Screw the Earth and its smoking habit. The end of 2023 approaches, so let’s talk about the whole universe, which is its own special kind of mess.
As I’ve related before, our current cosmology, LCDM, was established over the course of the 1990s through a steady drip, drip, drip of results in observational cosmology – what Peebles calls the classic cosmological tests. There were many contributory results; I’m not going to attempt to go through them all. Important among them were the age problem, the realization that the mass density was lower than expected, and that there was more structure on large scales+ than predicted. These established LCDM in the mid-1990s as the “concordance model” – the most probable flavor of FLRW universe. Here is the key figure from Ostriker & Steinhardt depicting the then-allowed region of the density parameter and Hubble constant:
The addition of the cosmological constant to the standard model – replacing SCDM with LCDM – was a brain-wrenching ordeal. Lambda had long been anathema, and there was a region in which an open universe was possible, even reasonable (stripes over shade in the figure above). Moreover, this strange new LCDM made the seemingly inconceivable prediction that not only was the universe expanding [itself the older mind-bender brought to us by Hubble (and Slipher and Lemaître)], the expansion rate should be accelerating. This sounded like crazy talk at the time, so it was greeted with great rejoicing when corroborated by observations of Type Ia supernovae.
A further prediction that could distinguish LCDM from then-viable open models was the geometry of the universe. Open models have a negative curvature (Ωk < 0, in which initially parallel light beams diverge) while the geometry in LCDM should be uniquely flat (Ωk = 0, in which initially parallel light beams remain parallel forever). Uniqueness is important, as it makes for a strong prediction, such as the location of the first peak of the acoustic power spectrum of the cosmic microwave background. In LCDM, this location was predicted to be ℓ ≈ 200 with little flexibility. For viable open models, it was more like ℓ ≈ 800 with a great deal of flexibility. The interpretation of the supernova data relied heavily on the assumption of a flat geometry, so I recall breathing a sigh of relief* when ℓ ≈ 200 was clearly observed.
Where are we now? I decided to reconstruct the Ostriker & Steinhardt plot with modern data. Here it is, with the axes swapped for reasons unrelated to this post. Deal with it.
There is lots to be said here. First, note the scale. As the accuracy of data have improved, it has become possible to zoom in. My version of the figure is a wee postage stamp on that of Ostriker & Steinhardt. Nevertheless, the concordance region is in pretty much the same spot. Not exactly, of course; the biggest thing that has changed is that the age constraint is now completely incompatible with an open universe, so I haven’t bothered depicting it. Indeed, for the illustrated Hubble constant, the Hubble time (the age of a completely empty, “coasting” universe) is 13.4 Gyr. This is consistent with the illustrated age (13.80 ± 0.75 Gyr) only for Ωm ≈ 0, which is far off the left edge of the plot.
Second, the CMB best-fit values follow a line of constant ΩmH03. This is a deep trench in χ2 space. The region outside this trench is strongly excluded – it’s kinda the grand canyon of cosmology. Even a little off, and you’re standing on the rim looking a long way down, knowing that a much better fit is only a short step away. Once you’re in the valley of χ2, one must hunt along its bottom to find the true minimum. In the mid-`00s, a decade after Ostriker & Steinhardt, the best fit fell smack in the middle of the concordance region defined by completely independent data. It was this additional concordance that impressed me most, more than the detailed CMB fits themselves. This convinced the vast majority of scientists practicing in the field that it had to be LCDM and could only be LCDM and nothing but LCDM.
Since that time, the best-fit CMB value has wandered down the trench, away from the concordance region. These are the results that changed, not everything else. This temporal variation suggests a systematic in the interpretation of the CMB data rather than in the local distance scale.
I recall being at a conference (the Bright & Dark Universe in Naples in 2017) when the latest Planck results were announced. There was a palpable sense in the audience of having been whacked by a blunt object, like walking into a closed door you thought was open. We’d been doing precision cosmology for a long time and had settled on an answer informed by lots of independent lines of evidence, but they were telling us the One True answer was off over there. Not crazy far, but not consistent with the concordance we had come to expect. Worse, they had these crazy tiny error bars – not only were they getting an answer outside the concordance region, it was in tension with pretty much everything else. Not strong tension, but enough to make us all uncomfortable if not outright object. Indeed, there was a definite vibe that people were afraid to object. Not terrified, but nervous. Worried about being on the wrong side of the community. I get it. I know a lot about that.
People are remarkably talented at refashioning the past. Over the past five years, the Planck best-fit parameters have come to be synonymous with LCDM: all else is moot. Young scientists can be forgiven for not realizing it was ever otherwise, just as they might have been taught that cosmic acceleration was discovered by the supernova experiments totally out of the blue. These are convenient oversimplifications that elide so many pertinent events as to be tantamount to gaslighting. We refashion the past until there was never a serious controversy, then it seems strange that some of us think there still is. Sorry, not so fast, there definitely is: if you use the Planck value of the Hubble constant to estimate distances to local galaxies, you will get it wrong%, along with all distance-dependent quantities.
I’m old enough to remember a time when there was a factor of two uncertainty in the Hubble constant (50 vs. 1000) and the age constraint was the most accurate one in this plot. Thanks to genuine progress, the Hubble constant is now the more precise. Consequently, of all the data one could plot above, this is the choice that matters most to where the concordance region falls. If I adopt our own estimate (H0 = 75.1 ± 2.3 km/s/Mpc), then the concordance band gets wider and slides up a little but is basically the same as above. If instead I adopt the lowest highly accurate value, H0 = 69.8 ± 0.8 km/s/Mpc, the window slides down, but not enough to be consistent with the Planck results. Indeed, it stays to the left of the CMB constraint, becoming inconsistent with the mass density as well as the expansion rate.
Dang it, now I want to make that plot. Processing… OK, here it is:
Yes, as I expected: the allowed range slides down but remains to the left of the green line. It is less inconsistent with the Planck H0, but that isn’t the only thing that matters. It is also inconsistent with the matter density. Indeed, it misses the CMB-allowed trench entirely. There is no allowed FLRW universe here.
These are only two parameters. Though arguably the most important, there are others, all of which matter to CMB fits. These are difficult to visualize simultaneously. We could, for starters, plot the baryon density as a third axis. If we did so, the concordance region would become a 3D object. It would also get squeezed, depending on what we think the baryon density actually is. Even restricting ourselves to the above-plotted constraints, there is some tension between the cluster baryon fraction and large scale structure constraint along the new third axis. I’m sure I could find in the literature more or less consistent values; this way the madness of cherry-picking lies.
There are many other constraints that could be added here. I’ve tried to stay consistent with the spirit of the original plot without making it illegible by overburdening it with lots and lots of data that all say pretty much the same thing. Nor do I wish to engage in cherry-picking. There are so many results out there that I’m sure one could find some combination that slides the allowed box this way or that – but only a little.
Whenever I’ve taught cosmology, I’ve made it a class exercise$ to investigate diagrams like this, with each student choosing an observational constraint to explore and champion. as a result, I’ve seen many variations on the above plots over the years, but since I first taught it in 1999 they’ve always been consistent with pretty much the same concordance region. It often happens that there is no concordance region; there are so many constraints that when you put them all together, nothing is left. We then debate which results to believe, or not, a process that has always been a part of the practice of cosmology.
We have painted ourselves into a corner. The usual interpretation is that we have painted ourselves into the correct corner: we live in this strange LCDM universe. It is also possible that there really is nothing left, the concordance window is closed, and we’ve falsified FLRW cosmology. That is a fate most fear to contemplate, and it seems less likely than mistakes in some discordant results, so we inevitably go down the path of cognitive dissonance, giving more credence to results that are consistent with our favorite set of LCDM parameters and less to those that do not. This is widely done without contemplating the possibility that the weird FLRW parameters we’ve ended up with are weird because they are just an approximation to some deeper theory.
So, as 2023 winds to an end, we [still] know pretty well what the parameters of cosmology are. While the tension between H0 = 67 and 73 km/s/Mpc is real, it seems like small beans compared to the successful isolation of a narrow concordance window. Sure beats arguing between 50 and 100! Even deciding which concordance window is right seems like a small matter compared to the deeper issues raised by LCDM: what is the cold dark matter? Does it really exist, or is it just a mythical entity we’ve invented for the convenient calculation of cosmic quantities? What the heck do we even mean by Lambda? Does the whole picture hang together so well that it must be correct? Or can it be falsified? Has it already been? How do we decide?
I’m sure we’ll be arguing over these questions for a long time to come.
+Structure formation is often depicted as a great success of cosmology, but it was the failure of the previous standard model, SCDM, to predict enough structure on large scales that led to its demise and its replacement by LCDM, which now faces a similar problem. The observer’s experience has consistently been that there is more structure in place earlier and on larger scales than had been anticipated before its observation.
*I believe in giving theories credit where credit is due. Putting on a cosmologist’s hat, the location of the first peak was a great success of LCDM. It was the amplitude of the second peak that came as a great surprise – unless you can take off the cosmology hat and don a MOND hat – then it was predicted. What is surprising from that perspective is the amplitude of the third peak, which makes more sense in LCDM. It seems impossible to some people that I can wear both hats without my head exploding, so they seem to simply assume I don’t think about it from their perspective when in reality it is the other way around.
%As adjudicated by galaxies with distances known from direct measurements provided by Cepheids or the tip of the red giant branch or surface brightness fluctuations or geometric methods, etc., etc., etc.
$This is a great exercise, but only works if CMB results are excluded. There has to be some narrative suspense: will the various disparate lines of evidence indeed line up? Since CMB fits constrain all parameters simultaneously, and brook no dissent, they suck the joy away from everything else in the sky and drain all interest in the debate.
I think you are correct to suggest that the FLRW model has been falsified but it would be wrong to conclude that FLRW is at the root of problems besetting modern cosmology and therefore all that need be done is to find a replacement for FLRW. Underlying FLRW is a metaphysical conceit that has no scientific basis under well known physical constraints. So let us indeed talk about the whole universe.
That the observed Cosmos can be subsumed under the term the whole universe is, I would argue, not justifiable for two fundamental reasons. The speed of light has a finite maximum of 3×10^8 m/s and the current radius of our cosmological observations extends out beyond 10 billion light years.
Combining those two statements leads to the unavoidable conclusion that it is physically impossible to have any knowledge of the “current state” of any of the individual galactic components within our cosmological horizon. It is also clear that our unique cosmological horizon is only a technological horizon, one that does not have any physical implications beyond that and the simple fact that it is unique to our particular cosmological location – it is only our point of view. Other observers in other galaxies would each have their own unique views of the Cosmos. All might be similar but none would be the same.
Consequently, in terms of known physics, the whole universe is not an observable, detectable, measurable or accessible entity in any scientifically meaningful way. Simply put, there ain’t no such animal. Certainly FLRW needs to be replaced but if the alternative retains the whole universe conceit the results will be similarly messy, albeit in a different way.
I might disagree with your specific reasoning on the basis that space and time appear relative, while light (at least the speed of light) is fundamental. So to conjecture about a smooth extension of space and time that exists independent of any light (as we do in the FLRW metric) doesn’t really hold water for me. I just don’t like saying, “beyond where we can receive any information lies x, y, z and t.
I didn’t say anything about space and time, but I think of them as relational concepts like distance or temperature. I think that’s what you mean by saying they appear relative, is that right? They describe the relationship between observable entities and events in my view but are not “things” in themselves.
The substantival vs relative debate is an ancient one in philosophy that has never been resolved by logical arguments. Science however has the sword of empiricism and empirically speaking there is no evidence supporting the substantival interpretation other than the circular argument that it resolves certain issues with the standard model.
I have an alternative to FLRW. It’s called “the time dilated past hypothesis.” If clocks (ie, time itself) consistently gets faster, by looking into the past we should see it slower.
Time dilation. And time dilated light is redshifted light. You just add a little time dilation to each step, and you get the same light cone as a de Sitter universe.
https://raw.githubusercontent.com/mikehelland/hubbles-law/master/img/tdptimes.png
https://raw.githubusercontent.com/mikehelland/hubbles-law/master/img/tdpmath.png
Do you mean that our clocks are running faster than those in the past? Seems like it would have to be that way if we see a redshifted signal from a source in the past. And then what happens with space?
Space is static.
You can interpret the spacetime diagram as light’s change in proper distance over time as dx/dt = c/(1+z) = c – Hd.
We interpret that as the expansion of space.
We could just as validly interpret it as clock rates being dynamic.
If time is dilated, then why not length? In the case of clocks running slower in the past, maybe space contacts in the past as well. Maybe the cosmological horizon could be mapped to a much smaller space, and there would be implications for the relative energy density if both time dilates and lengths contract.
Quote from Seldovich:
“Cosmologists are often wrong, but they are never tormented by doubt.”
Merry Christmas!
I’ve hear that attributed to Landau, but the sentiment is evergreen: I’ve even heard modern cosmologists argue that this phrase should be “retired” because they aren’t in any doubt.
First of all, it never made sense to me that large-mass Black Holes weren’t created along with the first stars. It seems reasonable to expect a range of masses collapsing. The standard model allows for mass variations so why not the direct creation of supermassive Black Holes, bypassing any stellar stage at the Big Bang? Their early appearance could allow the early onset of galaxy formation that JWST seems to be reporting. In other words, at least some, top down galaxy formation.
Next, the LSS shows that gravitationally bound structures are confined to the hyper surfaces of the Voids. And since we know that expansion can’t occur within these structures the expansion of the universe must be confined to the Voids. So, couldn’t we consider the Voids as discrete volumes of deSitter-like metric abutting the stationary metric of gravitationally bound matter structures? There might be unrecognized Physics at these hypothetical metric junctions.
Finally, the FLRW cosmology is based on the old ideas of “island galaxies” imbedded in an expanding Spacetime. The LSS refutes this. It seems to me that any conclusions, including “pressure-less” expansion, based on this theory no longer seem viable.
Having said all this, it still won’t move the concordance window closer to the CMB unless we can show that the expanding metric of Voids actively ejects baryons from within their volumes, In other words “pressurized” expansion. This might appear, across the distances of time, as an enhancement to gravity. It might appear as MONDian physics.
Try this https://www.youtube.com/watch?v=3DLylJZBBLo Start at 4:23 in for the beginning of Dr Becky’s discussion of direct collapse back holes and to avoid the promo. You don’t need SMBH formed in the Big Bang to produce what is observed, just direct collapse of gas clouds with masses ~1000 solar masses or above when galaxies were beginning to form. What I like about her videos is that she gives links to everything on ArXiv so you can easily find the papers she is referencing.