How mapping galaxies can teach us what the CMB can’t

Imagine you want to know about the Universe, and what its properties were like when it was first born. There are two ways to go about it: the “clean” way and the “messy” way. The clean way involves looking back to the earliest possible cosmic times — i.e., the stages where early, primordial signals are most pristine — and look for the relics of the signals as they were back in those early stages. However, not every piece of information is obtainable in this “clean” fashion; sometimes, all we can do is look at the signals that exist at late, modern times in our Universe, which leaves us with the “messy” option: look for the imprints of those early signals in the modern, late-time data that we can acquire today.

When we look for a “clean” signal, it’s harder to do better than the CMB, or cosmic microwave background. It represents a specific event in cosmic history: the transition from the Universe being an ionized plasma — full of electrons, atomic nuclei, and photons — to being full of those same photons, but with neutral atoms instead of ionized, charged particles. This powerful probe of the early Universe has not only shown us our cosmic origins, but has strongly validated the idea of cosmic inflation as a predecessor state to the hot Big Bang.

And yet, there are vital cosmic questions that those clean, pristine, early signals can’t answer on their own. Here’s how mapping galaxies, even though they’re a messy, late-time signal, can teach us what the CMB can’t.

The quantum fluctuations inherent to space, stretched across the Universe during cosmic inflation, gave rise to the density fluctuations imprinted in the cosmic microwave background, which in turn gave rise to the stars, galaxies, and other large-scale structures in the Universe today. This is the best picture we have of how the entire Universe behaves, where inflation precedes and sets up the Big Bang. Unfortunately, we can only access the information contained inside our cosmic horizon, which is all part of the same fraction of one region where inflation ended some 13.8 billion years ago.

We have, through a variety of lines of evidence, assembled a “consensus” picture for what our Universe was like in its earliest stages, and how those early cosmic seeds grew into the structure-rich cosmos we inhabit, observe, and recognize today. That picture is as follows.

• First, a period of cosmic inflation occurred, stretching the Universe flat, imbuing it with the same temperature/density properties everywhere, and seeding it with primordial quantum fluctuations that get stretched to all cosmic scales.
• Second, inflation comes to an end, transforming our Universe from one dominated by inflation (with energy inherent to space, or a field in space, itself) to one dominated by quanta: matter, radiation, antimatter, and more, including dark matter and dark energy: the hot Big Bang.
• Third, this particle-filled Universe expands and cools, going from a hot, dense, almost-perfectly uniform initial state to one that cools and clumps while undergoing a number of phase transitions, leading to the formation of protons and neutrons, then atomic nuclei, and then neutral atoms.
• And finally, the Universe continues to gravitate on large cosmic scales, forming stars, galaxies, galaxy clusters, and the great filamentary cosmic web, with cosmic voids separating the structure-rich regions at late times.

If we want to probe the earliest stages of the cosmos, it only makes sense to look to the earliest signals of all for confirmation.

We can look arbitrarily far back in the Universe if our telescopes allow, and the clustering of galaxies should reveal a specific distance scale – the acoustic scale – that should evolve with time in a particular fashion, just as the acoustic “peaks and valleys” in the cosmic microwave background reveal this scale as well. The evolution of this scale, over time, is an early relic that reveals a low expansion rate of ~67 km/s/Mpc, and is consistent from CMB features to BAO features.

But there’s immediately a tremendous limitation if that’s where we’re looking: we only get one “snapshot” of the Universe from each of those early signals. Looking at neutrino decoupling from the primeval plasma? Those relic signals will only display an imprint from that moment in cosmic history: ~1 second after the start of the hot Big Bang. Looking for the nucleosynthesis of the light elements? Those pristine abundances tell you what the ratios of hydrogen, helium, lithium, and their isotopes were just a few minutes after the start of the hot Big Bang, but before any stars had formed. And the CMB, similarly, tells us what the Universe was like 380,000 years after the Big Bang: when neutral atoms formed and photons decoupled from the (no longer existent) primeval plasma.

The CMB, of course, is an incredibly information-rich cosmic signal, and represents where we get arguably the great majority of our information about the Universe’s earliest stages. The blackbody spectrum of the CMB proves its primordial, cosmic nature, validating the hot Big Bang. The magnitude of the temperature fluctuations, on all scales, show that the Universe never reached arbitrarily high temperatures, and instead show evidence for an almost-perfectly scale-invariant spectrum of seed fluctuations, but with slightly (~3%) larger fluctuations on larger cosmic scales, including super-horizon scales. Further, they validate the adiabatic (and not isocurvature) nature of those initial, seed fluctuations.

The fluctuations in the cosmic microwave background, as measured by COBE (on large scales), WMAP (on intermediate scales), and Planck (on small scales), are all consistent with not only arising from a (slightly tilted, but almost-perfectly) scale-invariant set of quantum fluctuations, but of being so low in magnitude that they could not possibly have arisen from an arbitrarily hot, dense state. The horizontal line represents the initial spectrum of fluctuations (from inflation), while the wiggly one represents how gravity and radiation/matter interactions have shaped the expanding Universe in the early stages.

Taking all of this into account, we can understand why inflation is no longer a speculative add-on to the hot Big Bang, but that instead it’s a well-validated, well-tested hypothesis that agrees with our observations of the Universe. However, there are still realms where inflation makes predictions that have not yet been put to the critical test, and that’s precisely where the scientific spirit of inquiry demands that we look next. In particular, there are three realms that inflation makes strong predictions about, but that have yet to be sufficiently tested.

1. Spatial curvature that slightly departs from perfect flatness. Although inflation stretches the Universe flat, it also creates fluctuations that depart from perfect flatness: at somewhere between the 0.01% and the 0.0001% level. We’ve only been able to probe flatness down to the ~1% level, but future observations could detect these predicted departures.
2. A particular spectrum of primordial gravitational wave fluctuations. It isn’t just temperature/density (scalar) fluctuations that inflation generates, but gravitational wave (tensor) fluctuations as well. Inflation makes a prediction for the spectral shape that these fluctuations should possess, but practically any amplitude is admissible. We’ll have to get lucky to see these: to have a Universe where the gravitational wave amplitude is large enough to be practically detectable.
3. Initial, seed density fluctuations that are perfectly Gaussian in nature. How are these temperature fluctuations distributed? Do they follow the normal, Gaussian distribution on each and every cosmic distance scale? According to inflation, they should.

While the first two may require enormous improvements in our measurement capabilities to yield a positive detection, that third one is within reach, even going beyond what the CMB can teach us.

This illustration of the de Moivre-Laplace theorem shows that by beginning with a binomial distribution with a certain probability of success, going from 4 to 8 to 16 to 32 to 64 to 128 to 256 to 512 samplings, you very swiftly approach a perfectly normal distribution. In detail, the greatest errors are at the far ends of the tails, which require the greatest number of trials to reproduce accurately.

Most of us don’t think about it very often, but the sky is both enormous and frustratingly finite at the same time. There are a total of about 40,000 square degrees to “look at” when we sum up the entire sky in total, which is, again, both enormous but still finite. It’s enormous in a particular sense: if you want to examine the Universe on relatively small cosmic scales — say, the scale of one square degree, or a “box” that’s one degree on a side from our perspective — then there are a great number of independent regions you can probe. As we look to smaller and smaller angular scales, even back at the epoch at which the CMB was emitted, we can get fantastic statistics (i.e., large numbers of samples) of the Universe’s temperature/density on those scales, and determine whether they’re Gaussian in nature or not.

After all, determining whether a set of fluctuations is Gaussian or not is just asking whether or not they follow a Bell curve (or a normal distribution) in their departure from the central, median value. Whenever you have large numbers of statistics, or a large sample set to choose from, it’s easy to determine whether or not your distribution is normal or not, or equivalently, whether the things you’re looking at behave as a Gaussian random variable. When it comes to the density/temperature fluctuations generated during inflation, we expect either perfect or near-perfect Gaussianity; detecting anything other than that would cause us to re-examine our notion that inflation, as we understand it, accurately represents the earliest stages of cosmic history.

This decomposition of the CMB shows the first 12 multipole moments: dipole, quadrupole, octupole, etc., from top-left to bottom-right. There are only a small number of ways to “break the sky up” for these low multipole moments, meaning that we cannot probe those scales with any one “snapshot” very well: even with a source signal as pristine as the CMB: the cosmic microwave background.

However, we run into a fundamental limitation almost immediately when we start asking the question, “are the fluctuations that the Universe was born with, at the start of the hot Big Bang, Gaussian in nature on all cosmic scales?” According to inflation’s predictions, the answer ought to be “yes,” unequivocally. If we look at the CMB — all 40,000 square degrees of it — we find that the temperature fluctuations on small cosmic scales are very, very Gaussian: with thousands, tens of thousands, or even millions of individual data points to aggregate and compare with one another. They show us that not only are the fluctuations Gaussian, they’re as perfectly Gaussian as we can imagine: to the limits of the quality of the measurements we can take and to the amount of data the Universe gives us.

But if we instead look to larger cosmic scales, we find that the Universe appears to be consistent with the idea that these temperature/density fluctuations are Gaussian and random in nature, but it’s only very poorly constrained. On the largest of angular scales, the entire sky might be broken into just a handful of chunks: as few as five on scales of the cosmic quadrupole. The Universe may indeed have Gaussian random fluctuations on all scales: small, medium, and large ones, but through the CMB, we can only genuinely probe the small and medium scales. The largest cosmic scales have the fewest data points to observe, meaning that the CMB is insufficient for determining whether these initial, seed fluctuations do indeed follow the predicted, normal distribution on the grandest scales of all.

The fluctuations in the Cosmic Microwave Background were first measured accurately by COBE in the 1990s, then more accurately by WMAP in the 2000s and Planck (above) in the 2010s. This image encodes a huge amount of information about the early Universe, including its composition, age, and history. The fluctuations are only tens to hundreds of microkelvin in magnitude. On large cosmic scales, the error bars are very large, as only a few data points exist, highlighting a large inherent uncertainty.

This is where galaxy mapping comes in. Sure, the primordial signals from the Universe that show up in the large-scale structure of the cosmos are no longer primordial by the present time; they’ve been subject to all the forces in the Universe that have been exerted over the past 13.8 billion years. Structures undergo gravitational growth, they clump and cluster in the overdense regions, they give up their matter to denser surroundings in the underdense regions, etc. However, on the largest scales of all, gravitation hasn’t yet had time — even at the speed of light — to collapse matter down on these grand cosmic scales. Simply by estimating the overall mass density, which we can do by literally counting galaxies, we can see if a large-scale region is of average density, is underdense, or is overdense, as well as by how much.

Even though galaxy mapping has the disadvantage that we can only perform it at late cosmic times, as galaxies require hundreds of millions to billions of years to emerge at all, it comes along with a huge advantage that shouldn’t be underappreciated. That advantage is this: we can perform galaxy mapping, even on the largest of cosmic scales:

• nearby,
• at distances of around ~1 billion light-years away,
• at distances of around ~3 billion light-years away,
• at distances of around ~6 billion light-years away,
• at distances of around ~10 billion light-years away,
• at distances of around ~15 billion light-years away,

and so on. After all, the most distant galaxies that we know of are more than 30 billion light-years away, at present, and so instead of just getting one “snapshot” of the Universe, today, galaxy mapping allows us to measure the Universe at many different cosmic epochs.

This image shows a slice of the matter distribution in the Universe as simulated by the GiggleZ complement to the WiggleZ survey. As we look farther away, we’re seeing farther back in time: to a less evolved cosmic state. By looking at the Universe at a wide variety of distances, we can get a series of independent probes of our cosmic history, as well as the overall properties of our Universe.

The wonderful thing about this fact is this: the structures that form in the Universe at these different epochs in cosmic history represent independent probes of the seeds of cosmic structure that were planted at the start of the hot Big Bang. Remember, these “seed fluctuations” were planted all at once, temporally speaking, but they evolve as the Universe evolves: gravitationally and in every other way. The structures that are 13.8 billion years old, today, were seeded here 13.8 billion years ago; the structures that are farther away, however, are younger. They were seeded elsewhere some 13.8 billion years ago, evolved for fewer than 13.8 billion years, and then those light signals that are arriving right now had to travel through the Universe during the remainder of cosmic history in order to reach us.

For the largest cosmic scales, then, we aren’t restricted — like we are with the CMB — to only having a handful of useful, usable data point to probe whether these initial fluctuations were Gaussian. Instead, we can prove that same handful of points, but with independent data, for every “shell” of galactic distances that we care to survey. The type of tool we’d need for that is very different from something like JWST or Hubble, as they probe the Universe incredibly deeply, but only over very small regions of the sky.

Instead, we’d need a very wide-field view of the Universe, capable of going relatively deep and faint, but still with the ability to acquire spectra of each galaxy in question. All told, we’d need hundreds of millions of galaxies, mapped out exquisitely, to probe Gaussianity in a way that the CMB, on its own, can’t.

In the aftermath of inflation, signatures are imprinted onto the Universe that are unmistakably inflationary in origin. While the CMB provides an early-time “snapshot” of these features, that’s just one moment in history. By probing the large variety of times/distances accessible to us throughout cosmic time, such as with large-scale structure, we can obtain information that would otherwise be obscure from any single snapshot.

And that, precisely, is why cosmologists are so excited about the upcoming SphereX mission. Scheduled for launch on February 28, 2025, SphereX (the Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer mission) will map out the entire sky in a matter of mere months, collecting spectroscopic data on approximately 1 billion galaxies, ranging from present-day galaxies to galaxies whose light is arriving now after a journey of more than 10 billion years through space. SphereX measures these galaxies in infrared light, which is why going to space and cooling the observatory down to ~45 K is required, but it has another reason for using the infrared: it allows us to measure galaxies at significant redshifts/distances, while simultaneously peering through the dusty, neutral matter that makes so many galaxies so difficult to observe. In other words, we can truly construct a 3D map of the structures in the Universe with this new tool.

The simplest models of inflation — models, by the way, which are consistent with all the data we’ve ever collected so far — assume that inflation is simple, in the sense that it’s governed by a single quantum field. However, multi-field models are possible, and whereas single-field inflation produces perfectly Gaussian fluctuations, multi-field models can admit large amounts of non-Gaussianity. If we want to know which “flavor” of inflation best represents our Universe, it’s this technique of galaxy mapping over the entire sky at a wide variety of distances that will best help us discern between single-field and multi-field inflationary models. The scientific stakes of SphereX are as high as can be: new specifics about the origin of our Universe will be delivered from it.

This image shows the SPHEREx observatory and its nested metallic cones, which passively radiate excess heat back out into space. SphereX will be at a frosty 45 K as far as its operating temperature goes, which is why it must be launched into space to be successful.

Sure, SphereX will also conduct other science as well; you don’t build and launch a spacecraft like this and just throw away the data that doesn’t suit your main scientific purpose. In addition to the spectra of hundreds of millions, and perhaps even over a billion, galaxies, it will also:

• take spectroscopic images of ~100 million stars within the Milky Way,
• take the spectra of more than ~10,000 asteroids within our own Solar System,
• identify water-containing and possible bio-signature molecules in gas clouds within our galaxy,
• provide a complete census of icy, biogenic molecules such as carbon dioxide and methanol,
• and much more,

but the main science goal is to quantify the magnitude of cosmic overdensities and underdensities on a variety of cosmic scales, especially the largest ones. That’s the main science goal of the SphereX mission.

But while the mission itself is very exciting, the principle behind it is even more profound: that if you want to know about the Universe, you shouldn’t limit yourself to just a “snapshot” in time, as the information you’ll acquire will be fundamentally limited. Instead, to augment even the best, most accurate “moments” that we can measure exquisitely, we can also examine how the Universe behaves at all different epochs throughout cosmic time, simply by performing sufficiently accurate, large-scale 3D mapping of the objects out there in space. The most essential questions about the cosmos itself, including how it was born and what properties it began with, are at stake, and it’s vital to get it as right as humanly possible.