Is this an accurate summary of the current status quo?
1. The universe is expanding
2. The velocity at which the universe is expanding is increasing, since there is non-zero acceleration.
3. The acceleration is actually slowing down, but it is not heading towards zero. It is approaching some steady state acceleration.
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In Exploring Black Holes by Edwin Taylor and John Wheeler, published in 2000, I recently read the following passage by Wheeler:
> An article by John Noble Wilford in the Science Times section of the New York Times for Tuesday March 3, 1998, reports observations by two separate groups of investigators which they interpret as showing that today the expansion of the Universe is speeding up rather than undergoing the slowdown expected for any approach to maximum expansion. Later that day I encountered a hard-bitten veteran gravitation physics colleague in the elevator of the Princeton physics building and asked him if he believed the purported evidence of accelerating expansion. "No," he replied. Neither do I. Why not? Two reasons: (1) Because the speed-up argument relies too trustingly on the supernovas being standard candles, (2) Because such an expansion would, it seems to me, contradict a view of cosmology too simple to be wrong. Such clashes between theory and experiment have often triggered decisive advances in physics. We can hope that some decisive advance is in the offing.
Now, Wheeler was one of the most preeminent physicists of the 20th century and spearheaded several fields and was not afraid of wild ideas. I am curious if anyone knows if he had any inklings that further his thoughts here. Was he just wrong here, before new measurements came out? Or is there something missing in these calculations and the theory that we're missing? I'm also not sure what means in (1).
> 3. The acceleration is actually slowing down, but it is not heading towards zero. It is approaching some steady state acceleration.
No. The scale factor in LCDM (the current concordance model) is proportional to sinh^(2/3)(t/t_Lambda), which means it's asymptotically exponential. Acceleration will always increase.
(Edit: The expansion rate, so a'/a, will go to a constant value, though.)
Caveat: If the Hubble tension proves real, LCDM is wrong.
Thanks! So the currently accepted model says the acceleration will grow indefinitely but our observations are saying that the acceleration levels out to a non-zero, positive constant?
a is the scale factor, which goes as sinh^(2/3). a' and a'' will always increase, but the _expansion rate_ a'/a will approach a constant value from above.
Besides the Hubble tension discussed in the article, there is no real discrepancy between observations and theory.
> a is the scale factor, which goes as sinh^(2/3). a' and a'' will always increase, but the _expansion rate_ a'/a will approach a constant value from above.
Thanks for that. I didn't realize there was such a definition of expansion rate and was going off the intuitive meaning of the terms. Thank you for the clarifications.
To the Wheeler question, I would say he was just wrong. Pre-eminent physicist of the 20th century he may have been, smarter that I'll ever be, but he was also nearly 90 at that point and had retired 22 years earlier.
To (1), he's talking about the distance ladder. Distances to various galaxies were computed by the teams involved in developing the LCDM model by scouring the skies for instances of type IA supernovae in this galaxies. When these are called "standard candles," what that means is that the luminosity is known and thus the distance can be computed using the inverse square law by comparing the observed brightness to the known luminosity. Historically, this wasn't a super-reliable method and yielded some bounded error rate for various reasons, including dust causing some reddening of the light that could be mistaken for redshift, as well as the fact that type IA supernovae are not all collapsing stars of exactly equal mass and you might catch them at different times after the initial supernova.
What Wheeler probably didn't realize at that point was the methods and frankly just downright tedious repeated measurement work over the course of decades that astronomers had been doing to make this more reliable and accurate. If you want to know all about this via first-hand account from one of the astronomers credited with the dark energy discovery, read The Extravagant Universe by Robert Kirschner. It's very accessible, not super-technical, but goes into painstaking detail on exactly how astronomers made the type IA work as a standard candle.
It's also just a great testament to the work involved in experimental astronomy, down to the logistics of convincing a scheduling committee for the various telescopes capable of seeing that far that what you're looking for is worth looking for.
Thank you for this! I didn't realize that "standard candle" is an actual term, and I thought it was Wheeler being playful with language, which he quite often does. I have some reading to do on this distance ladder stuff.
Have the standard siren's in gravitational waves confirmed these expansion measurements?
I realized Wheeler was older at the time of publication and given his death in 2008, he obviously couldn't know the measurements that have occurred in the last 15 years. I think by his last two sentences he wasn't outright rejecting it but rather being suspicious of both the measurements and the theory. There is a second edition of the book, published well after Wheeler's death, so I wonder if Taylor kept that section of the book. To Wheeler's credit, the section was in a specific box entitled: "Opinion: The Bang-to-Crunch Universe Too Simple to be Wrong!".
Edit: I checked the second edition (again, Wheeler didn't appear to work on this edition), located here https://www.eftaylor.com/exploringblackholes/, and it does indeed appear that there are now entire chapters dedicated to the expanding universe and cosmology and that the above quoted opinion section is removed.
Possibly a dumb question: can the tension between the two rates simply be resolved because one method measures an old historical rate and one method measures the current rate, and it’s been dropping over time? Or are they both measuring the same time periods?
(I assume it’s not that simple, but it’s very hard for me to understand and reason about data that involves looking back in time and space simultaneously)
Both methods measure H_0, which is the Hubble parameter today. It's a bit confusing that it's sometimes called the Hubble constant, because it's not really a constant. The expansion rate H changes over time, so we write H(t) and by H_0 we mean H(t_today). It's probably the case that they didn't directly measure H_0 with the early universe probes, so they measured H at that time and then used the standard model to extrapolate this value to H_0, roughly speaking. This means, that if the measurements didn't suffer from some unknown systematic error, that the model is wrong. That's what they call "new physics" and could be the most exciting thing in cosmology since the 90s.
Way back when, we used to joke about "Murphy's Variable Constant", the fiddle factor required to make any equation balance nicely. It's sad that the Hubble Constant is now a variable.
H(t) is not an arbitrary function. Up to an overall scaling factor (H_0), it's fully determined by the relative abundance of baryonic (normal) matter, dark matter, dark energy, radiation, and other constituents of the Universe.
It's fully determined, given the densities of the various constituents I listed above.
There are separate constraints on almost all of those densities, from different observations. For example, big bang nucleosynthesis puts constraints on the density of baryonic matter, dark matter and radiation, while the CMB essentially tells us the density of radiation.
Cosmology is based on a web of different observations, tied together by well understood physics. It's very difficult to fudge things to match one observation without messing up the results for other observations.
> Cosmology is based on a web of different observations, tied together by well understood physics.
It turns out that roughly 68% of the universe is dark energy. Dark matter makes up about 27%. The rest - everything on Earth, everything ever observed with all of our instruments, all normal matter - adds up to less than 5% of the universe. [1]
That doesn't quite live up to my idea of "well understood physics".
The particle nature of dark matter is not understood, but it's not necessary to understand that in order to understand how it will interact gravitationally. There are a lot of well understood physical processes that produce clear predictions about what we should observe with X amount of dark matter, Y amount of baryonic matter, etc.
There are lots of well understood physical processes that produce clear predictions of what we should observe if pigs were able to fly. Does that make flying pigs "well established physics"?
Here's cosmology in a nutshell for you:
You take the commonly accepted theory of gravity (precision-tested on solar system scale [1]) and assume that it works unmodified on cosmological scales, impose the "cosmological principle" (actually a maximally simplifying assumption rather than a bona fide principle) and get the FRW model [3].
The instability of FRW's static solution, the observed redshift of distant galaxies and the cosmic microwave background then lead you to the big bang, and applying (actually well-established!) nuclear physics to primordial nucleosynthesis results in good agreement with observed element abundances [4] - apart from lithium, of course [5].
But never mind that, you have bigger fish to fry, like solving the horizon [6] and flatness [7] problems which you inadvertently introduced along with the big bang.
Happily, it occurs to you (following Guth and Starobinsky) that an early period of exponential expansion would help there, and also explain the apparent absence of exotic relics from GUT symmetry breaking. GUTs are of course anything but well-established physics [8], but if high energy physicists can dream, then why can't you? Thus, inflation is born [9]. Some naysayers may claim that you have no idea what supposedly drove it, but you know better: you actually have way too many ideas. There are actually more inflationary models than any sensible person could possibly keep track of, and no way to tell which - if any - of them is correct. That's by design. Known physics can't do the job, so they must be based on hypothetical new physics capable of escaping detection in every physics experiment ever performed to date.
But never mind that, because once again, you have a more pressing problem to solve: even granting that all assumptions you've stacked up so far are correct, your model doesn't fit the data. There's just not nearly enough matter in the universe to reproduce the observed flatness, expansion history and element abundance which you just tied up so brilliantly with inflation. Then again, if you are willing to assume an undetected (and quite possibly undetectable) inflaton, why not some far more mundane, pretty much ordinary matter which just happens to be undetected (and quite possibly undetectable) too? There are even boring astronomical reasons to take the notion seriously. Crank up the density of this unknown dark matter [10] to 85% (!) of all mass in the universe, and your model works - kind of.
See, after you stuffed all that matter into your model, some enterprising astronomers went out and did their best to measure the rate at which it's causing universal expansion to slow down. Surprise: they obtain a far better fit to the data by adding a freak term to your model, Einstein's old cosmological constant [11] and making it so large (about 70% of all energy in the universe!) that it dwarfs your dark matter. Which means that according to the once-again patched model [12], the expansion is not slowing down; it's accelerating.
Oh well, you say, if I can have exponential expansion in the early universe, why not now? A flood of dark energy models follows, again more than any sensible person could possibly keep track of, again based on anything-but well established or even verifiable physics, for the same old reason: known physics can't do the job, so it must be something which eluded every physics experiment ever performed to date.
But that's still not the end of the story. Because as noted in the article linked at the top of this page, even this latest iteration produces inconsistent results when fit to two different measurements of the same quantity. So to the extent that there are "a lot of well understood physical processes that produce clear predictions about what we should observe", they are saying that the model is, in fact, wrong. Again.
We can infer these densities just fine, subject to the assumption that the model is correct. Nobody has ever produced a measurement of dark matter density or dark energy density, for the simple reason that nobody has ever managed to detect a single particle with the expected properties of either one (e.g. a WIMP and an inflaton, respectively).
Dark matter interacts gravitationally, so its density can be measured, and has been in many different environments. Weak lensing is one method of measuring dark matter density, for example.
Dark matter cannot do anything one needs it to do.
There are very few assumptions in the cold dark matter paradigm (you can describe them all with just a few parameters). Meanwhile, there are many different observational probes of dark matter, and they all have to agree with the predictions of the theory.
There are many ways that one could seek to falsify the cold dark matter paradigm. The thing is, so far, the paradigm has passed all the tests people can think of.
> Possibly a dumb question: can the tension between the two rates simply be resolved because one method measures an old historical rate and one method measures the current rate
This is already generally being accounted for (assuming we have the correct cosmological model for the Universe). The CMB measurement is probing the Universe at an early state (when the Universe was ~380,000 years old) and the Hubble "constant", H(t=380,000 yr), was different at that point from what it is now, H_0 = H(t=13.7 billion years). The comparison to the current Hubble constant (e.g., determined from Cepheids) is made by evolving the CMB Hubble "constant" value to today, under the assumption of our best cosmological model model.
Of course, if we have the wrong cosmological model, then that could be a reason for the discrepancy, and that might point to "new physics". Alternately there may be some systematic in the Cepheid technique that is causing our H_0 estimate to be somewhat off.
That idea is mentioned in the article, with the hypothesis that there was more dark energy in the past that has since dissipated. They label that idea as "New Physics" in the chart above that comment.
So does this require new physics to solve? What should the layman take away from this?
>distant galaxies have been speeding up in their recession, and the expansion rate, though still dropping, is not headed toward zero.
If the expansion rate is dropping, surely it is headed towards zero? Or are they using expansion rate to mean acceleration and the zero refers to the recession. Or am I misunderstanding something?
Imagine the expansion rate starts out at 2. Then 1 day later it's 1.5, after 1 more day it's 1.25 and after another day it's 1.125.
Hopefully you can see that if this series continues then the expansion rate is always dropping, but it's headed towards 1, not 0. (And if expansion rate of 1 is too confusing in this context imagine if it starts out at 3 and goes to 2.5, 2.25, 2.125, ..., it still is always decreasing, but it will never be less than 2 which means the universe keeps expanding).
> What's the mechanism that allows the acceleration to drop, without dropping to zero though?
The expansion rate drops because the energy density goes down due to the expansion. However, the dark energy density aka cosmological constant does not go down, therefore providing a nonzero floor.
> Is the dark matter not expanding with everything else
This has nothing to do with dark matter in particular, and it’s space itself that’s expanding, not matter. Also, the expansion has no center, the universe is expanding at every point. Some types of matter expanding and others not would imply a center.
> The expansion rate drops because the energy density goes down due to the expansion.
I thought the idea was that Dark Energy increased with the amount of empty space; so as the space between galaxies expands, the energy driving the expansion also expands - hence the acceleration.
I wrote “density”, i.e. the amount of dark energy remains constant per unit volume. Since the volume increases due to the expansion, the total amount of dark energy increases accordingly, but its density remains the same. This is as opposed to the matter and radiation density, which decreases.
Thank you for clarifying (you said "energy density goes down due to the expansion").
Can you also clarify why galaxies don't expand, but empty space does? I suppose this is something to do with "vacuum energy", but it's not obvious to me that vacuum energy actually requires a vacuum; I thought it was present everywhere, but was only significant in the absence of other "stuff".
I also understand vacuum energy to be related to Hawking Radiation, which is black-body. But black-body radiation is EM radiation; DE is neither black-body nor electromagnetic. Why does vacuum energy not produce observable EM radiation? Is it just too weak to observe?
> you said "energy density goes down due to the expansion"
Yes, the overall energy density (dark energy plus matter/radiation) goes down, but since the dark-energy part of the density remains constant, it provides a floor.
> Can you also clarify why galaxies don't expand, but empty space does?
Gravity. Within a certain range (the size of small galaxy clusters), gravity dominates.
> I suppose this is something to do with "vacuum energy"
Vacuum energy is predicted by quantum mechanics and contributes to (or entirely constitutes) the cosmological constant, and thus is a candidate explanation for dark energy.
Not necessarily. First the distance ladder could have another problem. Second to look at the early universe, for the early universe observations you are looking through the entire universe at the CMB and that requires foreground subtraction, which is very much a non trivial task. And finally from theory, General Relativity is a non-linear theory which means taking the average and then evolving the average does not necessarily yield the same result as evolving the initial state and then taking the average. Either of this could explain the tension, though an actually dynamic cosmological constant would be more fun.
> If the expansion rate is dropping, surely it is headed towards zero?
Expansion rate could be dropping but converging to a non-zero value. That seems unlikely to me, but it's an answer that would fit that description just fine.
The language is a bit imprecise, though, which I expect is the problem. The (to me) obvious technical interpretation of "expansion rate is headed towards zero" is that d size(t)/dt -> 0 as t -> infinity, but the (again, to me) obvious non-technical interpretation is "expansion will completely stop at some point". So "*not* headed towards zero" means "derivative isn't going to zero", or "expansion never quite stops", respectively.
The derivative of ln(t) does go to zero, but it has unbounded growth, so it fails the first test but passes the second. The universe experiencing logarithmic expansion seems reasonable enough.
It's confusing because that quote about "expansion rate decreasing" is in the caption of a picture with a giant "Accelerating Expansion" label at present time.
Agreed; the presentation was, IMHO, terrible. You had to read each image's relatively hard to read annotation to make sense of what they were trying to say. Hell, 95% of the entire article was image annotations, with single sentences between. Really difficult to follow along.
>However, for the past ~6 billion years, distant galaxies have been speeding up in their recession, and the expansion rate, though still dropping, is not headed toward zero.
Am I not getting something here or is this sentence not make sense?
So the first derivative was already understood to remain nonzero forever[1], now we know that the second derivative probably will also remain nonzero, and the third is slowing down but still positive for the moment?
[1] IIRC in the 80s the big bang/big crunch model was preferred
The first image depicting space expansion in that article: what happens if some is to travel beyond that space boundary? Is it because of speed of light that no one can catch up beyond it or is it something else?
The graphic is an attempt to project the 3D observable universe down to 2D and then depict the time evolution of it to show that it has expanded in spatial volume, with the bell shape showing extremely rapid expansion during cosmic inflation, then slowing expansion, then accelerating expansion again as matter density became low enough for dark energy density to take over. But the observable universe is not the entire universe. There is no known boundary to space and there probably is no boundary at all. We'll never have any way of knowing, but space could easily be infinite in extent, while still expanding at every point. If you were on the boundary depicted (the cosmic horizon of the Earth-centered observable universe), or even if you were outside of that completely, the picture from your vantage point should look exactly the same.
As for what the horizon represents, it's all light that could have reached Earth within 13.7 billion years, that is, Earth's past light cone. It isn't necessarily the case that nothing leaving Earth today could ever get past that horizon. Light can travel forever if nothing ever scatters it. Given some very large amount of time, it can beyond the boundary depicted there. Because of the expansion of space, however, that time is likely to be more than 13.7 billion years, and given the acclerating expansion of space, there will eventually come a time that no light leaving any point within our local supercluster can ever reach any other supercluster. They will become forever outside of each other's horizons.
>It isn't necessarily the case that nothing leaving Earth today could ever get past that horizon. Light can travel forever if nothing ever scatters it. Given some very large amount of time, it can beyond the boundary depicted there.
Careful with that. You could indeed aim a beam of light to deep space trying to reach something on the edge of the observable universe, and that beam could indeed some day travel 46.6 billion light years[1] away from the Earth, however the beam could never reach the stars[2] that were right on the edge when you shot out the beam, because those stars[3] would have receded out into the event horizon in the intervening time.
[1] The current radius of the observable universe is greater than the age of the universe due to expansion.
[2] Or whatever happened to be at that same location after countless billions of years.
[3] Actually it's not the stars receding, but the space those stars reside in.
I think the key point is the event horizon, or effective boundary, is relative to the observer. From the earth there’s a point beyond which we can never observe, even if we left today at the speed of light. However for a planet at that point everything looks “the same” to them - except the earth is at their boundary. The boundaries here aren’t absolute - they’re only relative to the observer.
The Hubble tension is "bad" (i.e. shows a problem with) for current models of cosmology, hence strengthening it is making it "worse." Its like a hurricane, a strengthening hurricane is worse.
Where's the positive? If you've got a strengthening tension headache, there's no mixing there. Tension in your head, tension in the room, tension in a Hubble, it's all bad.
1. The universe is expanding
2. The velocity at which the universe is expanding is increasing, since there is non-zero acceleration.
3. The acceleration is actually slowing down, but it is not heading towards zero. It is approaching some steady state acceleration.
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In Exploring Black Holes by Edwin Taylor and John Wheeler, published in 2000, I recently read the following passage by Wheeler:
> An article by John Noble Wilford in the Science Times section of the New York Times for Tuesday March 3, 1998, reports observations by two separate groups of investigators which they interpret as showing that today the expansion of the Universe is speeding up rather than undergoing the slowdown expected for any approach to maximum expansion. Later that day I encountered a hard-bitten veteran gravitation physics colleague in the elevator of the Princeton physics building and asked him if he believed the purported evidence of accelerating expansion. "No," he replied. Neither do I. Why not? Two reasons: (1) Because the speed-up argument relies too trustingly on the supernovas being standard candles, (2) Because such an expansion would, it seems to me, contradict a view of cosmology too simple to be wrong. Such clashes between theory and experiment have often triggered decisive advances in physics. We can hope that some decisive advance is in the offing.
Now, Wheeler was one of the most preeminent physicists of the 20th century and spearheaded several fields and was not afraid of wild ideas. I am curious if anyone knows if he had any inklings that further his thoughts here. Was he just wrong here, before new measurements came out? Or is there something missing in these calculations and the theory that we're missing? I'm also not sure what means in (1).