By: Skylar Grayson, Cole Meldorf, Brandon Pries, Bill Smith

Contents

I. What is ΛCDM and what is Cosmology?

Since about 1998, ΛCDM has been our best model of cosmology. Cosmology is a subfield of astrophysics that is specifically concerned about the universe at the largest scales. Cosmologists ask questions like: “How old is the Universe?”, “How big is the Universe?”, and “How do I explain to my parents what I do for a living?”. ΛCDM is cosmologists’ best answer to (some of) those questions.

ΛCDM has a lot to say about our universe but let’s start with the most basic: what does it even stand for? (Astrophysicists have a problem with not explaining their acronyms, so allow us to right this wrong.) Λ is the capital greek letter lambda, (Λ) which stands for dark energy. Dark energy is a mysterious source of energy that is driving the acceleration of the expansion of the universe – we’ll talk more in depth about what this means a bit later. For now, know that dark energy is the name we give to the thing that is pushing our universe to spread out faster and faster. CDM stands for cold dark matter. Dark matter, confusingly, has absolutely nothing to do with dark energy. Dark matter is the name we give to the poorly understood matter in our universe that does not interact with the electromagnetic field. This means it does not emit, absorb, reflect, or scatter light at all. We can only tell that it exists through its gravitational interaction with the surrounding universe. Think of how you can’t see the wind, but you know it’s there as it’s moving the leaves on those trees. Since dark matter can’t block light, there is nothing really “dark” about it other than our lack of understanding about it. Some have correctly pointed out that this means it should probably be called “transparent matter” or “invisible matter”, but that isn’t nearly as cool. Speaking of cool, why do we say this is cold dark matter? Recall that at the particle level, temperature is really a description of the kinetic energy or speed of individual atoms. Therefore, in this context, “cold” means that we think the dark matter particles (if they even are particles – more on that later) have very little energy, and are moving slowly compared to the speed of light. Of course, in the ΛCDM model there is more to the universe than just dark energy and dark matter. There’s also radiation (aka light), and of course all the normal matter we’re used to interacting with every day. From now on, we’ll be calling  all that normal stuff if we ever say “baryonic matter”.

Great, so that’s the name out of the way. What questions about the universe does ΛCDM answer about the universe? Let’s take a look at the story and components of the universe, and its potential future, according to ΛCDM.

II. The Dark Universe

One of the first things that comes up when you start to talk about dark matter or dark energy is: how do we know any of this stuff is real? So let’s unpack some of the key pieces of evidence for the dark components of the universe, starting with dark matter.

A. Dark Matter

As mentioned above, by definition dark matter does not interact with electromagnetic radiation. Which is a problem, given an astronomer’s number one tool is light! This means that all our evidence for dark matter is indirect, coming from how it gravitationally influences the stuff we can see. The first key piece of evidence comes from the rotation curves of spiral galaxies. As defined by Newtonian mechanics and Kepler’s laws, the speed of a star orbiting at some radius r around the center of its galaxy should be

v(r) = [G M(r) / r]^1/2

where M(r) gives the total mass within a sphere of radius r. However, when we actually look at the speed of the stars, this is not what we observe. As shown in Figure 1, the velocities at large radii are much larger than what we predict given the baryonic mass we observe in galaxies (i.e., all the mass in stars, gas, and dust). This seems to imply that something else contributes a significant amount of mass to galaxies that we aren’t seeing.

Another piece of evidence for dark matter comes from looking at galaxy clusters. One of the most famous is the Bullet Cluster, which is actually two clusters of galaxies in the process of colliding. The gas in these clusters interacts with itself, causing it to accumulate near the central region, as shown by the pink area in Figure 2. However, when we use gravitational lensing to map out the total mass distribution, we find that most of the mass is much more widely distributed than the gas, as shown by the blue coloring in Figure 2. This again points to there being a lot of matter in these environments that we can’t see.

One final piece of the puzzle is more theoretical in nature. In order for stuff like galaxies to form, matter needs to fall into a gravitational well; that is, one part of the universe needs to be denser than the others. However, thanks to the cosmic microwave background (CMB), we have a pretty good picture of the size of denser spots of the universe just after it was born. If you run the clock forward on these overdense spots based on our understanding of physics, the universe is simply not old enough for galaxies to have formed as much as they have. That’s where dark matter comes in. Since dark matter does not interact electromagnetically, it can collapse under gravity much easier. If one accounts for the fact that dark matter would collapse first, and then normal matter would follow, then it makes sense to see as much structure having formed as we do (more on this later).

So observations of galactic rotation curves and lensed galaxy clusters provide strong evidence for the existence of dark matter, models of galaxy formation provide a theoretical backing, but pinpointing exactly what it is is much more difficult. Our observations and large-scale models can tell us about the total mass distribution, but beyond that, there is a lot we don’t know.

Understanding properties like the origin of dark matter, the mass of a dark matter particle, how it interacts with itself or normal matter, and how quickly it moves (i.e. is it “cold” or “warm/hot”) is incredibly difficult. There are currently a lot of ideas put forth by particle physicists and cosmologists, so here we’ll summarize just a couple of the main ones.

Weakly Interacting Massive Particle (WIMP)

WIMPs are a fairly wide-ranging model, but at its base, they are exactly as their name describes. They are massive particles (thus falling under the cold dark matter model) that interact only via gravity or some other similarly weak force. (Side note: gravity is actually an extremely weak force! It’s even weaker than the nuclear weak force, despite the name of the latter, but the weak nuclear force has basically no effect on scales larger than atoms or molecules, which is why we observe that the primary effect of dark matter is gravity.)

Self-Interacting/Asymmetric Dark Matter 

In yet another self-explanatory name, these models consider a version of dark matter that can interact with itself. This could mean the particles could scatter (bounce off each other) or, in more extreme cases, even form bound states analogous to the nuclei of atoms. A self-interacting model can explain some observations better than non- or weakly-interacting ones. Another possible way for particles to self-interact is annihilation, which is a process where a particle and an antiparticle (like an electron and a positron) collide and convert all of their mass into energy (think E = mc²). Some of this energy is then recycled to create new particles. Some models suggest that WIMPs may have this property, and researchers have developed experiments to search for the products of these interactions.

Axions

Axions are another candidate particle for dark matter. Unlike WIMPs, axions are incredibly light, but they would still be classified as cold dark matter. Axions were actually initially developed to explain a problem in the Standard Model of particle physics, but as they were long lived and weakly interacting, they became a good candidate for dark matter as well.

MAssive Compact Halo Objects (MACHOs)

MACHOs are somewhat unique amongst dark matter candidates in that they are largely made of baryonic matter. These are macroscopic objects (unlike a particle candidate such as a WIMP) that emit very little radiation and thus are hard to detect. These include objects like black holes, neutron stars, and brown dwarfs – all objects we know exist in the universe, yet often require indirect methods for detection. However, with our current understanding of how these objects form, it is hard to imagine enough of them exist to account for all the dark matter in the universe. An alternative idea is that of primordial black holes, which would form in the early universe and could be much smaller than the black holes we have discovered to date. While there could be many such black holes in the universe, there is still debate as to whether primordial black holes alone could account for all dark matter.

So we don’t know exactly what dark matter is, but there are several experiments currently underway to try and detect it. The design of these experiments vary based on what model of dark matter they are hunting for; for example, the Axion Dark Matter Experiment tries to convert axions into light in a microwave cavity, while WIMP detection experiments range from seeing if dark matter causes crystals to vibrate to looking for recoil when dark matter interacts with noble gases. So far there have been no confirmations of a direct detection of dark matter.

There are also searches for indirect evidence for dark matter. These searches assume that there is some process that allows dark matter to produce traditional Standard Model particles. The two most common are:

• decay, which assumes that dark matter particles are unstable and decay into stable particles, much like how radioactive nuclei are unstable and decay into stable nuclei; and
• annihilation, where dark matter particles collide with each other and explode, converting all their mass into energy. This energy is then used to create one or more Standard Model particles.

Detectors then search for the Standard Model particles that could be produced from these processes. For example, the IceCube neutrino observatory and the HAWC gamma-ray observatory have both searched for signals of dark matter annihilation and decay (e.g., here).

B. Dark Energy

To understand dark energy, we have to talk about the expansion of the universe. When we observe galaxies in our night sky, there are two key pieces of information we can learn about them: their velocity and their distance. The velocity component comes from the redshifting of light. We typically think about redshifting in terms of the Doppler effect. Think about standing on the sidewalk as a really fast sports car goes by. As the car is coming towards you, it makes a high pitched sound, and then as it moves away, the pitch drops (“vreeeoooowww”). What’s happening is as the car moves towards you, it’s compressing the sound waves in front of it, making them higher-pitched. When the car moves away, the sound waves are being stretched out behind it, thus making them lower pitched. As it turns out, light waves do this too! If something is emitting light and moving towards you, the light will be compressed into shorter wavelengths (often called blueshifting, because blue light has short wavelengths). If it’s moving away, the light will be stretched to longer wavelengths (similarly called redshifting, as red is on the long-wavelength range of the visible spectrum). How much the wavelength changes (Δλ) depends on how fast something is moving relative to the speed of light: Δλ/λ = v/c.

Very pedantic but worthwhile tangent incoming… In an expanding universe, light also gets stretched as galaxies move away from us, but for a slightly different reason. Galaxies can have a proper motion that causes them to have velocities relative to each other, but because the universe is expanding, galaxies are also getting carried away from each other. These may not sound so different, but there’s a key distinction to make here. Imagine two ants on a piece of elastic. The ants can walk around on the elastic and change positions relative to each other (this is proper motion). But like the expansion of the universe, we can stretch out the elastic. Even if the ants aren’t walking around, the stretching of the elastic will move them apart from each other so it will seem like they have some relative velocity. This carrying apart of galaxies will still lead to a redshifting of light, following the same mathematical rule as above. However, it’s worth remembering that there’s a different mechanism behind this so-called cosmological redshift. One of the fun things about cosmological redshifting is it can lead to galaxies appearing to move faster than the speed of light without breaking any rules of relativity.

So we can figure out the velocity of galaxies by looking at how their light gets stretched, but we also need to know something else: their distance. One of the best ways we have to determine the distance to galaxies is with what’s called a standard candle. This is an object that always has the same intrinsic brightness. Because brightness decreases with distance, if we know how bright an object is supposed to be, and compare it to how bright it actually looks in our sky, we can figure out how far away it is. There are several standard candles out there, like Cepheid variable stars, RR Lyrae variables, and stars at the tip of the red giant branch. Some of the best standard candles out there are Type Ia supernovae. These occur when a white dwarf becomes unstable and can no longer gravitationally support itself. Because this instability will always happen at the same mass limit, these supernovae should have the same intrinsic brightness. Thus, when we spot Type Ia supernovae in distant galaxies, we have a way to measure how far away they are!

With these tools, we can now determine the distance to and velocity of galaxies across the universe. With this data, we were able to see that the universe is expanding: the further away a galaxy is, the faster it is moving away from us, in a way that’s consistent no matter which direction in the sky we look. But as our observational techniques improved and we studied those recessional velocities more closely, we noticed that not only is the universe expanding, but that the expansion is happening at a faster and faster rate. Galaxies are moving apart from each other faster than ever in today’s universe. And that’s a problem. We would expect that over time the expansion propelled by the Big Bang would slow down, and gravity would draw galaxies together. The fact that it’s not suggests that we’re missing something. This isn’t a perfect analogy, but to illustrate how confounding this was to the scientists who first observed it, imagine throwing a ball straight up into the air as hard as you can. If you’ve studied basic physics or have any experience throwing balls, you’d expect the ball to slow down as it went up, hit some peak height, and then pick up speed again as it falls back down to the ground. If you were inhumanly strong, you might be able to throw it hard enough that it keeps going instead of coming back down (if you can throw it faster than what is called the escape velocity – on Earth about twenty five thousand miles per hour), but it would still slow down as it moved away. Now imagine you threw the ball into the air, but it sped up as it got further away from the ground. This would be so unexpected that you would need to add an entirely new thing to your model of physics to explain that.

On the scale of the universe, that missing thing is (you guessed it!) dark energy. It’s the name we give to whatever it is that’s responsible for accelerating the expansion of the universe. Currently, the best model for dark energy is as a cosmological constant. The idea of a cosmological constant was actually introduced by Einstein as he was developing his laws of general relativity to prevent the collapse of the universe in on itself. Later, when it was discovered that the universe was actually expanding, that constant was removed. But then when it was discovered that the expansion was accelerating, the constant was added back in! (Fun fact: Einstein actually called the inclusion of a cosmological constant in his equations his “biggest blunder” because, by the time he died, the accepted model of the universe was one that was expanding at a constant rate and thus didn’t need a cosmological constant. It’s gotta be some nice vindication for him that the constant is back!) The constant in Einstein’s equation is denoted by the Greek capital lambda, which is why we call it lambda CDM. The cosmological constant treatment suggests that dark energy is a sort of intrinsic property of space: where there is space, there is dark energy, and there is a constant density of dark energy even with the expansion of the universe. Figure 3 shows how weird this statement actually is! Density is dependent on volume, so one would expect that as the universe expands, density should drop. This is what we see for radiation and matter, but not for dark energy.

But what exactly is dark energy? We don’t know! To match our observations of the expanding universe, we know dark energy must be very homogenous (thus the constant density per unit volume) and also have a very low density, only around 6×10^-10 Joules per cubic meter. Some have proposed that dark energy is the vacuum energy of spacetime, caused by quantum fluctuations, but the calculated values you get for that energy is 120 orders of magnitude off from what we actually observe! So the true nature of dark energy, like that of dark matter, is currently a mystery.

III. The Cosmological Context

A. The Fundamental Parameters of  ΛCDM

ΛCDM is more than just a fun idea, it’s a mathematical model! This means it’s based on a few fundamental numbers. The values of these numbers give us a ton of information about our universe, its past, and its future. Let’s go through a few of them!

1. The Hubble Constant

The Hubble constant, usually written as H₀, is the current expansion rate of our universe. Specifically, it is a measure of the ratio of how fast something is moving away from us to how far away it is. It is given in the very weird units kilometers per second per megaparsec. This means that if H₀ was 70 km/s/Mpc, a galaxy 100 megaparsecs away is moving away at 7000 km/s on average. A slightly confusing clarification to be made is that the Hubble constant is not actually a constant – it has changed throughout the history of the universe. So, when people speak of the Hubble constant, they are speaking about its value right now; if they are trying to talk about it throughout the history of the universe they will usually call it the Hubble parameter instead. Famously (if you’re a cosmologist), the correct value of this parameter is currently very controversial, more on that later!

2. The Curvature Parameter

When Alexander Friedmann solved Einstein’s equations of general relativity for the case of a homogeneous universe, he found something interesting. The universe was allowed to be in one of 3 shapes. The first is what we call a “flat” universe. Here, “flat” means flat in three dimensions (string theorists DNI) , not like a plane. A flat universe is one that matches up with normal Euclidean geometry: parallel lines stay parallel forever, the angles of triangles add up to 180 degrees, etc.

However, this is not the only option! The universe could also be curved. This is extremely hard to visualize because we’re trying to imagine a three dimensional universe curving. It is much easier to picture their effects on geometry in the universe. In a closed universe (i.e., a universe with positive curvature), parallel lines actually eventually converge! If you shot two lasers straight forward next to each other, they would eventually collide. Also, if you draw a big enough triangle,  you would notice that its angles sum to more than 180 degrees. Perhaps most importantly, a closed universe would not be infinite, if you went far enough you’d loop back on yourself, like walking around on a sphere.

Finally, the universe is allowed to be open, meaning it would have negative curvature. In this type of curvature, parallel lines diverge and triangles have angles that add up to less than 180 degrees. A good example of an object with 2D negative curvature is a saddle or a Pringle chip. In a universe with negative curvature, parallel lines would eventually diverge. Figure 4 provides a visual for these different curvatures.

We have pretty decent reason to believe we live in a spatially flat universe, thanks to observations of Type Ia supernovae, baryon acoustic oscillations (BAO), and the CMB. However, the possibility of a closed universe has not been entirely ruled out. Even if the universe turns out to be purely flat, the fact that our data shows slight disagreement over this question is an interesting thread for cosmologists to tug at. 

3. Density Parameters

How much stuff is in the universe? This is another one of the fundamental parameters of the universe, and it measures the amount of energy divided by the volume of the universe. We use energy rather than “number of atoms” or “mass” or anything like that because all forms of mass and particles can be expressed as energy (think E = mc² again), so this will include every possible thing in the universe. The more stuff is in the universe, the more gravity can tug the universe together. Therefore, the overall density of the universe can tell us a lot about the shape of the universe. As it turns out, there is a special value for the density of the universe – called the critical density – where the universe is perfectly spatially flat. This value is currently measured to be 9.47×10^-27 kg/m³, which is 10²⁹ times less dense than water, or about 4 hydrogen atoms per cubic meter. Since there is this special value, it makes sense to write all of our densities as ratios of this critical density, so if our universe is at exactly the critical density this ratio would be 1. The grand total density parameter (the density of everything in the universe) is usually written using the greek letter omega: Ω₀. This value seems to be very close to 1, meaning we are very close to that ridiculously tiny critical density; our universe is mostly empty space.

If you like, you can split the total density up into its parts. For example, the energy density in the form of matter is written Ω_m, while the amount of energy in radiation is written as Ω_r. You can also go even further and split Ω_m into baryonic matter (the “normal matter” like rocks, dirt, gas, stars, neutron stars, and black holes) and dark matter, written as Ω_b and  Ω_dm, respectively. However, there are even more ingredients to Ω₀, things that are just purely energy. The most famous of these is dark energy: its overall contribution to the energy is written as Ω_Λ. Finally, the weirdest to try to understand is Ω_k, the energy stored in the curvature of the universe. What does that mean? Imagine one of those bendy plastic rulers you had in elementary school. If you bend it, and then let go, it can launch across the room: energy was stored in the curvature of the ruler. The universe is similar: if there is any curvature, that changes the overall energy. However, it seems that the universe is pretty much flat, and Ω_k is pretty much zero. However, if it is not zero, even a little, that has some pretty serious implications for cosmology. We’ll explore this a bit more in Section IV.

B. The History and Future of the Universe (We Think)

1 . The Big Bang and Inflation

“Our whole universe was in a hot, dense state then nearly fourteen billion years ago, expansion started.” So begins that holiest of mantras: the Big Bang Theory theme song. And they’re right!  According to this model of cosmology, the universe began as being infinitesimally small and extremely hot, and exploded outward into existence in what is known as the Big Bang. (From here on, I’ll drop the “according to  ΛCDM”.) Immediately after this, the universe underwent a period of extreme expansion known as inflation. There’s a lot still to be understood about inflation (including what came before it and why it happened), but it’s an idea that was developed to explain some key observables. Diving in deep to these issues would probably be better for an inflation-themed guide bite, but very briefly, it seems impossible that the universe is as uniform and flat as it is without some sort of mechanism to make it so uniform and flat. Inflation answers these issues. If you’re interested, read up on the horizon problem and the flatness problem. 

Inflation essentially states that in the span of 10^-35 seconds (yes you read that right, that is ten to the negative thirty-five seconds), the universe grew by a factor of 10²⁶ (and yes you also read that right, that is ten to the twenty-six!). This rapid growth helps explain why the universe is flat and sets the initial conditions for matter distribution, which – as you will soon see – is very important for our existence. After inflation, the observable universe, which is today 96 billion light years across, was only about a meter wide.  And hot. Very, very hot. Almost as hot as your average Astrobites author.

2. Big Bang Nucleosynthesis 

When the universe was hot enough, particles couldn’t stay particles. As soon as a few quarks coupled up to form a proton or neutron, a high energy photon would zip by and shatter them apart into quarks again. The entire universe was a soup of the most fundamental particles that we know of, called a quark-gluon plasma. (Abandon all hope ye who click that link.) As the universe expanded, things began to cool off, and eventually, the average energy was low enough to not immediately destroy protons and neutrons, and the first nucleons (meaning protons or neutrons, I just didn’t want to say protons and neutrons twice in the same sentence, oh wait shoot) were formed! Other light particles like photons, electrons, and neutrinos were also hanging around, as they are fundamental and hence can’t be broken up like the nucleons can. Neutrinos and neutrons can interact via the weak force, the same force responsible for beta decay in unstable isotopes. While this interaction was occurring, this allowed for protons to become neutrons by absorbing a neutrino and releasing a positron, and other interesting reactions. However, as the universe continued to expand and cool, these interactions happened less and less frequently, until eventually the rate of the expansion outpaced the rate of these weak interactions. This meant that from this point on, the total number of neutrons and neutrinos in the universe is now permanently fixed. This moment is called the weak interaction freeze-out, because after this moment the numbers of neutrons and neutrinos were “frozen” in place. If you’re keeping up so far, strap in, because at the point this occurs, the universe is only 1 second old. We’ve got a ways to go. 

Now we have a supply of protons, neutrons, and electrons to play with, when do we get those atoms I know and love? Well, it’s still too hot for electrons to buddy up with their proton and neutron cousins, but at this point, the nuclei of atoms began to form. A hydrogen nucleus is just a proton, so we can check that off the list. However, some of these protons could interact with and stick to a neutron, forming a nucleus of deuterium. Deuterium is an isotope of hydrogen that has one neutron rather than none. As more neutrons smack into this nucleus it quickly forms tritium (hydrogen isotope with 2 neutrons) and then helium-4 (2 protons and 2 neutrons). All of this so-called “nucleosynthesis” takes place over a mere few minutes, before the universe cooled to a point where fusing these nucleons together was too difficult. Combining the predictions of the Big Bang theory with particle physics, we are able to predict that the ratio of helium to hydrogen formed during this time should be about 25%. This number is so important to cosmology it gets a letter, capital Y. When we go out and observe objects in the universe we assume to be close to primordial, we find excellent agreement with this ratio! In fact, several other ratios such as the ratio of deuterium to hydrogen or helium-3 to hydrogen also match up with observations. This fact makes up one of the big three pillars of why we believe the Big Bang theory to be on the right track, along with the expansion of the Universe and the existence of the CMB.

3. Cosmic Microwave Background

Speaking of the CMB, when does that show up? Well, for that we’re going to have to wait a bit. To be precise, we’re going to have to wait 380,000 years. It took that long for the soup of ionized particles to cool enough that electrons could attach to atoms, in a process confusingly known as recombination (because, umm, when were they combined the first time???). While this helped put the baryons in the universe into the nice atomic state we’re all used to learning about, it had one big consequence: the universe became see-through. Before this time, all those loose electrons flying around meant that light couldn’t get very far before running into something. It was constantly being bounced around, which meant if you were standing there, you wouldn’t be able to see far at all. In fact, it would be like standing in the middle of a star: completely opaque, hot, and generally not recommended by medical professionals. But once the electrons stopped flying around everywhere, light could travel freely across the universe. This light has been streaming through space ever since, forming the omnipresent low energy radiation known as the CMB. The CMB provides crucial evidence for the Big Bang, as it shows the universe was once in a much hotter and denser state. It also serves as a snapshot of the early universe, helping us understand a whole bunch of really important stuff about how the universe came to look the way it does. Those parameters discussed earlier that tell us about the curvature of space and the relative densities of baryons, dark matter, and dark energy are all derived from observations of the CMB. It also tells us about how matter was distributed in the early universe, which is incredibly important for the formation of galaxies (more on that soon!). The CMB is a veritable treasure trove of information that unfortunately we can’t really get into here because this guide is long enough as it is. 

4. The Birth of Galaxies & Large Scale Structure

So for the sake of understanding the full story of ΛCDM cosmology, let’s keep going. The universe is now transparent, with a bunch of hydrogen and helium sitting around. But of course, that baryonic matter isn’t all there is, because dark matter has also been lurking in the background this whole time. This dark matter was omnipresent, but it wasn’t evenly distributed. There were small fluctuations in its density, and over time, those fluctuations grew as gravity drew more dark matter in. When the density in a given region reached a high enough point, it collapsed due to the Jeans instability and formed a structure called a dark matter halo. These halos formed a network throughout the universe, where large “nodes” are connected by tendril-like “filaments”, creating the majestic “cosmic web”. Figure 5 shows what this looks like in simulations of dark matter evolution. 

This is lovely, but now we have to turn back to the baryons, as they’re starting to do some interesting things themselves. As dark matter clumped up to form these structures, gas followed its gravitational pull, starting to cluster together in the center of these dark matter halos. Given enough time (meaning a few hundred million years), the densities in the gas reached a point where stars and eventually galaxies could form! Thus galaxies are built on top of this foundation of dark matter, and the large scale structure of the universe is born. 

We generally divide the universe into three scales for astronomy research purposes. “Small-scale” refers to distances of less than about a light-year and includes things like stars, planets, and solar systems. The intermediate scale is about one to a million light years and generally focuses on how galaxies and star clusters work. Large-scale is anything even larger, on the order of millions to billions of light years or more. Typically, galaxy clusters are the smallest objects of study in large-scale structure. We can actually observe this large-scale structure with surveys like the Sloan Digital Sky Survey (SDSS). Like our simulations of dark matter shown above, the distribution of galaxies in the universe looks like a cosmic web on large enough scales, as shown in Figure 6. The primary question of large-scale structure is how this specific web came about, as opposed to a more diffuse web, a more granular web, or any web at all. And it all comes back to the distribution of matter in the early universe, which we can trace from signatures in the CMB all the way to observations of galaxies today.

5. The Future 

So that brings us to today, but ΛCDM can also be used to predict the future! There are a lot of fun possibilities for how the universe could end, often depending on the exact properties of dark energy. In particular, the thing that seems to matter the most is the ratio between dark energy’s pressure and its density, often represented with the variable w. Weird values for w can lead to scenarios like the Big Rip  and the Big Crunch (someone please stop letting us name things). But current measurements suggest a rather calmer ending of everything: the Big Chill (seriously, enough is enough). (And if that wasn’t confusing enough, the Big Chill is also known as Heat Death – please, don’t allow us to name anything else). This future goes a little something like this. 

The expansion of the universe will continue, with galaxy clusters and, eventually, individual galaxies being pulled further and further apart. Stars will die, the gas reservoirs around galaxies that feed star formation will dry up, and the universe will start going dark. Stellar remnants will cool and fade. Any stray atoms or particles out there will decay into other particles and probably eventually into radiation. Eventually, all that’s left will be black holes, but via Hawking radiation, those too can slowly die. One day, all that will be left of the universe is radiation, slowly losing energy as the universe expands until the entire universe reaches an equilibrium state where entropy can’t go up. We’re left with nothing but a vast, dark bath of pretty much nothing. 

…sooooooo that sounds fun! Personally, I wouldn’t sweat it too much. The processes at play, like Hawking radiation and the potential decay of protons, happen on ridiculously huge timescales (we’re talking like 10¹⁰⁰ years before we reach that maximum entropy state). And there’s still a chance something could come out of that heat death, like a quantum fluctuation sparking a whole new universe, so really there’s no need to get upset about it.

IV. Major Issues and Possible Extensions

With everything put together, we can see the path of the universe as laid out by ΛCDM. There’s a lot of strong evidence built in there, but ΛCDM is still a model, and no model is perfect. So in our final section, we want to share some of the little things that maybe don’t work so well, and how modern cosmologists are trying to figure them out. 

A. The Hubble Tension 

One of the major problems in modern cosmology is something called the Hubble tension. The Hubble constant, which parametrizes the rate of the expansion of the universe (described more in Section III.A.1), takes on a different value for different ways of being calculated. Observations of the CMB yield a value around 67 km/s/Mpc, but calculations using the distance ladder place the value more at 73 km/s/Mpc. And the error bars don’t overlap, which all combines to a situation we scientists like to call an “uh oh”. The most obvious solution is that there is something going wrong within the analysis of observational data, leading to wrong answers. However, there has been so much work done on both sides looking for sources of error, and nothing has jumped out. This means some folks have started exploring other solutions. One is that we are located in a rather abnormal section of the universe, meaning our observations up the distance ladder could be skewed. But this violates a pretty basic underlying assumption of cosmology (so basic it’s literally called the cosmological principle) that essentially states that we are not special. On large enough scales, the universe is homogeneous and isotropic, so what we see around us should be pretty similar to everywhere else in the universe. 

Another possibility is that ΛCDM itself is the culprit. Since calculations of H₀ are so dependent on a ΛCDM paradigm, maybe the problem is that ΛCDM is wrong. There has been work done exploring how the tension could be explained by changing the behavior of dark energy (i.e., having it vary over time or decay in some way) or by using alternatives to dark matter like modified gravity models.  But while these changes can help explain the Hubble tension, they usually end up not explaining something else that ΛCDM does. So, for now, the Hubble tension remains an unsolved problem. 

B. The Age of the Universe

One of the things ΛCDM allows us to do is calculate the age of the universe. Given a value for the Hubble constant, density parameters, and an assumption about curvature, we can get an age since the universe was in its “hot dense speck” phase, about 13.8 billion years. However,  some past observations seemed to contradict this. One of the most well-known stars is Methuselah, whose age we can estimate based on elemental abundances and evolutionary stage. This age is 14.46 billion years, which would make it older than the universe! Something to note though: I was a bad scientist and didn’t give you error bars in that first report. The actual age is 14.46 +/- 0.8 billion years. A decent chunk of that error range would actually make Methusaleh not older than the universe at all, so it’s not time to panic yet.

You may also remember a slew of headlines after the launch of the James Webb Space Telescope claiming JWST “broke the universe” by discovering very massive galaxies early on. Some argued that these galaxies couldn’t have reached the size they were if the universe was actually 13.8 billion years old, that in fact the universe had to be much older. But as we got better data back, it became clear that most of these universe-breaking, massive, young galaxies were either not that massive, not that young, or both. When you additionally bring in the possibility of some of these galaxies having active galactic nuclei, the crisis is pretty well solved. This still points to estimations of age as a way to probe the accuracy of ΛCDM models, and as we peer further back into time with telescopes like JWST, this is a factor that undoubtedly will continue to arise.

C. The Lithium Problem

As explored in Section III.B.2, ΛCDM plays a big role in the evolution of the universe, including in the process of Big Bang Nucleosynthesis, or the creation of atoms in the early universe. While theoretical predictions of abundances are generally quite consistent, there is one problem: lithium. Stars in the Milky Way contain much less lithium than we would expect given ΛCDM predictions! There has been a lot of work trying to resolve this discrepancy, with ideas ranging from biases in observations to variations of fundamental parameters and (you guessed it!) moving into other DM/DE models as opposed to ΛCDM.

D. Missing Satellites and the Core/Cusp Problem

There are some other issues that relate directly to the dark matter side of  ΛCDM. One problem that was first discovered in the late 1990s is the so-called “missing satellites” issue. As its name suggests, this arises from a discrepancy between the predicted number of satellite galaxies around a galaxy like the Milky Way and the actual observed number of satellites our galaxy has. As predictions of sub-halo structure are highly dependent on the dark matter model used, this called into question the accuracy of CDM. However, there are several possible solutions that have made this less of a concern in recent years. Some have argued that there isn’t really a discrepancy at all, but rather we are just limited by our current observational capabilities. Some dwarf galaxies could have very low amounts of baryonic matter, making them very dim and difficult to detect via observation. To help support this idea is the simple fact that since the discrepancy was first noticed, we’ve discovered more dwarf galaxies around the Milky Way, with the number of nearby galaxies going from 10 in 1999 to over 60 today. Some of the teams who have discovered more recent satellites have made estimates on what the total should be, taking into account observational limitations, and actually predict more dwarf galaxies than CDM models! However, as there are still fewer confirmed observations than CDM predicts, there are teams who are probing other solutions to the discrepancy. One such solution is using a Self-Interacting Dark Matter Model. Annihilation interactions between dark matter particles would release energy and act to suppress sub-structure formation, thus reducing the number of predicted satellite galaxies. Some groups have even shown that this suppression is possible even with CDM models that are collisionless (non self-interacting) with the inclusion of baryonic physics in simulations.

Another issue that is much less resolved than the missing satellites problem comes from analyzing the radial density distributions of dark matter around galaxies. As shown in Figure 8, predictions from CDM models have an increasing density towards the center of the halo, a so-called “core” model. However, observations suggest that dark matter densities actually flatten out, producing a “cusp” in the central regions of the halo. There have been many possible solutions suggested for this issue, ranging from supernovae impacting mass distribution (this one generally doesn’t work super well), to considering other dark matter models (which has had more success). Once again, Self-Interacting Dark Matter is proposed to solve this issue, as particles scatter and transfer energy, allowing the density profile to flatten.

E. A Curved Universe

So far, we have been working in the realm of a perfectly flat universe. But it is potentially possible that the universe does have some slight curvature, which kind of changes everything…

The predominant opinion in the cosmology community is that the universe is flat, but how do we know? One excellent way is via the CMB. As we mentioned in Section III.A.2, the amount of curvature affects the way in which photons will travel through the universe. In a positively curved universe they converge, and in a negatively curved universe they spread apart. If photons are converging when they reach us, that makes it seem as though they come from a larger object than they really do. Vice versa, photons that are diverging when they reach us seem to come from a smaller object than they really do. Therefore, the appearance of the size of patches on the CMB will be affected by the curvature of the universe. For an example of how this might look, take a look at Figure 9:

As we mentioned in the section on the curvature parameter, the general consensus amongst cosmologists is that the universe is flat. However, there are some slight wrinkles to this story. Using data from the Planck Satellite’s 2018 data release predicts a universe that is actually slightly closed, but using different data sets – even different data sets from the same Planck mission – we predict a flat universe! This has been called the curvature tension in the literature. Why might we care if the universe has a very slight curve to it? Isn’t mostly flat just as good as flat? Well while it’s certainly not enough to be noticeable here on Earth, it could spell trouble for early universe cosmology. One of the reasons inflation was considered as a possibility in the first place was the fact that inflation could explain why the universe is so flat. If the universe isn’t actually flat, we may have to reconsider our understanding of inflation.

F. Time-dependent Dark Energy

One big assumption that goes into ΛCDM is that that big old Λ out front represents a constant. That is, we expect that the amount of dark energy in the universe stays constant over time. However, nothing requires this to be the case. Recently, two papers from two large teams of cosmologists have independently predicted that dark energy may be changing with time!

To understand their findings, let’s quickly dive a little deeper into dark energy. Dark energy, like most things in the universe, can be described by what is called the equation of state parameter, w. This parameter measures the ratio of a substance’s pressure to its energy density. For example, normal matter has an equation of state parameter of 0 because it exerts essentially no pressure. If you plug some component of the universe (matter, radiation, dark energy, etc.) into the Friedmann equations and specify its equation of state parameter, the Friedmann equations will tell you how that thing changes in time. In Einstein’s original formulation, dark energy was supposed to be a constant, and the equation of state parameter that corresponds to an unchanging component of the universe is w= -1. This seemed to match up to observations quite well. However, two recent papers coming out of the Dark Energy Survey (DES) and the Dark Energy Spectroscopic Instrument (DESI) (Are their acronyms similar? Yes. Did I think they were the same people until embarrassingly recently? Also yes.) Both teams allowed for the possibility that w was close to -1, but could change in time a bit. Specifically, if the default value of the equation of state parameter is w₀, the authors give it a time varying component with a coefficient of w_a. Then, when fitting your cosmological model, if you recover a w_a of 0, dark energy really is constant. Take a quick peek at Figure 10, from the DESI paper on this topic, and you’ll see a plot that shows what different data sets predict for the values of w₀ and w_a. All 3 combinations of data sets do not include a w_a of 0 in their 95% confidence interval. The DES paper found similar results. These results are still extremely new (this is from April 2024) and the implications on cosmology are not yet fully understood, but it is possible that cosmology is about to undergo a fundamental rewrite. If I may get a bit personal, to quote my advisor from our lab group meeting: “I remember being a graduate student when the [paper that announced the accelerating expansion of the universe] came out and changed everything, this is starting to feel a lot like that.” To say that now is an exciting time for cosmology would be an extreme understatement.

G. Non-Detection

Finally, arguably the biggest issue facing ΛCDM is the lack of detection for either dark matter or dark energy. While there are a range of experiments trying to directly detect dark matter, no successful detection has been made to date. Detecting dark energy is an even greater hurdle, as it has an extremely low predicted value, and there’s no consensus as to what its actual mechanism is. 

While these are significant problems, the fact remains that no other model is as successful as describing as much of the universe as ΛCDM. As we’ve explored here, it helps us explain observations of gravitational lensing, stellar orbits, galaxy evolution and large scale structure, Type Ia supernova, and many properties of the CMB. It’s not perfect – no model is – and there’s always more to figure out about the universe. But we’re in a wonderful era filled with groundbreaking discoveries and exciting new developments, and ΛCDM continues to serve as a strong foundation for our understanding of cosmology.

Featured Image Credit: NASA, ESA, CSA, and STScI