Deep divefrom Episode 11Cosmology8 November 202618 min

Do the Rungs of the Cosmic Distance Ladder Line Up?

A deep dive into one paper: what was known before, what the researchers did, what the numbers say and what they don't.

The paper: A cosmological intercept tension in local distance ladders (arXiv preprint)

Chapters

Also linked

Two-rung ladder companion: 1.8 per cent measurement of H0 from Cepheids alone (Stiskalek et al.)

Transcript

The script the two AI voices read from. The times are worked out from the script, not heard, so a line can start a few seconds early or late.

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Cold open

Host 1You heard the trailer — this is the whole story. Welcome to the Hastrup Review of Science, where artificial intelligence reads real science, so you don't have to pretend you understood the paper.

Host 2Today is one paper, a preprint posted in October by four physicists, Haotian Dong, Marek Biesiada, Zhoujian Cao and Shao-Jiang Wang, working in Beijing, Warsaw, Hangzhou and Pohang. It checks whether two steps of the ladder astronomers use to measure the universe actually fit together.

Host 1Before anything else, has this paper been checked by other scientists yet, or is it a first draft?

Host 2It is a preprint, so nobody independent has reviewed it for a journal yet. It is also short and openly preliminary in places: the authors call one of their key tests a quick check ahead of a fuller analysis.

Why astronomers build ladders

Host 1Why do astronomers need a ladder at all to measure how far away things are?

Host 2Because no single method works at every distance. Nearby you can use pure geometry, further out you need objects of known brightness, and each method is calibrated by the one below it, like the rungs of a ladder.

Host 1What does the geometry step at the bottom look like in practice?

Host 2The first rung, as the paper describes it, uses parallax, the small shift of a nearby star as the Earth goes around the Sun, and pairs of stars that eclipse each other. Those give distances without assuming anything about how bright the stars really are.

Host 1And the second rung is where those pulsing stars come in, the Cepheids?

Host 2Yes. Cepheids brighten and dim on a regular cycle, and the length of the cycle tells you how bright they truly are, a link found by Henrietta Leavitt in nineteen twelve, which the paper cites. Compare that true brightness with how bright the star looks, and you have its distance.

Host 1How does that get us out to galaxies that are really far away?

Host 2Through the third rung, Type one A supernovae, exploding stars bright enough to see across billions of light years, and very uniform once you correct for the shape and colour of their light. Some galaxies host both Cepheids and such a supernova, and those shared galaxies are the joints between the second and third rungs.

Host 1Where does the expansion of the universe come into all this?

Host 2For the wider picture, since Edwin Hubble's work in the nineteen twenties astronomers have known that more distant galaxies recede faster, and the redshift of their light tells you how fast. The ratio of that speed to the distance is the Hubble constant, today's expansion rate.

Host 1What does the unit of the Hubble constant actually mean in everyday terms?

Host 2It is quoted in kilometres per second per megaparsec, and a megaparsec is about three and a quarter million light years. A value of seventy means a galaxy one megaparsec further away is receding seventy kilometres per second faster.

What was known before

Host 1So what is the famous disagreement that people call the Hubble tension?

Host 2Two kinds of measurement give different expansion rates. The full ladder, in the version led by Adam Riess's team, gives about seventy three, while the Planck satellite's map of the afterglow of the early universe, read through the standard cosmological model, gives sixty seven point three six, give or take about half a unit.

Host 1Is a gap of about six between those numbers a lot, or is it small?

Host 2It is about nine percent, which sounds modest, but both sides claim uncertainties around one percent, so they cannot both be right. Across the field, a decade of checks has not found a single error that closes it, which is why some suspect new physics.

Host 1When people say a result is so many sigma apart, what does that mean in plain words?

Host 2Sigma measures how far apart two results are compared with their uncertainties. Roughly, a two sigma gap turns up by chance about one time in twenty, and physicists by convention want five sigma, odds of a few in a million, before claiming a discovery.

Host 1Has anyone tried measuring the expansion with only the bottom two rungs?

Host 2Yes, and the paper leans on two such studies. Kenworthy and colleagues used thirty five Cepheid host galaxies and their redshifts directly, skipping supernovae, and got seventy three point one, about two point six sigma from Planck.

Host 2A later reanalysis of the same thirty five hosts by Stiskalek and colleagues modelled the Cepheids in more detail and corrected for the motions of nearby galaxies using a map called Manticore Local. They got seventy one point one, plus or minus one point four, still two point eight sigma from Planck.

Host 1Why does the motion of nearby galaxies matter so much for this?

Host 2Because a galaxy's redshift mixes two things: the expansion carrying it away, and its own local motion, which astronomers call peculiar velocity. For a very distant galaxy the local motion is a rounding error, but the paper notes that most of these Cepheid hosts recede at under about three thousand kilometres per second, where it can matter a lot.

Host 1So peculiar here just means the galaxy's own movement, not that anything is strange about it?

Host 2Exactly, it means particular to that galaxy, like a passenger walking down the aisle of a moving train. Typical random galaxy motions are a few hundred kilometres per second, so for a nearby host that can be a ten percent error in distance.

The open question

Host 1What is the intercept that appears in the title of the paper?

Host 2Plot supernova brightness against redshift and you get a line, the Hubble diagram. The intercept is how high or low that line sits, and it bundles together two things you cannot separate from the diagram alone: how bright supernovae truly are, and the expansion rate.

Host 1Why is it impossible to pull those two apart from the diagram?

Host 2Because a universe expanding faster puts the supernovae nearer, so they look brighter, and supernovae that are truly brighter also look brighter. From apparent brightness and redshift alone those are the same shift, so the paper tracks their combination, the intercept, as a diagnostic.

Host 1So what question exactly did these authors set out to answer?

Host 2Whether the second and third rungs, the nearby supernovae in Cepheid galaxies and the distant ones riding the smooth expansion, sit on the same line. If they do, a calibration taken from one group should give the same answer applied to the other, and earlier papers, some by the same group, had reported that it does not.

Host 1Is the smooth expansion you mention just a way of saying the far-away galaxies?

Host 2Roughly, astronomers call it the Hubble flow: galaxies far enough away that the expansion dominates their motion, so redshift is a clean measure of distance.

What the team did

Host 1What data did they actually work with?

Host 2The public Pantheon plus supernova compilation, split in two. One sample is the calibrators, forty two supernovae in Cepheid host galaxies; the other is the Hubble flow supernovae further out, using the standardised brightnesses Pantheon plus already released, without refitting them.

Host 1Wait, so the Cepheid distances themselves are not used in this test at all?

Host 2Right, and that is the unusual part. Instead of calibrating supernovae with Cepheid distances, they assume the Planck expansion rate, work out how bright supernovae must be for that to hold, and then check whether the other sample agrees.

Host 1How does the forward version of the check work, step by step?

Host 2Step one: fit the nearby calibrators with the expansion rate held near Planck's sixty seven point three six and the amount of matter near Planck's value, and read off the supernovae's true brightness. Step two: carry that brightness to the distant sample and let the expansion rate float free. If the two rungs agree, you get sixty seven back.

Host 1And I assume the backward check is the same thing run in reverse?

Host 2Yes: calibrate the brightness on the distant sample under Planck's numbers, then carry it to the nearby sample and see what expansion rate comes out. Running both directions shows the mismatch does not depend on which sample you start from.

Host 1So it is a bit like checking two rulers against each other by copying a mark from one onto the other?

Host 2That is a fair picture. If a mark copied from the first ruler lands in a different place on the second, the rulers disagree, whatever the true length of the table is.

Host 1Where do the motions of the galaxies come into the calculation?

Host 2They ran everything twice, once with the standard redshifts and once with each nearby host's redshift corrected using the Manticore Local velocities published by Stiskalek and colleagues. That table covers thirty five host galaxies, so the corrected analysis uses only the supernovae in those hosts.

Host 1How can a map like Manticore Local know how a galaxy is moving?

Host 2In broad terms, such maps reconstruct where the matter in our cosmic neighbourhood sits, then work out how its gravity pulls each galaxy around. This paper does not build the map, it takes the published velocities as given.

What they found

Host 1What came out of the forward check, then?

Host 2Without the velocity corrections, the distant sample returned seventy four point three, plus or minus about one point two, instead of the sixty seven that went in. With the corrections, it returned seventy one point three seven, with a similar uncertainty.

Host 1Is it a coincidence that seventy four sounds like the ladder's usual answer?

Host 2It is not really a coincidence, it is the same mismatch seen from a new angle: taken at Planck's rate, the nearby supernovae imply a brightness that pushes the far sample towards a high rate. The velocity correction made the calibrated supernovae slightly brighter, which lowered the recovered rate by about three.

Host 1And what did the backward check give?

Host 2It misses in the other direction: sixty point eight three without corrections, rising to sixty three point two five with them, both with uncertainties just under one. Both directions move towards sixty seven, and neither arrives.

Host 1How do those numbers turn into the intercept tension the title talks about?

Host 2They compare the intercept implied at each of the two stages. In the forward check the gap between the rungs fell from six point eight sigma to three point nine once velocities were corrected, and in the backward check from seven point three to four point three.

Host 1So if I have this right, correcting for how nearby galaxies move cuts the disagreement roughly in half, but not to nothing?

Host 2Nearly: the sigma values fall by a bit over forty percent, and the authors call it a partial alleviation. A gap of around four sigma remains in both directions.

Host 1How big is that leftover gap in actual brightness on the sky?

Host 2About zero point one three magnitudes, which the paper translates into roughly a six percent difference in distance. The magnitude scale is logarithmic, and a tenth of a magnitude is a brightness difference of about ten percent.

A word from our sponsor

Host 2This episode is brought to you by Middlestep, the kitchen stepladder whose second and third steps have finally been introduced to each other. Please read the following side effects before climbing.

Host 1Common side effects include a mild peculiar velocity, mostly towards the biscuit tin, and a feeling that the top shelf is six percent further away than yesterday.

Host 2Less common: the ladder may begin measuring the expansion of your kitchen, and get a different answer depending on which end it starts from.

Host 1I had that. I took out three of the steps, and now the rest of them agree within two sigma.

Host 2In rare cases the top step reaches the early universe, which asks to be left alone. Middlestep: climb within your error bars.

A second correction

Host 1Was there anything else that could explain the gap that was left over?

Host 2Yes, a statistical effect called volumetric bias, a form of what astronomers call Malmquist bias, and the authors thank Adam Riess for suggesting they check it. Their first analysis assumed a rough spread of random galaxy motions of two hundred fifty kilometres per second, but did not model this bias.

Host 1What is volumetric bias, in words a non-astronomer could follow?

Host 2Picture all the galaxies showing one particular redshift. Some are really further away and moving towards us, some are nearer and moving away, but a shell further out holds more galaxies because volume grows with the square of the distance, so more of that crowd comes from the far side.

Host 1So a galaxy at a given redshift is, on average, a bit further away than its redshift suggests?

Host 2Yes, and so its supernova looks a bit fainter than expected. That is the same direction as the offset the paper found for the nearby sample.

Host 1How large did they estimate that effect to be for these galaxies?

Host 2They took the leftover spread in galaxy motions found by Stiskalek and colleagues, about one hundred seventy two kilometres per second, and weighted each host's expected bias by the Pantheon plus uncertainties. The result was about zero point zero six magnitudes, roughly half of the zero point one two five offset.

Host 1Does that bias hit some galaxies much harder than others?

Host 2Yes, it grows fast as the redshift gets small, so the very nearest hosts carry most of it. The paper names three galaxies that contribute most, one of them the well-known Pinwheel Galaxy.

Host 1What did they do about those three galaxies?

Host 2A quick leave-out test: they reran both checks without them, using the supernovae in the remaining thirty two hosts. The intercept gap shrank to zero point zero five two magnitudes forward and zero point zero five six backward, close to the estimated bias.

Host 1And how many sigma of disagreement is left after that?

Host 2One point six sigma forward and one point eight backward, which the abstract rounds to about one point seven. By the usual standards, that is no longer a meaningful disagreement.

Why it matters

Host 1So what is the takeaway, is the ladder broken or is it fine?

Host 2Neither, quite. The paper shows that the apparent mismatch between nearby and distant supernovae is very sensitive to how you handle the motions and the selection of the nearest galaxies, and that after two corrections most of it goes away.

Host 1Does that mean the Hubble tension itself has been solved?

Host 2No, and it is important to keep the two apart. This test assumes Planck's rate and asks whether two rungs agree with each other; it says nothing about whether the Cepheids or the geometry beneath them are right, and the earlier two-rung studies still landed above Planck.

Host 1Who should care about this, beyond the people measuring the Hubble constant?

Host 2The authors point to studies that use supernova distances without the Cepheid anchor, for example combined with other cosmological measurements. Elsewhere, some of the same group have argued that nearby supernovae can bias claims about evolving dark energy, so a well-behaved nearby sample matters there too.

Host 1Does any of this change something for an ordinary person?

Host 2Nothing practical, honestly. It is a careful bookkeeping check on how we measure the size and age of the universe, and its lesson is that the nearest galaxies are, oddly, among the hardest to measure well.

Host 1What is the general principle I should take away from it?

Host 2A gap of many sigma can still come from one assumption in the analysis rather than from nature, because sigma only compares two numbers using the errors you chose to include. Here the motions of nearby galaxies, and the way they are selected, were what was missing.

Honest caveats

Host 1What are the main weaknesses I should keep in mind?

Host 2First, the leave-out is a quick check, not a correction. Dropping the three hosts most affected is not the same as modelling the bias for all of them, and the authors say the full statistical treatment is future work.

Host 1Is it a problem that everything depends on a single map of galaxy motions?

Host 2It is a real limit. All the corrections come from Manticore Local, and the paper itself says the uncertainties in those velocities and in matching hosts to supernovae have to be weighed, and calls for other velocity models and other low redshift cuts.

Host 1Doesn't dropping galaxies also widen the error bars, so the sigma would fall anyway?

Host 2Partly, fewer supernovae means more uncertainty, which lowers the sigma on its own. But the gap in magnitudes also shrank, from about zero point one two five to about zero point zero five, so it is not only wider error bars.

Host 1Are the forward and backward checks really two separate confirmations?

Host 2Not independent ones: they use the same supernovae in two orders, so their agreement shows the result does not hinge on the method, not twice the evidence. The paper also says plainly that the intercept is another view of the same mismatch, not a separate measurement.

Host 1Is there anything about the basic setup that limits what it can show?

Host 2It assumes the standard cosmological model with Planck's numbers as input, and it takes the Pantheon plus brightness corrections as released. If those corrections had a problem at the nearby end, this test would not catch it.

Host 1The authors mention new physics at the end, how seriously should I take that?

Host 2As a conditional. They say that only if none of these systematic effects explains the leftover gap might it hint at new physics on the scale where the universe starts to look smooth, and their own numbers so far point towards the systematics.

What to watch next

Host 1What should I look out for next on this?

Host 2The full analysis the authors promise, which models distance and selection for every host instead of dropping three. Then the same test repeated with other velocity maps and other redshift cuts.

Host 1Will new telescope data change this picture any time soon?

Host 2More widely, the James Webb telescope is adding Cepheid and supernova host galaxies, and larger supernova samples are on the way. More calibrators, especially slightly further out, would make the nearby rung less sensitive to galaxy motions.

Host 1So the story so far is that the two rungs mostly line up once the nearest galaxies are treated carefully, and a full analysis has to confirm it?

Host 2Yes, with one addition: the bigger gap between the whole ladder and Planck is a separate question, and this paper does not settle it.

Sign-off

Host 1That's the deep dive for this week. Every weekend this same feed carries the roundup, the week's new papers in one short episode. Thanks for listening to the Hastrup Review of Science.