption behind using SN1a as standard candles is not that they all have exactly the same absolute brightness, but that there is a reliable relationship between the light curve (the curve of apparent brightness vs. time) and the absolute brightness. This relationship takes into account variation in the chemical composition of the supernova, which is what "doping" would affect.

However, what this particular paper seems to be saying is that there might not be just one light curve-brightness relationship, but two, corresponding to two different explosion processes. If that's true, astronomers would need to go back and review the SN1a data with this new classification scheme in mind.


> the finding of accelerated expansion on which the dark energy model is based

Dark energy arises because of the decomposition of 4-d spacetime into volumes of 3-d space each distinguishable by a time coordinate, and choosing as the timelike axis the one in which matter is -- on average and at the largest scales -- at rest against the 3-d spatial coordinates.

That fixes a preferred frame -- the cosmological frame -- for observers who are comoving with the spatial coordinates. Such observers will see no dipole anisotropy in the cosmic microwave background (or the cosmic neutrino background, or other relic fields), and will be comfortable with approximating the distribution of visible matter far from them as a homogeneous isotropic fluid, in spite of local inhomogeneities and local anisotropies (like, for example, the planet each of us has between her- or himself and a large percentage of the rest of the universe).

All comoving observers in such a universe will generally agree that in one timelike direction the visible matter is denser and the CMB is hotter and that in the other timelike direction the visible matter is sparser and the CMB is colder. Let's pick the former direction as the past.

All observers in such a universe -- even non-comoving ones -- will agree that it takes energy to separate two massive bodies that are gravitationally bound.

So in the past, when comoving matter was denser, it would take more energy to separate the bits of matter from one another than in the present, when comoving matter is sparser. Something is keeping objects like galaxy clusters fixed against the comoving coordinates, instead of giving them peculiar velocities against these coordinates as they gravitationally attract one another.[1] That is dark energy, and we can experimentally determine its value in the cosmological frame.

The rate at which visible matter is diluting away along the cosmological frame's past->future direction is what what we try to measure.

Standard candles are useful for helping fix a distant galaxy to comoving coordinates. As our confidence in the location of distant matter improves, so does our confidence in the average value of dark energy. There are a sizable number of relationships involving measurable quantities like angular diameter, surface brightness, emission/absorption line "forests", and so forth that help us fix galaxies in the cosmological frame of reference, so throwing questions upon only one coordinate:observable relationship is far from fatal to our estimates of dark energy density. It sure is interesting though!

So, back to "accelerated expansion": dark energy represents something working against the tendency of matter to gravitatonally collapse. Whether that something is constant or evolves is something we can determine by observation. Whether that something is uniform everywhere outside galaxy clusters or not is also something we can determine by observation. Current evidence is consistent with a constant uniform feature of the action of large scale structures. In particular, while normally gravitating matter is diluting away in the past->future direction we picked out in our cosmological frame of reference, dark energy is not diluting away.

If, still staying in the cosmological frame, we switch our spatial coordinates from comoving coordinates on the cosmological frame to spherical Earth-centric coordinates, we have to adjust our understanding a little. A distant galaxy has a lower radial distance at earlier times than at later times. We can identify this with a recession velocity, and use that to explain the cosmological redshift and the presence of various cosmological horizons. But this is a coordinate-dependent explanation. It is perfectly fine to stick with comoving coordinates and resort to other explanations for the cosmological redshift.

Indeed, it was that galaxies at extreme distances still look like galaxies that led to the metric expansion of space in the first place: small-angular-diameter galaxy clusters can't really be moving relativistically away from us or they would look VERY different structurally. Additionally, we haven't abandoned Lorentz covariance, so treating matter receding over the horizon as moving superluminally has to be considered a non-physical artifact of a choice of coordinates and frame of reference. And sure enough, just by changing the coordinates alone, these problems disappear.

[1] individual galaxies within a cluster have peculiar velocities against the comoving coordinates that the cluster's centre of momentum stays fixed against. Likewise, massive elements within galaxies (e.g. Earth) have peculiar velocities against the comoving coordinates thanks to local gravitational interactions (e.g. Earth orbits the sun). Each of these introduces an anisotropy in the view of the overall distribution of matter in the universe and in the view of the CMB by an observer with a peculiar velocity. Such observers are not strictly comoving ones. But they're generally awfully close to comoving, because they're almost certainly embedded within a larger structure that is comoving.


I just enjoy the way you use all these words to say that the theoretical entities exist when experiment has not shown any evidence of their existence.

Try to remember that a model is only a model and a theory is only a theory that is one possible explanation of the reality we observe.

It is an attempt to get a handle on understanding the universe around us. When you and others go off and start proclaiming the actual existence of these theoretical entities without at least the experimental confirmation of such, then you are setting yourself to be considered in the same light as attendees at the local ufo conventions.

It annoys me when theoretical entities are declared as existing when the evidence is only slightly in their direction or the only evidence is that they need to exist based on the current mathematical models being used.

When said and done, dark energy and dark matter are mathematical entities required by the prevailing theory. The prevailing theory is only one of a number of possible models. Which one you subscribe to is up to you and your view of how the current evidence stacks up.

At this point, none of the models seems to cover enough bases to make it the most likely scenario. So, for me, this is still an open question. The current prevalent model has at it basis, some, from my point of view, untenable inconsistencies.

The first and foremost is that gravity (whatever model you might ascribe to) is the majority controlling force. The inconsistency is that model uses gravity to give rise to "Black Holes" and yet has not stopped the "Big Bang" from happening. When you start to play around with reconciling both entities, it becomes a bit of a problem. You then add time dilation effects due to gravity (as per the various models in use) and you get other strange quirks/inconsistencies appearing.

The upshot of this is that people should be careful to not declare the actual existence of theoretical entities from incomplete models just based on belief. This just turns the supposed science into religion and religion is considered anathema amongst certain groups within the science communities.

The theories and models are supposed to be helpful working explanations that can change or be thrown out based on new evidence. They have a particular usage profile and range of applicability. If you go outside of that usability or applicability range then the theory/model will start to fail. As we were taught in undergraduate engineering all those decades, you use the applicable model/theory for the specific circumstances being investigated.


> not shown any evidence of their existence

What?

Do you deny that highly similar spiral galaxes seen face-on are roughly similar in star-count?

Do you deny the observation that there are highly similar spiral galaxies that occupy very different angular diameters on the sky?

Do you deny the observation that spiral galaxies with lower angular diameters have higher redshifts? And that the redshifts squeeze the entire emissions spectrum from such galaxies?

Do you deny the Lyman-alpha forest?

These are all observations that someone with a decent back-yard observatory could make on his or her own.

So what observations do you want to throw out? Parallax? The observation that stars within our galaxy and M31 differ on average only in the spectral redshifting from stars in the smaller-angular-diameter set that Vesto Slipher identified in 1914? Again, this is the sort of astronomy[1] you could do in a reasonably dark field near your home.

> It is an attempt to get a handle on understanding the universe around us.

Sure, that's what science is. And a viable theory is one that does not conflict with observations to date. Theories that are viable today can become inviable tomorrow; all it takes is a new observation. There are literally tens of thousands of theory-challenging astronomical observations made in any 24-hour period in 2017, and theorists get very excited by even the slightest inconsistency with the standard cosmology. Unfortunately such inconsistent observations are extremely rare, and tend to vanish under repeated observations (by the same and by other observatories).

> At this point, none of the models seems to cover enough bases to make it the most likely scenario

What exactly have you read about "the models" and the "bases"? Serious question. Is it anything more than mathless popsci articles or comments in technology-focused Internet discussion forums?

> gravity to give rise to "Black Holes" and yet has not stopped the "Big Bang" from happening

Go back and re-read the comment you replied to. The thrust of it is that galaxies exist even though in the past they were much closer together. Why haven't they collapsed gravitationally into something much denser? There are a variety of possible answers, but (paraphrasing myself), the most attractive one is that there is a component of the action of galaxies that acts against their mutual gravitational interactions. With suitable coordinate conditions, that can be seen as a fifth force, and with other coordinate conditions, that can be seen as a simple feature of the vacuum, and with other coordinate conditions, that can be seen as a fine balance between inertia and gravitation, and so forth. But unless you want to argue that the cosmological frame is an improper choice and defend that position, you're stuck with the reality that in that frame it is most natural to identify the action component with an energy density.

Put more simply, yes indeed, the crucial question is why hasn't all the visible matter collapsed into a big black hole?

Since you identified that question yourself, you're on the cusp of understanding, yet you reject the most obvious answer: there is something at work preventing the gravitational collapse of galaxies. The only additional step is that in certain frames of reference, preventing two massive objects from eventually moving closer together under their mutual gravitational interaction requires work to be done.

(Maybe there is an intermediate step: why don't galaxies individually collapse into giant black holes? Or why haven't the planets crashed into the sun? In both cases there is a lot of angular momentum that would have to be radiated away from the orbiting objects in order that they can get close enough for the gravitational interaction to produce a collision. That takes a long time. Gödel proposed that the entire universe is rotating around a central axis[2] so therefore there is a lot of angular momentum keeping distant galaxies in an orbit rather than colliding with nearby (to us) galaxies. Rotating metrics have been studied (thanks in large part to Gödel) and they produce very different observables of distant galaxies than the ones we have.)

> the supposed science into religion and religion is considered anathema amongst certain groups within the science communities

Georges Lemaître -- referenced in [1] below -- sure was religious! Nobody doubted his astrophysics chops. There are plenty of working cosmologists today who hold to some faith or other (they're certainly not all Christians! or even monotheists!). They go to where observations, experiments and other types of material evidence take them. As long as one does that, nobody will care what she or he believes about spirituality or even the presently extremely hard to observe early universe.

But you, who does not seriously challenge the observations or evidence, refuse to entertain their implications, and do not offer up anything to explain why other than that you argue (wrongly) that others' collaborative efforts to rigorously and formally follow those implications are "religious" because inter alia (a) incompleteness of models means the whole model is entirely wrong (b) General Relativity is self-inconsistent (it sure isn't!) (c) General Relativity is not a successful tool at the relevant length scales (d) strong gravity is in play at length scales in which one can observe galaxies at all.

Your argument is plainly based on ignorance and personal incredulity. It is easy to fix the ignorance part: there is a lot you can read; you might start with something like Carroll's textbook[3] working your way to Chapter 8. Wanting to reject the standard cosmology just because it doesn't sit right with your intuition is a character trait you'll just have to wrestle with, like any good scientist has to from time to time. But when your intuition isn't even informed and you insist that the standard cosmology (which you do not understand) is wrong, well, people will form adverse opinions.

- --

[1] https://arxiv.org/abs/1108.4864

[2] https://www.wikiwand.com/en/G%C3%B6del_metric#/Cosmological_...

[3] https://www.goodreads.com/book/show/259680.Spacetime_and_Geo...


What? Every experimental test of dark energy and dark matter has come up empty so far. Dark energy and dark matter are one possible explanation of the actual observations that you have referenced. Possible. The prevailing theory did not explain these observations and so in the course of trying to modify that theory, a number of additional theoretical entities were added to explain the anomalous observations.

Don't put the horse before the cart please. Observations are first, not theories. The development of theories is dependent on the observations and the predictions those theories give rise to experiments to test the veracity of the theory in question.

Your comments about my response regarding "black holes" and "big bang" miss the anomaly between the two concepts. You are replying in a theoretical sense not in any actual experimental sense.

What I find interesting is that you ask the question of why the universe hasn't collapsed, when it should be why did singularity from the theory ever explode?

Yes, what is it that holds the universe as it is? Your obvious answer is a continuation of the "big bang" model, but is that model actually valid? I don't believe it is, nor do I believe that gravity is the prevailing force that the model suggests. The reason for not thinking so is related to the underlying basis for the model that the universe is electrically neutral. Since that is incorrect, too many plasmas occurring all over the place, we must look at including electromagnetic effects within the models we develop. If we ignore these effects, which is what occurs in the prevailing theory, then additional other entities must be added to explain the actual observations made.

You ask the question of why don't galaxies collapse into black holes. Well, the simple answer may be that there are no "black holes" because the theoretical entity cannot exist in the universe. Does that in turn mean that there are no large gravitational bodies? No, but it does mean that what people are calling "black holes" are, in fact, not "black holes" but some other body for which our models have not yet found an effective theoretical base. Remember that "black holes" have very specific properties in theory, one of them being a singularity and the other an event horizon at which time has stopped as seen from outside the event horizon.

You miss the religious reference. I am not referring to men and women who believe in God, a god or gods and accept the theory or model. But I am referring to those who have turned science itself into a religion, or more the point, have turned the belief in the theory/model into a religion. That is a major concern and should be addressed.

Why would I challenge the observations? What I am challenging, if you like, is the interpretation of those observations. The observations stand and fall by precision by which they are made.

The simple point is that too many of the observations indicate that the basis for the model theory is not only incomplete but wrong. As I said above, the theory depends on an electrically neutral universe so that the only force of any consequence is gravity. The universe is too big for the time since the "big bang" so a unknown, unknowable process called inflation has had to be incorporated, movements with a galaxy are doing things that are not according to what the theory says they should so then "dark matter" had to be incorporated into the model, and then movement between galaxies wasn't occurring in the manner predicted, so "dark energy" was added.

Now for the last twenty years or so, no experiment devised to find "dark matter" or "dark energy" has found either of those entities. Hence, there is a significant possibility that they don't exist.

Mayhaps, the model is wrong and there needs to be a revisiting of the observations to see if some alternate theory might have more success. Is this occurring? Not that I can see. If anything, it appears that those who believe in the theory are doubling down and doing everything to justify their theory.

This is supposed to be science, you know, that process by which we systematically observe the universe around and try to develop viable theories that help us understand what we are seeing. If a model doesn't work, we are allowed to throw it out, you know. If we can't do that and look for better explanations, then what are we doing?

I have been wrong about many things during my lifetime and when I have been shown that, I give up the old and take up the new. This was a fundamental part of my science and engineering education.

Let me put something to you, I am not hung up on any particular model as being the "right" model. If the theory/model in question has problems explaining some observations, it just means that there is a better explanation, we just haven't worked it out yet.

My personal belief is that God (personal Christian Trinity) created the universe and that He takes great delight in us learning about His creation and how it works. It works according to the rules He has put in place and it is up to us to investigate and find out those rules, laws, etc.

What you believe is up to you. If you don't believe that there is a creator then you also have to come up with a reason for why the rules are precisely as they are.

Irrespective of the cause of the universe and what you believe about that, we need to be capable of modifying and/or dropping theories that no longer match what we see.

You can consider me ignorant if you wish, but I think I have a greater wonder about the universe than you do. It is for exploring and there are ever more complexities than our simplistic theories will ever uncover. That is the fun part.


You keep adding in dark matter, but this article has nothing to do with dark matter. I didn't discuss dark matter.

The article is about the metric expansion of space, or if you're really really really stubborn about that (you appear to be) the redshift-distance relation sans mechanism.

That relation is an empirical fact and has been known for more than a century. Indeed, the discovery of that relation both predated the discovery of galaxy clusters and enabled the discovery that galaxies are collections of billions to hundreds of trillions of stars.

> experiment

You are being way too fussy about this. Sure, you can take an ultra-Popperian attitude towards cosmology, but that would make you an extremist rather than a scientist; science generally doesn't work that way. You'll be hard pressed to find any scientist who advocates ignoring observational evidence simply because local direct testing is infeasible with current technology. Heck, we still can only demonstrate the inverse square law for gravitation down to micrometer scales in laboratory settings, and there was no experimental value for the gravitational constant until the start of 19th century. Yet there Neptune is.

At any rate, you do not really seem interested in learning about the theoretical underpinnings of dark energy in any way, and if you're as uninterested as you appear to be in advancing your own understanding of the standard cosmological model and the many observations and experimentally well-validated theories that it wholly captures (notably the Standard Model of Particle Physics and General Relativity), then it seems wasteful to continue this thread. I have no need or desire to "convert" you, and am uninterested in your personal beliefs or what you believe I believe or why I believe it. Honestly, I hope my withdrawing from the conversation will make you feel better.


"proven the existence of dark matter," to me, says that we've proven that there's a thing with some known properties that needs a lot more explaining. And that's the actual intent of the people who are saying it, too.

Same thing with dark energy, although even fewer of the properties of dark energy are known.


It is interesting that those who are looking experimentally for both dark matter and dark energy have come up empty in every experiment so far performed.

The theorists seem to ignore this and rely more on faith in their mathematical theories and models leading to dogmatic reliance on their belief not on experimental evidence.

Reminds me of the "The Neverending Debate" between String Theorists and Non-String Theorists.

Mathematics is a very useful tool, but if reality differs from the mathematic model then the mathematics is not sufficient and is only a simplistic view for us to use.


> It is interesting that those who are looking experimentally for both dark matter and dark energy have come up empty in every experiment so far performed.

Given that <1% of the dark matter search space has been covered, this is an entirely unsurprising result.

The ΛCDM model doesn't come out of theory, it comes out of observation - the only thing we can make fit our observations of the universe is cold dark matter (and a cosmological constant, aka dark energy)

The thing a lot of people don't seem to get is that astronomers hate¹ dark energy and dark matter - they're really quite inelegant - but nothing else fits. Every other attempt (and lots and lots of time and energy have been spent on this) to explain our observations without hypothesising the existence of a lot of weakly interacting matter out there (e.g. MOND) has failed to match them

¹ In much the same way physicists dislike the standard model in all of its' ugliness - even though it works


The theory doesn't match the observations, so how do we tweak the theory to match the observations - oh wait - let's add dark matter to the theory. Partial fix - oh wait - we need something to add something else to he theory now - let's add ..... dark energy.

Oh yeah, this seems to fix the theory to now match observation.

The observations do not require dark energy or dark matter to fix things. It is the interpretation of those observations via the theory that requires these entities.

Observations are theory neutral. It should be fun to try an come up with a good model/theory and if new observations break the theory, then it should be more fun to see what is a better explanation.

For many, many years, I have watched very intelligent people get emotionally caught up in defending their theories and models, when it should be a case of just moving on. They just don't make it fun.


(And to put things another way: of course we've come back empty in all searches so far. If we hadn't, we'd stop looking!)


Second thing first:

> ... much the same way physicists dislike the standard model in all of its' ugliness - even though it works

Personally I think the U(1)xSU(2)xSU(3) group theory of the Standard Model of Particle Physics is quite pretty. AFAIK the problems with the Standard Model are rarely put as issues of "ugliness" but rather that it's known to be incomplete -- in particular the gravitational sector is not dealt with at all -- and is probably slightly incorrect (depending, for example, on how you deal with neutrino masses). It has some practical problems too, namely that there are at least nineteen parameters that so far can only be determined empirically, and there are questions about whether the allowed symmetry breaking can resolve the hierarchy and strong CP problems.

However, the overall mathematical details are so attractive that perhaps most attempts to fix these problems introduce new internal symmetries (so far unsuccessfully) into the gauge QFT rather than take seriously the idea that the mathematical objects are inappropriate or unattractive.

So I think you have it very slightly backwards. We are probing the effective field theory limit of the SM and finding that likely the Standard Model doesn't work at accessible energies. (Unfortunately conclusive evidence of beyond-the-Standard-Model -- in the sense of an experimental result that the SM cannot explain -- hasn't been found yet). And unfortunately the most obvious and elegant approaches to extending the SM so far conflict with experimental results.

FWIW, Carroll at one point said that all physical cosmologists are gauge theorists. That's pretty hard to argue with these days. So I think you may have trouble enlisting many cosmologists into supporting your footnote.

> astronomers hate dark energy

I doubt many astronomers even care; it's a problem for cosmology since it literally only operates at extragalactic scales; there is no DE within galaxies. [4]

I'd bet that most astronomers mostly only care that astrophysics works as expected at high redshifts, i.e., that dark energy does not introduce Lorentz invariance violating terms into their calculations.

Cosmologists, being relativists, know that dark energy is reference-frame dependent, and in particular that DE is a feature of the cosmological frame. There are good reasons for using the cosmological frame when dealing with gigaparsec length scales, and so good reasons for calling it "dark energy" without clarifying that the very concept of energy in General Relativity (GR) is complicated. (To be fair, the concept of energy in Newtonian mechanics can be complicated too: how do you define potential energy in a rotating frame? The classical bead-on-a-rotating-hoop problem often shows up in graduate-level university exams.)

> astronomers hate ... dark matter

Do they? I mean it's frustrating that it's invisible, but so are neutrinos for all practical purposes, and astronomers don't hate those (at least not the astronomers studying solar neutrinos or the fine energy balance of supernovae, for example). Surely though it's more a puzzle which they also scratch their heads about when dealing with the motions of stars within galaxies and so forth.

> the only thing we can make fit our observations of the universe is cold dark matter

Firstly, I fully endorse the standard model of physical cosmology, \Lambda-CDM.

However, CDM is far from the only thing that can match our observations of galaxy-scale kinematics and dynamic stability. It is always possible to modify the LHS of G = T (pardon the dropping of indices and constant terms), it is generally possible to treat that modification as a (classical) field, and often possible to move that classical field over to the T side as a source term. So the space of solutions to the galaxy scale problems that CDM resolves is huge.

CDM's attraction is mainly in the hopes that beyond the Standard Model there lies a sterile neutrino or similar particle, but there are nearly endless ways the Standard Model could be extended into the dark matter sector. One line of thought behind this preference is that if such a particle is discovered, it's relativized and quantized "for free" within the BTSM QFT. MOND is hard to relativize [1] and may resist perturbative renormalization.

> (and a cosmological constant

Well, you've got me there. :-) Alternatives to the CC so far all have stability problems. They do exist though; for example one can find them in bimetric theories where the second metric decays away no later than the inflationary epoch. (There's some robust technical discussion at [2]).

> [dark energy] is inelegant

I have to disagree there. So would Schrödinger! [3] All you need is a representation of matter as a homogeneous and isotropic fluid with some density and pressure and a reasonable slicing of spacetime: if your spacelike slices expand and the matter stays homogeneous and isotropic on average then a negative pressure (or tension) with a value of ~ 1/3 of the density falls right out of practically any reasonable set of equations you might use.

In the FLRW model for the cosmological constant (CC) we just fix density_CC = const, pressure_CC = - density_CC -- the beauty of "dark energy" is that we can parametrize this pressure/density (it's the "w" parameter in the standard cosmology) and not have to worry about the microscopic details of the new component(s), other than that the microscopic behaviours of the component(s) and the bulk contribution to w must match. I think that's pretty elegant.

- --

[1] Famaey & McGaugh, https://arxiv.org/abs/1112.3960 ch. 7.

[2] https://physics.stackexchange.com/questions/123131/what-are-...

[3] Harvey, [physics.hist-ph] https://arxiv.org/abs/1211.6338v1

[4] DE is a set of non-metric-invariant quantities that arise in the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. It is inappropriate to use the FLRW metric when matter is not (on average) homogeneous and isotropic. The matter in real galaxies is neither homogeneous nor isotropic, so one must use another metric to describe them, almost always a non-expanding one (e.g. Schwarzschild) which admits a boundary condition that one can use to patch that local non-expanding space into the expanding FLRW space. (I use "space" here rather than "spacetime", since the slicing of 4-d spacetime into 3+1 space + time is relevant.) If we do a lot of abuse we can pseudo-transport the DE into this other metric, wherein the best interpretation is that it contributes to the momentum tensor (but cf. Einstein's reply (his point 1) to that interpretation in [3] chapter 3, and also the Schwarzschild-de Sitter metric which we can with more work also stitch into FLRW).




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