Freeze
Marta texts at five forty. The peppers go in at six. You text back almost done, which is the lie you have told every weekday for three years and will tell again tonight, because the freeze is Friday and the fitter is still chewing on release twenty-five.
Your job, as the collaboration defines it, is simple. Galaxies do not sit still. They fall toward the lumps, and the lumps pull them, and when you measure a galaxy’s distance from its redshift you are mixing two velocities into one number: the smooth expansion of space, and the small peculiar motion the lumps wrote on top of it. Clustering shows up as an extra smear along the line of sight, an elongation, the thing everyone still calls fingers of God on the small scales and the linear Kaiser plateau on the large ones. You measure the smear. You report it as fσ8: the growth rate f, times the amplitude of the matter power spectrum σ8. Two numbers multiplied together because no redshift-space measurement can cleanly separate them.
Twenty-four points, nine surveys, one compilation. Your survey contributes six of them. You own the reduction. You have re-fit the growth curve by hand twenty-four times because re-fitting takes four hours and teaching anyone else the repository would take six weeks, and the repository has a dependency that breaks if you look at it wrong.
You pull up the residual plot. The data are the black points. The model is the blue line, and the blue line is not the truth, the blue line is the promise: a universe of cold dark matter and a cosmological constant, seeded in the inflationary epoch, grown by gravity for thirteen point eight billion years, its growth index f ≈ Ωm^γ with γ sitting at zero point five five in general relativity and drifting only slightly in most of the alternatives. The blue line is what the recipe says the clumping should be doing at each redshift, once you have accounted for how the survey observed.
The black points are lower. They have been lower every release since release nineteen. Not by much. By less than the error bars, most of them.
You have found a systematic in twenty-three of twenty-three releases. You are good at this. You are the defense attorney of the clustering working group, and the defendant is always the same client.
Release twenty-one was the one that made your reputation, if a person in your position can be said to have a reputation outside the eleven people who read the data papers. A deviation appeared in the low-redshift bins. The clustering was the part that made your stomach hurt, because structure that clusters in coordinate space is usually the survey’s own geometry leaking in. You spent nine days on it. You tried the alternate fiber-assignment completeness maps. You tried masking the bright stars and re-running, then masking a wider radius around the bright stars and re-running again, and then, out of superstition rather than theory, you cut a wedge out of the sky entirely, thirty degrees of good data thrown in the bin, and the deviation went with it.
It was the tiling. The completeness had a sawtooth with the period of the overlap between plates, or anyway with the period of something in the observing plan that nobody had thought to smooth, and the standard mock catalogs had the same sawtooth baked into them because the people who built the mocks had been handed the same observing plan. Every null test that compared your data to the mocks came back clean. Of course they did. The mocks had the disease and the cure in the same file.
You wrote it up in fourteen pages. There is a table in it you are unreasonably proud of, a table of six estimators run on four alternate masks, each entry a number with an uncertainty, and the reader can see the deviation drain out of the sequence from top to bottom. Iron filings leave a magnet. The collaboration thanked you with a footnote, and the working group chair bought you a beer at the next meeting, a Heineken, which you do not drink, and you drank it anyway.
You believed in your job after release twenty-one. The tiredness is the whole reason you keep the fitting code on your own machine instead of in the shared container: the container image takes forty minutes to build and the local build takes ninety seconds.
The covariance block that will not die is named for Anneke, not because she invented it but because she has been defending it for three releases like a woman defending a house she no longer wants to live in.
The problem with twenty-four points from nine surveys is that the points are not independent. Every survey shares sky, shares tracers, shares the large-scale modes that are too big to fit inside the survey volume. A density fluctuation larger than the volume you observed does not average away; it shifts everything at once, a common-mode error, and the covariance term that captures it is called the super-sample covariance. You cannot measure it from the data. You can only estimate it, and every estimation scheme has a knob, and every knob is a trench.
Anneke’s position, stated fairly, is that the super-sample term is being overestimated by the mock-derived piece, because the mocks are finite and the covariance estimated from a finite set of mocks is rank-limited: with N mocks you can invert a covariance matrix only up to something like N/2 dimensions without regularization, and the regularization itself biases the fit. Her position, as it lands in email at ten at night, is that you are letting a numerical artifact set the error bars on the most important number the collaboration produces.
Your position is that the term is real and she is trying to wish it away because it makes her favorite bin look worse. Your position, as it sits in your own head at ten at night, is less certain than that.
You have argued about this at three consecutive collaboration meetings. There were slides. There was a breakout group, six people and a whiteboard, and by the end of the breakout group everyone agreed to defer to a joint task force.
In release twenty-five you ran the fit with the super-sample block deleted entirely, then with Anneke’s rank-corrected version, then with yours. The best-fit number moved by zero point zero zero four. The uncertainty moved by zero point zero zero three. The deviation, the one that has been sitting under the error bars like a sound you can’t place, did not move at all.
You beat the term three ways and the number stayed exactly where it was.
The deviation reappeared in release twenty-five on a Tuesday, which is the day the pipeline dumps the unblinded diagnostic, which is a day you have never told anyone about.
The collaboration blinds. Before each release, an independent person applies a small deliberate offset to the cosmological parameters, hidden from everyone including the pipeline, so that no one can unconsciously steer a result toward a favored answer. It is a good protocol. You have never had time to re-blind yourself, because blinding the pipeline requires a wrapper, and the wrapper requires a build, and the build requires the container, and you have six redshift bins and a Thursday.
So you see the number first, alone, on a Tuesday, in a directory whose name is a timestamp.
You have a playbook. You have run it twenty-three times, and it works, and it works because the universe is generous with ways to be wrong. Null tests: split the sample by color, by magnitude, by the airmass of the night the spectra were taken, by which of the two spectrographs the fiber fed, by whether the target lived near a bright star. Jackknife regions: eleven contiguous chunks of sky, drop one, refit, see if the number lurches. Alternate masks: three of them, including one you built yourself from scratch in a weekend because you did not trust anyone else’s. Mock catalogs: a thousand of them, each a universe that is not ours, run through the same code, and the spread of their answers tells you what your error bar should be.
You ran all of it. It took eleven days. Marta went to her sister’s without you, which was not a fight, which was worse than a fight.
The null tests came back clean. So did the jackknives and the alternate masks. The thousand mocks returned a distribution of fσ8 centered on the model to three decimal places, because the mocks were built from an initial conditions generator, a gravity solver, and a halo bias that all assume the model. The mocks cannot find this failure mode. The mocks are the failure mode.
You knew this before you ran them. You have always known it. The only control sample you have for the universe is a universe you made yourself, and it agrees with you, and its agreement means nothing, and you run it anyway because the collaboration meeting wants a plot with a histogram behind the points, and because forty minutes of a histogram is forty minutes you do not have to spend looking at the points.
The free fit runs on a Wednesday, which is a day you have also never told anyone about.
The default fitter is a template. It asks: given this growth curve, what value of the matter density makes the data happiest, with everything else pinned to the numbers from the microwave background. That is the right question for ninety-five percent of the work. It is a question with a prior, and a prior is a hand on the scale.
You take the hand off. You tell the fitter to choose its own functional form for fσ8 as a function of redshift, no functional prior, a spline with knots loose enough to describe almost anything, and you give it the data and you go to make coffee because the four minutes it takes are four minutes you have learned not to watch.
When you come back the screen has a result and your coffee is on the desk and you have not tasted it.
The spline collapses. It does not wander. It does not reveal a feature at redshift zero point eight or a turn at one point one. Across all six of your bins and every bin the other surveys contribute, from redshift zero point four to one point one, the fitter’s preferred description of the growth of structure is a horizontal line: fσ8 equal to zero point three eight one, plus or minus zero point zero zero nine.
The model does not do that. Extrapolated from the microwave background through thirteen billion years of gravitational bookkeeping, it wants zero point four seven in your lowest bin and slides down to about zero point three five by redshift one point one. The data say zero point three eight one all the way across.
You put the prior back on. The fit snaps to zero point four five, and the residuals tighten, and the blue line is blue again, and the plot is the plot you have shown at every collaboration meeting for six years. You take the prior off. Zero point three eight one. You take it off again. Different optimizer, different seeds, different knots. Zero point three eight zero.
Two runs with the prior off agree with each other better than they agree with the universe the prior describes. You sit there for a while.
There is a chi-square. Of course there is a chi-square. The constant model, one free parameter, gives twenty-six point one for twenty-three degrees of freedom. The full model, the one with the prior, gives twenty-four point nine for twenty degrees. Neither is a disaster. Both are the sort of thing you would publish with a shrug. The constant fits the data as well as the machinery of dark energy and dark matter, and it does so with three fewer parameters.
Marta’s text is on your phone. Peppers are in. Save you some?
You do not answer. That is the first thing you will apologize for, and the apology will take the form of washing the pans, which she hates, because the pans are hers.
There is a folder on your machine that does not go in the shared drive. It is called releases_backup and it contains twenty-four subdirectories and each subdirectory contains the same three files: the fit configuration, the covariance matrix, and a single line of text with the number in it.
You open the earliest. Release zero one. You were a postdoc then, and the file has a comment at the top, in your own handwriting, that says checked against DESI-like mocks, looks good!! Two exclamation points. You have not used exclamation points in a config file since the year you turned thirty.
You open release nineteen, the first one that was low. The number is zero point four zero two, plus or minus zero point zero three one. At the time it was nothing. It was a fluctuation, and you said so, in a paragraph of a data paper that four people read, and you meant it. Release twenty: zero point three nine eight, and you said nothing, because you were busy finding a covariance issue in the fourth bin that turned out to be real and took two months. Release twenty-one: the tiling, and after you fixed it, zero point four zero nine, and you wrote in the release notes that the residual deviation was consistent with the model at one point three sigma, which was true, and was still a hand over the scale.
One per release. An aperture, a mask, a covariance mis-estimated. You wrote them up. The release came out right. Nothing changed.
Some of those systematics were real. Some of them were you, competent and tired, rescuing the model with a haircut and a smile. You will never know the ratio. Nobody else in the collaboration has a copy of releases_backup.
The group meeting is on Thursday, the day the freeze is approved, in the room with the projector that eats the HDMI adapter, which has been missing since March and which everyone keeps blaming on a different person.
Sunmi, who chairs the working group, goes through the agenda. Fiber assignment. Fiber assignment again, under a different heading. Then the release candidate, and she puts your plot on the wall, the one with the black points and the blue line, and she says, in the tone of someone reading a weather report, that the low bins are running a little under the model, as they have for several releases, and that the deviation is within the tolerance and the freeze is approved for Friday.
Noor is sitting two chairs from you. Noor knows the repository. Noor is the only other person who has read the fitting code, and Noor left the collaboration two years ago for a job that pays properly, and still comes to these meetings out of what you hope is loyalty and suspect is boredom.
Noor looks at the plot for a long time. Her eyes go along the low bins, then back, then along them again. She is counting something.
Then the parking. The lot behind the building has been closed for resurfacing since the second week of the month and everyone has been parking on the street and getting tickets, and there are eleven people in the room and for six minutes there are eleven opinions about who is responsible for the sign. You look at your hands. You have found systematics in this collaboration in front of this room. You have stood up and described your own mistakes in enough detail that people took notes. Tonight your mouth does not open.
After the parking, resolved in the usual manner, which is to say it is not resolved, a graduate student at the end of the table raises her hand and asks whether anyone has tried a jackknife split by spectrograph.
You have. It is in the directory. It came back clean. You ran it on the fourth day, at one in the morning, and you remember the run because you were eating cereal out of the saucepan, which is another thing Marta hates, and the answer was clean.
You say nothing. The student looks around the room. Sunmi says that’s a good suggestion and asks whether someone will pick it up next week. Someone will. It will come back clean, in a week.
After the meeting you stand at the coffee machine, which is decorative, and Noor stands next to you, and Noor says, without looking at you: you still re-fit these by hand.
It is not a question. You say you do. Noor says: how many times.
Twenty-five, you say. Twenty-four, then twenty-five.
Noor waits. You can feel the waiting: a door left open behind you in a house at night. Then someone asks Noor about the job, and Noor goes, and the conversation is about salary, and the half hour ends without ceremony.
You stand there longer than you need to. The coffee machine has a light on it that means it is warm.
There is an email from a theorist you have met twice. She has seen the slide, or a slide like it, from a talk someone gave in Pasadena, and she wants to know if the working group has considered the implications for early dark energy, and she is careful to say that she understands the significance is not there yet and she is not asking you to rush; in the third paragraph she mentions the weak lensing people and their S8, the one number in modern cosmology that two honest measurements still cannot agree on, the one that has been sitting at the door of every cosmology talk for a decade like a guest who will not take a hint.
If growth is really that suppressed, she writes, then it is not a matter of raising or lowering one parameter. It is a different engine. Modified gravity. Something in the dark sector that does not stay put. Or early dark energy that diluted at the wrong moment and left the initial conditions subtly off, so that thirteen billion years later the lumps are smaller than the recipe promised. She does not say or your pipeline is wrong, because she is a theorist and it is not her job to say the thing that everyone in the room is thinking.
You do not reply. The email stays unread, which is a lie you can only maintain because you opened it in a different tab.
At two in the morning your cheek is on the desk and the workstation fan is making the sound it makes when it is deciding whether to live, and this is what a flat fσ8 would mean. If it is real, the lumps stopped growing as advertised. Not that the universe is empty. Not that the lumps flew apart. The opposite: the contrast between a void and a filament is lower than the model predicts. Voids no wider, filaments no thinner, everything closer to the average than it should be, because the thing that was supposed to be pulling matter out of the empties and into the walls has been doing its job with less conviction for a while now. Nobody knows why. And the one person watching it happen has twenty-four files in a folder that is not backed up.
You re-fit one more time, because you are you.
This time you run it with the prior back on, and you watch the residual plot as the optimizer walks, and the black points lift, obedient, toward the blue line, and the chi-square improves by one point two, which is nothing.
Zero point four five. The number everyone expects. On the screen it looks healthy.
You put both runs in the same directory. You do not delete either one. You look at the two numbers next to each other, zero point four five and zero point three eight one, and they look like two answers, and they are, and the collaboration will get one of them on Friday, and which one depends on a choice that is not in any config file.
The peppers are cold. You knew they would be cold. You reheat them in the pan with a little water and you serve them over rice and you put the plate in front of Marta and you sit down, and for two minutes you are a person who has brought dinner to the table.
She asks how the meeting was. You say fine. She asks whether the release went. You say it went. She says you have something on your collar and reaches across and takes it off with her fingers, and her hand is warm, and you look at her hand for a second longer than a piece of rice warrants.
She says your name.
You are somewhere else. You know you are somewhere else because she says your name again, slower this time, the tone people use on someone standing in the wrong room in their own house, and you come back, and you say sorry, and she says it’s fine in the tone that has been not fine for eleven days, and you eat the peppers, and they are good, they are always good, and you cannot taste them.
Later. She is asleep. The apartment is down to the refrigerator and the building and nothing else.
You open the laptop on the kitchen table because the kitchen table is where the light is. The two runs are still there. The free fit. The obedient one. You look at them for a while, and then you write an email to Sunmi, and you write it four times.
The first version explains. The second explains more carefully. The third has a table in it, the one with the six estimators and the four masks, the one you are proud of, and you delete the table. The fourth version says that the release candidate has a residual deviation in the low bins that is not currently accounted for, that the null tests do not identify a source, and that I would like one more week before the freeze.
The subject line you send it under is: release 25, small thing.
You send it at one eleven in the morning. Then you open the messaging app and you find Noor, who has not deleted your number, and you type four words. No context. No attachment.
It does not grow.
You set the alarm for eight. You leave the laptop open on the table. In the morning the screen will have timed out, and the number will still be there. Flat. Waiting for whoever looks at it first.