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In 2014, the pale electromagnetic ghosts of an ancient exploded star barely grazed the camera
of the Hubble Space Telescope. Four points of dim light revealing the same supernova, framing the
galaxy whose gravitational field had bent this light to us. After a 9.3 billion year journey,
the images arrived in rapid succession. But other, longer paths wove the spacetime
contortions of the surrounding galaxy cluster. Astronomers spun up their models and predicted
a single explosive encore the following year. They waited, they prepared Hubble,
and 12 months later their it was -- the laggard afterimage of the supernova just as predicted.
Ridiculous that we were even able to predict this. But more incredible is its scientific
value. In a 1964 paper, Sjur Refsdal pointed out that the time-delay between gravitationally lensed
supernova images could give a way to measure the expansion rate of the whole universe.
We've now done that with the eponymous Supernova Refsdal, but we've now also built this up into
what may become the most powerful method for unlocking the nature of dark energy.
black hole hoodies and shirts are still available. Links in the description. Now, onto the episode.
We've known that the universe is expanding since 1929, and that the
expansion is accelerating since 1998. The culprit behind the acceleration is unknown,
so we live with a stand-in term "dark energy". Our modern cosmological model assumes that dark energy
has a constant density--always the same amount of the outward-shoving stuff per volume of space.
But there's recent evidence to the contrary--which may be why our primary efforts to measure
the expansion rate of the universe disagree with each other. Let's review those methods.
On the one hand, studying the oldest light in the universe—the cosmic microwave background,
the CMB—gives us exquisite information about a time soon after the Big Bang.
Combined with our cosmological model we can predict how fast
the universe should be expanding now, and that modern expansion is
characterized as a measure of the Hubble constant. On the other hand,
observations of supernova explosions allow us to track that expansion history in the
relatively modern universe. Exploding white dwarf stars—type 1a supernovae—have very
predictable intrinsic brightnesses, allowing us to determine distances based on how faint
they appear to us. And those distances give us another measure of the Hubble constant,
in a sense more directly measuring that modern expansion rate.
If our measurements are good and our cosmological model is good then the
CMB and supernova results should match. But they don’t. The supernova program finds an
expansion rate a few percent higher than the extrapolation of the CMB measurements. So,
either the CMB or the supernova result is flawed, or the cosmological model we use to extrapolate
between the two is wrong. This so-called hubble tension has been lurking around for some years,
and stubbornly refuses to go away even as we improve our measurements. That
hints that we may really need new physics in our cosmological model. For example,
that model assumes constant dark energy, but what if dark energy really changes over time.
But before we jump to conclusions, it’s absolutely critical that we make independent
measurements of the expansion history. The supernova results are particularly
vulnerable to systematic errors because they need to be bootstrapped off a series
of distance calibration steps. More room for weak links in the calculation chain.
Now, some would say, me included, that one of the most promising
independent methods is something called time-delay cosmography.
This is the method outlined by Sjur Refsdal
and was applied to the eponymous supernova. But it turns out we can also use a different cosmic
cataclysm that’s far brighter and more common that the supernova—the quasar—and
the best time-delay cosmography has been done with quasars. So I will start by talking about quasars,
but supernovae do have a bright future in this field as we’ll see.
So a quasar is what you get when the supermassive black hole in the center of every galaxy enters
a feeding frenzy, as happens from time to time. Active galactic nucleus is more general,
quasars are the bright ones that we care about. So, matter driven into the galactic
core is caught in the colossal gravitational field and spirals in to feed the black hole.
The gas also generates such prodigious heat on its way that these “accretion disks” glow bright
enough to be seen across the universe. Quasars are messy eaters. The infalling material comes
in fits and bursts and the bright central region fluctuates wildly. This causes the
entire beast to flicker on timescales of hours to months. By itself a quasar isn’t great for
measuring distances. But if we introduce a new level of chaos then the magic happens.
In Einstein’s universe, light does not travel to us in straight lines. Mass curves spacetime,
and light is bound to follow those curves. We see the effects of gravitational lensing
everywhere in the universe. Most of the lensing is subtle—manifesting as changing
brightness and warping of shapes. But in rare cases, a “gravitational lens” is so perfectly
situated between us and a distant source that the latter’s light follows multiple paths to reach us.
We literally see the same object through different paths through space,
and that looks like duplications of the source around the lens. This is “strong
lensing” and strongly lensed quasars are going to become our new cosmic expansion tracker.
The core concept is simple enough. The 2 or 4 different paths taken by the quasar’s light are
different lengths, and so the light we see in each of the images has taken a different
amount of time to reach us. So, although we’re looking at the same quasar in each,
we’re looking at the quasar as it was at slightly different times. And this is where the quasar
variability comes in. Its brightness fluctuations are pretty random, but they still form distinct
patterns in the lightcurve—the plot of brightness over time. If we can record the lightcurves of
different images in one lensed quasar, then we can find where the lightcurve patterns match up
and that gives us the time difference of the paths of different images. We call this the
time delay. That in turn gives us a way to measure the actual distances to the lens and the quasar.
This is the first level description. Let’s dig deeper because it’s not as easy as it sounds.
First up—the actual math. It’s based on Fermats principle of least time—light
will always take the path between two points that takes the least time.
This can be used to derive the bending of light by regular lenses,
but it also applies to gravitational lenses. The paths taken in a gravitational lens represent
local minima in the light travel time—paths for which, the photon, if deviated slightly,
would take longer to reach us. The path lengths give us one aspect of the time delay. The other
is the Shapiro or gravitational time delay— just passing through different parts of the galaxy’s
gravitational field leads to an additional time difference. The resulting time delay formula is
surprisingly simple for such a complex system. And the most important thing about this expression
is that the front term scales with the Hubble constant—with the expansion speed of the universe.
That means the time delay goes straight to a Hubble constant measurement. And
none of this depends on a chain of other distance measurements.
Sounds too easy—so why hasn’t this become the standard for measuring
cosmic expansion over the supernovae method?
Well several reasons actually. One is the rarity of good gravitationally lensed quasars.
These objects are rare already due to the precise alignment needed between observer,
lens and quasar. And most lensed quasars aren’t
great for this purpose due to the next issue: modeling the lensing galaxy.
This is by far the biggest challenge. Galaxies make pretty terrible lenses compared
to precision-ground glass lenses.They are lumpy, irregular objects made of stars and dark matter.
In order to properly calculate time delays we need to know the gravitational field of that galaxy.
It’s kind of amazing that lens modeling is even possible at all. One particular trick
is especially important: we can pretend that all of the galaxy’s mass is collapsed into a
flat plane due to the extreme distances compared to the size of the galaxy. This is the thin-lens
approximation, and it turns gravitational lensing into a classic geometric optics problem. So we
build a lens model based on the light of the lensing galaxy’s stars and the positions of
the lensed images themselves. That works pretty well when the lensing galaxy is simple—and that
requirement for an easily modelable lens reduces the number of useful objects dramatically.
But even in the case of a simple lens, there are confounding factors that we can’t completely rule
out. Even if we can see the light from the lens’s stars, we can’t see its dark
matter so have to make some assumptions about how it’s spread through the galaxy.
We also have to try to model the gravitational effects of nearby objects like other galaxies.
One of the trickiest issues is called the mass-sheet degeneracy. We tend to assume
that the lensing galaxy is the only significant source of bending for a given quasar’s light. But
that light is actually traveling billions of light years, and may well pass through other
gravitational fields—other “mass sheets”--on the way. It’s very difficult to rule that out.
These issues are best solved by making a different type of measurement of the lens’s
gravitational field. The stars of a galaxy move in the mutual gravity of each other. And it’s
possible to get a bead on that motion by looking for average Doppler shifts in their starlight.
This lets us build a much less ambiguous map of the galaxy’s gravitational field.
But these sorts of “kinematic” measurements are very difficult to make,
and typically only possible for relatively nearby lensing galaxies.
Okay, so let’s say we have a perfect lens model. How do we get time delays?
Well by monitoring the system for years with a decent-sized professional telescope and building
a lightcurve for each image in the lens. But even building the lightcurve isn’t easy.
The separation between lens images is tiny and they’re often blended together when observed
from the ground. They need to be pried apart with clever algorithms. That plus the faintness
of these objects means every measurement has an uncertainty attached to it. On top of that
we can’t monitor continuously. There are gaps in the lightcurve during the day and a long “season
gap” every year when the Sun gets in the way of our lens. All of this adds to the uncertainty
in the time delay measurement when we try to line up the light curves from different quasar images.
Combine the observing constraints with the lens model uncertainties and we end up with some big
error bars in our measurement of the time delay,
and in the resulting Hubble constant for any one lens.
OK, so where are we with this whole program? In 2019, the Holicow collaboration published
their latest measurement of H0 based on the 6 best lensed quasars,
getting a value of 73.3 plus or minus. And just last year Holicow’s successor
TDCOSMO improved the analysis and added two more lenses to get a slightly smaller 71.8.
These numbers are more consistent with the late universe supernova value than the CMB value,
but the error bars are larger that the supernova uncertainties. Taken on their
own the time delay cosmography results don’t confirm the tension between the
late and early expansion measurements. But when these new results are actually
combined with the supernova results they actually do strengthen that tension,
and suggest a less than one in 10 million chance that
these values are so different due to random noise.
But we’re not quite there in confirming the Hubble tension. There could be some unknown systematic
error that is pushing the supernova result to be higher than the CMB result.
In that case the lensing value on its own isn’t tight enough to confirm the
tension. Now I’ll come back to how that’s soon going to change.
First though, quasars are awesome for this work because they are,
perhaps horrifically, extremely abundant in the universe. But time-delay cosmography
was first conceived for use with supernovae, so how supernovae do?
Well, precise measurement of time delay for the late 5th image of supernova Refsdal gave us a
Hubble constant measurement of around 70, but with pretty large error bars.
There’s also the lensed supernova SN H0pe, which is extra special because it’s the same
sort of type-1a supernova that are used to do our other late universe Hubble constant
measurements. So in a sense, this one gave us two independent measures of the Hubble
constant in one object. In practice these were combined—the lensing side gave us a fairly
direct H0 measure, while the type 1a supernova analysis
allowed us to break some of the degeneracies in the lensing analysis. H0pe yielded a Hubble
constant that's also consistent with other modern-universe expansion measurements,
but again with huge error bars.
For both of these supernovae, the error bars are large, but no larger than we get
for any single quasar. The advantage of the quasars is we have more of them. Statistics
lets us whittle down uncertainty. In general, increasing the number of both lensed quasars
and lensed supernovae is going to be the key to moving forward. And that is about to happen.
In early 2026 the Vera Rubin Observatory will start its LSST survey,
in which it’ll image the entire southern sky every few days for
a full 10 years. Combined with other new facilities like ESO’s Euclid satellite,
we expect to discover thousands new lensed quasars and hundreds of lensed supernovae.
It’s been estimated that the H0 uncertainty will be pushed down to a percent or less,
which, if it happens, will render the hubble tension incontrovertible.
But Rubin may be able to do a lot more. With enough lensed quasars and supernovae,
we may be able to do more than measure the modern expansion rate. We may be
able to trace the evolution of the expansion history over cosmic time.
In the current standard cosmological model—Lambda CDM—dark energy is assumed
to have a constant density. But there’s evidence that this isn’t the case I mentioned earlier.
In 2025 the Dark Energy Spectroscopic Instrument team reported the results of
its expansion history study using baryon acoustic oscillations,
and obviously we covered that. When combined with the CMB and supernova
results DESI reports strong indication that dark energy has weakened over cosmic time.
This was the dark energy news of the decade. If we can measure that change somewhat accurately,
we can actually start to nail down the physics or dark energy—and figure out what the stuff
actually is. Time-delay cosmography with gravitational lensing may be the
key to doing that. In fact, this could be the most important result that will come out of Rubin-LSST,
and many people are working on it. No big deal really. We just clock the flickering echoes
of a thousand ancient cataclysms and discover the culprit behind our accelerating spacetime.