Everpresent Lambda: Why Six Universes Passed, Then Failed
They fit the supernova data slightly better than standard cosmology. A second observation exposed what the first had missed.
Six Everpresent Lambda histories beat standard cosmology on supernovae, then failed a second test built around the Universe's ancient cosmic ruler.
Our paper asks a simple question: can the same simulated Universe pass two independent tests of cosmic expansion?
The model we tested is Everpresent Λ. Standard cosmology treats dark energy as constant. Everpresent Λ allows it to fluctuate over time, so each random seed produces a different possible history of cosmic expansion.
The first test uses Type Ia supernovae. Once calibrated, their brightness tells us how far their light has travelled. We independently searched 90,000 histories and found six that fit these distances slightly better than the standard model.
The second test uses baryon acoustic oscillations, or BAO. They preserve a standard ruler created in the early Universe. Its apparent size gives a different measurement of cosmic expansion.
All six histories predicted a ruler that was 15% to 38% too short. When we added BAO and other expansion data, their small advantage on supernovae became a large overall failure.
This does not rule out every possible version of Everpresent Λ. It shows that these six apparent successes were incomplete: they could reproduce the supernova distances, but not the early-Universe ruler.
Why change dark energy at all?
The expansion of the Universe is accelerating. We call the unknown cause of that acceleration dark energy, but the name does not tell us what it is.
The standard cosmological model uses the simplest possible answer: a fixed quantity called the cosmological constant, written as Λ, or Lambda.
This model describes observations remarkably well. Yet it leaves a famous puzzle. Why does dark energy have the particular strength we observe today, neither overwhelmingly large nor completely negligible?
Everpresent Λ explores a different possibility. Instead of staying fixed, Λ fluctuates as the Universe evolves. It can become positive or negative while remaining tied to the overall cosmic energy density.
The idea comes from causal set theory, an approach in which spacetime is fundamentally discrete rather than perfectly smooth. Tiny statistical fluctuations at that level might appear on cosmic scales as a changing Λ.
This is attractive because dark energy would no longer need to switch on at one suspiciously convenient moment. It is also dangerous, because an everpresent effect must influence the early Universe as well as the recent one.
Ninety thousand possible universes
A stochastic model does not produce one unique history. It produces many possible histories, each determined by a random seed.
A seed is simply a number that lets a computer recreate the same sequence of random events. Seed 52987, for example, always generates the same version of the model's cosmic history.
In 2024, Suddhasattwa Das, Azadeh Nasiri and Yasaman K. Yazdi
against the Pantheon+SH0ES supernova sample.They reported sixteen histories that fit the supernova observations better than the standard model, known as flat ΛCDM.
This did not mean that Everpresent Λ was preferred overall. It meant that rare, unusually successful histories existed inside a much larger population.
Results in the far end of a random population are difficult to reproduce. Small differences in code, calibration, or the definition of success can change which rare cases survive.
Figure 1
Finding a winner means searching the tail
Both analyses searched the same 90,000 random histories. Only a tiny fraction fit the supernova data better than the standard model.
Source paper
16reported winners1 in 5,625 historiesIndependent reproduction
6reproduced winners1 in 15,000 historiesThe counts differ. The rarity does not.
We rebuilt the experiment from scratch
We reconstructed the published model using public data. Before scanning the seeds, we fixed the rule that would decide whether a history counted as a winner.
Our first implementation found six winners. Their properties resembled those described by the original authors, although six is substantially fewer than sixteen.
We then built a second implementation and scanned all 90,000 seeds again. It found exactly the same six histories.
We also repeated the search using both redshift conventions in the public supernova data. Redshift is the stretching of light that astronomers use to track cosmic expansion. The same six seeds survived both.
This independently reproduces the central existence claim: rare Everpresent Λ histories can outperform the standard model on supernovae. It does not reproduce the original success rate, and we do not yet know why.
What the rare winners had in common
The original authors found a clue in a diagnostic called Om(z). It compresses the expansion history into a curve. For the standard model, that curve should stay nearly flat.
Their best supernova fits tended to settle near a steady level after strong fluctuations very close to the present. Poor fits more often formed a broad bump around redshift 0.3.
This pattern cannot identify a winner by itself. It shows what the rare successes were doing: despite a fluctuating Λ, their recent expansion could imitate the smoother standard model.
Figure 2
What the rare winners had in common
A diagnostic built from the expansion rate reveals two different shapes. A nearly flat line is the signature of the standard model.
Better supernova fits
Settled toward a steady pattern
Poorer supernova fits
Often kept a broad bump
Supernovae add up the whole journey
Some exploding stars have a predictable intrinsic brightness. By comparing that known brightness with how faint the star appears, astronomers can estimate how far its light has travelled.
These supernovae act like cosmic lamps. They do not measure the expansion rate at one instant. Their distance contains the accumulated effect of the expansion across the light's entire journey.
That accumulation can hide irregularities. If Λ pushes the expansion up during one period and down during another, the two effects can partly cancel in the final distance.
One of our six histories used this freedom especially well. Its recent fluctuations imitated the accelerated expansion seen by the supernova survey.
BAO keeps an early cosmic ruler
Before atoms formed, ordinary matter and light filled the Universe as a hot plasma. Pressure waves travelled through that plasma until matter and light separated.
The maximum distance travelled by those waves became a preferred scale in the distribution of matter. Cosmologists call it the sound horizon, written as r_d.
Traces of that scale remain in the way galaxies cluster today. Baryon acoustic oscillation measurements, or BAO, use it as a standard ruler.
If we know the ruler's true length, its apparent size tells us about cosmic distances. But Everpresent Λ changes the early expansion history, so it can also change the ruler itself.
This is why supernovae and BAO can judge the same simulated universe differently. One adds up the journey of light; the other compares later distances with a scale inherited from the early Universe.
Figure 3
Why the two tests see different things
Supernovae add up a journey through cosmic time. BAO compares later distances with a ruler inherited from the early Universe.
Add up the full journey
DL(z) = (1 + z)c ∫0zdz′ / H(z′)
Fluctuations in opposite directions can partly cancel in the final distance.
Compare distance with an early ruler
DM(z) / rdand DH(z) / rd
A shorter ruler shifts several related BAO measurements together.
The ruler was too short
In our reference fit, the sound horizon measured 145.5 megaparsecs. A megaparsec is about 3.26 million light-years.
After fitting all the data, the six selected histories produced rulers between 89.8 and 123.5 megaparsecs. They were 15% to 38% shorter than the reference ruler.
The main pressure came from a high matter density, while each stochastic history added its own early fluctuations.
BAO measurements are precise enough that a ruler this short shifts several related observations together. A history can compensate for one mismatch, but it becomes much harder to compensate for all of them at once.
Figure 4
The six rulers compared with the reference
Select a row to inspect one result. Every simulated ruler falls short of the dashed 145.5 Mpc reference.
A small win became a decisive loss
To compare models, cosmologists often use a score called chi-squared, written as χ². A lower score means that the model follows the observations more closely.
We report the difference from the standard model as Δχ². A negative value favors the simulated history. A positive value favors flat ΛCDM.
On supernovae alone, the six histories improved the score by only 0.53 to 3.85 points. These were interesting but modest gains.
After adding BAO and cosmic expansion-rate measurements, every gain disappeared. The six penalties ranged from +128 to +1,974.
The two panels below use different scales because the supernova gains are tiny beside the joint penalties.
Figure 5
A small win became a decisive loss
Each row is the same simulated universe tested first with supernovae, then with all three datasets. The panels use different scales.
Could an imperfect ruler calculation change the answer?
Our sound-horizon calculation uses a calibrated approximation. We did not build a complete simulation of atom formation and the growth of small density variations in a Universe with fluctuating Λ.
We therefore gave each of the six histories a deliberately generous margin of error. We allowed its ruler to move within that margin, then refitted the other parameters in whichever direction helped it most.
Even then, the smallest penalty remained close to +83. Before running this test, we had chosen +30 as the level below which the result would no longer look secure.
The disagreement is therefore not balanced on one precise ruler calibration. But this exercise is a stress test, not a proof that every missing physical effect must be small.
What did we actually show?
We showed that the same six histories emerge from two independent implementations and from two supernova redshift conventions.
We also showed that those six histories fail our combined background test by a large margin, even after we give the sound horizon substantial room to move.
We did not test every possible history of Everpresent Λ. We started with the six histories selected for doing unusually well on supernovae.
We did not calculate the full physics of atom formation and evolving density variations for a fluctuating Λ. That is the most important remaining physics question.
We also did not resolve why the original study found sixteen winners while we found six, or why its quoted reference χ² could not be recovered from the public versions of the statistical analysis that we tested.
The conclusion is strong but conditional: these six reproduced supernova winners cannot also describe the stated BAO measurements. It would be wrong to shorten that sentence to “Everpresent Λ is disproved.”
Where AI helped, and where it did not
Claude and Codex assisted with literature work, code, a second implementation, critical review, and drafting.
The evidence did not come from model confidence. We fixed the selection rules before the decisive runs, required two code paths to agree, checksummed the important files, and tested the public release from a clean directory.
This process caught a real error. Our first stress test examined only the two ends of an allowed interval instead of searching continuously inside it.
We corrected the code, weakened the claim, and preserved the correction history. That is exactly why independent checks matter when AI makes it easy to produce plausible-looking work quickly.
The human author remains responsible for the method and conclusions. The preprint is public, but it has not yet been peer reviewed.
The larger lesson
The feature that makes Everpresent Λ appealing also makes it vulnerable. If dark energy tracks the cosmic environment, it cannot influence only the recent period where acceleration needs an explanation.
Its earlier behavior changes the ruler that later observations use. Supernovae can average over that behavior; BAO remembers it.
There is a broader lesson about stochastic science. Reproducing one impressive example is not enough. We must reproduce the population from which that example was selected, including the failures around it.
AI can accelerate this work. It also makes preregistration, independent code, public artifacts, and visible corrections more important, not less.
Read the paper and reproduce the result
The
include the paper, source package, checksums, and reproducibility archive.The
contains both implementations, machine-readable results, and focused verification commands.The source papers are
and .The paper contains the exact claim, caveats, and numerical method. This article is the map for readers who want to understand why the experiment was worth doing and what its outcome means.
