Do not be frightened: choose wisely and you may only need to read half of this
As a cosmology PhD student, I spend my days trying to figure out what the Universe is made of and how it evolves (and where to get my next cup of coffee). Early on in my training, I was confronted with the cruel fact that there are some things which we will never be able to see, such as the (approximately) quarter of the Universe made up of the aptly named “dark matter” which does not interact with light; or any regions of the Universe that are so far away from us, that their light has simply not had enough time to reach us in the 13.8 billion years that the world has existed; or, more down to Earth, the end of my to-do list, which, much like the Universe it belongs to, keeps expanding in an accelerated manner.
Yet another such invisible thing is the birth of the Universe – a sudden and violent process that left the freshly created particles of light (photons) tightly attached to the matter particles that make up everything that we do see (baryons). Though baryons were held together by gravity, photons pushed them away, the two effects competing with each other and creating pressure waves, which travelled out much like ripples on a water surface. The early times are completely invisible to us with photons trapped in this hot dense plasma of the early Universe, unable to escape. As the Universe expanded and cooled, eventually the photons were able to break free from baryons and start their long journey towards what would become our planet Earth, to be caught by our telescopes. This ancient light is the earliest Universe we will ever be able to see – and we’ve already seen it! We map these photons by assigning them temperature, based on the wavelength of the radiation, and call it The Cosmic Microwave Background (CMB for short). This is also the start of our murder mystery.
I am about to take you on a journey to figure out one of the puzzles that I am trying to understand day-to-day as a cosmology graduate student. I have tried to structure this in a way that resembles the work of a scientist as closely as possible and I am inviting you to choose your own adventure as you go through this article. Just like in the actual process, with some luck, you may only need to read half of the text to arrive at the conclusion, however, I do invite you to consider every aspect of the journey to get a fuller picture.
The murder we are investigating here is that of the standard model, also known by its catchy cool name of CDM, which suggests that the Universe today is made up mainly of the already mentioned cold dark matter (CDM), that is invisible but which we know exists through its gravitational effects, and dark energy (Λ), which is responsible for the accelerating expansion of the Universe today. If these descriptions have left you in the dark (pun intended), fear not, you’re not alone! The truth is, we don’t know much about either of these components beyond the effect that they have on the evolution of the Universe and the structures within it. Despite these flaws, our standard model is in pretty good shape, describing a number of our observations extremely well – it can predict the distribution of the galaxies we see as well as the amount by which the light coming from them will be deflected by the structures (nearby galaxies and their clusters) in front of them. It can also explain the CMB maps with incredible precision! The model does, however, require some parameters (like the amount of dark energy or dark matter present) to be known in order to provide accurate descriptions. We may, therefore, adjust the values of these parameters until the model predictions match our observations and in this way “measure the Universe”.
What we find when we do so is intriguing! While we do an excellent job fitting individual measurements, the values of some of the parameters that we get do not quite agree when we compare the results coming from different observations. In particular, we see some small disagreements (or “tensions”) between the CMB results and those coming from the nearby Universe. While the difference is not very big yet, a natural question arises: is our standard model dead (or, to put it in less dramatic terms, inaccurate) and if so, what is it that killed it? Before we dive into the case, let’s meet the witnesses and take a closer look at the crime scene.
CMB. The name of the satellite that provided the most precise observations of the CMB radiation is Planck and it is a trusted witness: the cosmic microwave background photons come from the baby Universe before a lot of complex processes ever took place. Planck, therefore, measures the CDM parameters extremely well and is the most powerful dataset we have for such analysis. Nevertheless, the photons that Planck eventually caught met a lot of challenges on their way to us (such as dust! Yes, it is an annoying problem on a cosmic scale and not just in your living room) and all of these need to be properly accounted for. We think we’re pretty good at it though!
Galaxy clustering. I already mentioned that our model can predict galaxy distribution – this is less trivial than it might seem at first sight, as galaxies are not spread out randomly but rather form a web-like pattern of overdense regions of galaxy clusters connected by filaments with underdense voids in between. This non-uniform distribution is due to small variations in matter density in the early Universe which grew as the Universe expanded. We can calculate the probability of finding two galaxies some distance apart and use this to describe the web structure. The photon-baryon oscillations I mentioned at the beginning are also reflected in such measurements, as we find many more galaxies with separation that corresponds to the distance the oscillations travelled before photons and baryons broke free of each other. Galaxy clustering is a knowledgeable witness as well and it can tell us about more recent Universe long after the first photons that reach us. However, this is a pretty complex Universe as well and we don’t always understand everything that this witness says – on small scales, galaxy distribution is affected by many different astrophysical effects and is not easily modelled. It is, furthermore, important to note that the thing we are really interested in here is not the web of galaxies, but rather that of the dark matter underneath (yes, dark matter forms a web pattern as well!). The galaxies we map trace this web, allowing us to understand the underlying dark matter distribution. However, it turns out this witness is not faithful and tends to exaggerate the truth: only the most massive concentrations of dark matter will host a galaxy and the connection between the two is not easily described.
Weak lensing. Weak lensing was briefly mentioned before and refers to the fact that as light travels from galaxies towards us, it will be deflected (or lensed) by the galaxies and their clusters (in fact, any mass it meets on its way). This will manifest as a distortion of the observed images, which we can only detect by looking at millions of galaxies and measuring their shapes! Understanding this witness is very hard though, as we need to observe so many galaxies and the effect is very small – any movement in the atmosphere of Earth will completely overwhelm the signal if not enough galaxies are observed. Modelling weak lensing signal also involves even more complexity than galaxy cluster models, as all of the astrophysical processes become more important due to the small scales involved. Nevertheless, this witness is truthful: the amount of distortion (lensing) depends on the amount of the total matter encountered on the way – galaxies as well as dark matter. This is very convenient because we do not need to try to guess how the two are related! To keep this murder mystery short, we will assume that weak lensing is innocent and there is nothing wrong with these measurements. That is, however, not at all granted to be true and a lot of cosmologists are working hard to prove otherwise!
The crime scene. So what injuries might the standard model suffer? The focus of this crime scene (which actually does not cover the greatest tension we see in the values of the expansion rate of the Universe, but this is a tale for another murder mystery…) is the amplitude of the weak lensing signal which is described by a combination of two parameters of the cosmological model – one that describes the matter density in the Universe and one that describes the clumpiness of the cosmic web structure. The amplitude of a weak lensing signal depends on both of these because the effect cannot tell whether the light gets bent more because the same amount of matter is more concentrated or because there is more matter in general: both of these cases will result in light getting more bent. It turns out that the amplitude of this signal, as predicted by Planck, is higher than what is actually measured by weak lensing surveys!
It, therefore, seems like there was an attempt to kill the standard model of cosmology, it’s time to choose your path of investigation! So, dear detective, what would you like to do next? If you would like to question an independent witness and look at galaxy clustering, please proceed to section “Clustering speaks up”. If you, however, don’t trust clustering or do not believe it will be able to provide conclusive insight and you’re instead interested to hear Planck’s side of the story, please go to “Planck’s point of view”.
Testimony 1: Clustering speaks up
As mentioned before, clustering is perhaps the most precise probe of the recent Universe that we have. The data that I work with come from Sloan Digital Sky Survey, which observed over a million galaxies! By investigating their distribution, we can figure out how much lensing by the cosmic web we might expect to see and the result that we find is… Somewhere in the middle between the values directly measured by weak lensing and the ones predicted by Planck! But could it be inaccurate? There are a number of things that can go wrong when modelling any observation (or when carrying out a measurement!), though, generally, the groups of scientists working with these data will have entire teams dedicated to testing various points of the process, making sure that every assumption is valid and its effects on the results are well understood. You might be interested in the fact that galaxy clustering generally still gives slightly low values for weak lensing amplitude, compared to the Planck prediction – is there, perhaps something more hiding behind this? I will offer you two routes to proceed down next. First, you may be interested in looking at (even) more data – what happens if we go and observe even further objects, whose light travelled for an even longer time and, therefore, shows Universe in a deeper past? The answers to this question are given in the section “Digging deeper in the past: quasar clustering”. If you are happy with the galaxy results but are worried about whether we are performing an appropriate comparison when comparing measurements from two such different things as galaxy shapes and their distribution, please proceed to “Comparing apples to galaxies”.
Digging deeper in the past: quasar clustering
It is fascinating to remember that telescopes are, in fact, time machines – since light takes some time to travel from its source towards us, we never see the object as it is right now, but rather its image at the time when the light left it. Therefore, if we want to stare further back to the past, galaxies will no longer suffice, we need something even further away and even brighter, still visible from all the light-years away. Enter quasars – these objects are powered by black holes that accelerate and heat up the infalling gas so much that it starts shining (and an average quasar can be brighter than tens of trillions of suns). Quasars are so distant that the light that reaches us now, left when the Universe was just 7 billion years old (which is just over half of its total age and long before Earth existed itself). These objects, therefore, allow us to look at a very different Universe than the one probed by the more nearby galaxies. However, this knowledge does come at a price – we were able to observe ten times fewer quasars than galaxies and determining their exact distances is somewhat more complicated as well. While our hopes when interviewing this witness were high, we find that their story does not add all that much to galaxy clustering alone because of the large associated errors. Nevertheless, within the standard model, quasars predict the Universe to be quite a bit more clumpy than both galaxy clustering and Planck. This is certainly interesting, but, for now, it’s just a hint, we will need to wait for future surveys to observe more objects and reduce the measurement errors to know for sure (do not worry though, we are already on it with Dark Energy Spectroscopic Instrument which is already observing and will provide the most detailed map of the Universe yet)!
More clustering data has not given us the answers we were looking for, but the mystery remains, what do you choose to investigate next? If you’re curious to find out what can go wrong when we’re comparing different types of measurements (galaxy positions versus their shapes), I once again invite you to look at “Comparing apples to galaxies”. If instead, you are done with galaxies and, inspired by our journey back in time, you want to continue looking deeper into the past and interrogate Planck, I invite you to consider “Planck’s point of view”.
Comparing apples to galaxies
When describing the crime scene, I told you that the injury to the standard model seems to be in the parameter that describes the amplitude of the weak lensing signal. However, you might be rightfully wondering, what galaxy clustering or cosmic radiation have to do with it. Indeed, while measuring cosmological parameters using any probe will allow us to predict what sort of signal we expect from looking at galaxy shapes, this is not a natural description for any of the other measurements. The weak lensing amplitude prediction that we will get from our models might, therefore, come with large errors.
In order to meaningfully interpret our measurements it is important to choose what properties we want to compare – we must make sure we’re comparing apples to apples (or galaxies to galaxies, if you will!). A good way to do so is to focus on what it is that weak lensing amplitude measures (since our problem relates to this quantity) and how we can translate this to a universal property. I already described how weak lensing signal gets larger the more matter we have or the more clustered it is. Put together we may say that our galaxy shape measurements describe the amount of structure. The cosmic web grows in time, as galaxies (and underlying dark matter) are pulled together by the gravitational force, moving from underdense regions towards the overdense ones and the amount of structure increases. All of our witnesses (all of our probes) are sensitive to this, each of them providing a snapshot of the amount of structure at some point in the history of the Universe.
A simple way to try and compare all of these measurements is then to define a separate parameter that describes the amount of structure at some given time and look at the relationship that the measurements predict between the initial and final amounts of structure – the total growth. Once we do so, we do, indeed find some difference! It turns out that for a given amount of structure today, Planck will predict less initial structure – so more total growth, than weak lensing or its combination with galaxy clustering. While this difference is not so great as to cause concern just yet, it is indicative of the fact that the issue we saw with weak lensing signal amplitude shows up in our measurements even when we compare them on a more equal footing.
This test allows us to build our understanding of the physical property of the Universe behind the differences in measurement amplitudes and ensures that we are comparing the same, well-defined property, but does not add any more certainty when trying to figure out whether our model truly is injured or if what we’re seeing is just an expected difference (the processes in our Universe are somewhat random and uncertain, we, therefore, do not expect the observations to match our predictions perfectly). If you haven’t yet, you might try seeing what happens if we observe more further away objects in “Digging deeper in the past: quasar clustering”, or, if you are done with clustering, perhaps its time to listen to “Planck’s point of view”? Or, just in case you are done with everything, go and try “Closing the case?”.
Testimony 2: Planck’s point of view
Planck’s point of view tends to be questioned quite rarely – and that is no wonder! The early Universe from which the CMB radiation is coming is simple and smooth with only small density fluctuations to worry about. Cosmic microwave background is the Universe’s radio, broadcasting information about what it was made of at the time and it has the authority of a well-established and knowledgeable witness. So it might be considered sacrilegious to even question it, but, as detectives, we must do our due diligence. As our investigation will reveal, Planck’s reliability does depend on certain circumstances. First of all, some of the features of its measurements do not quite fit our expectations, if you are curious to find out about that, please look at “Planck against Flat Universers”. Secondly, Planck’s cosmology predictions are obtained by looking at the Universe’s infancy and using our standard model to predict the parameter values we would get today. You might, therefore, be concerned that the rules of the model, and the assumptions that we make, might result in wrong conclusions if we don’t understand the model well enough. If you’re interested in exploring this aspect, please look at “The dark expansion”.
Planck against Flat Universers
The majority of cosmologists are flat Universers. This essentially means that we believe that in our Universe two parallel lines will remain parallel and never intersect (you can easily imagine how this would not be the case for a spherical Universe by considering the meridians on Earth, which are parallel at the equator but intersect at the poles). All of our observations have so far been consistent with this picture, so much so that we often just assume that the Universe is flat to improve the precision of the measurements on other cosmological parameters (the fewer unknown parameters we have, the better we can measure them).
However, a strange thing happens if we look at the lensing of Planck’s CMB temperature measurements. We are already familiar with the lensing of galaxy images as their light travels through the structure in between and gets bent away from the straight path. Very similarly, the photons coming from the microwave background radiation will be lensed too and we can predict this effect. Nevertheless, as we’re interrogating this witness, they grow uneasy – turns out, when we look at our data, the temperature measurements seem to be lensed more than we predicted! How could this be? Well, first and foremost, it may just be some noise that affects the measurements that we are not removing properly. The travel all the way back from the early Universe to today is a long one and there are multiple obstacles that might scatter, absorb or otherwise affect the photons that make up the CMB light, as they go through the dust and the gas present around galaxies and their clusters. While cosmologists take great care to account for such effects, there is always a possibility that there is something that might get overlooked.
Another, perhaps more exciting explanation of this finding could be that the Universe is, indeed, curved. In such a Universe the parallel lines do eventually meet and you can imagine this curvature of the Universe mimicking that induced by the massive galaxy structures that lens the light. In this way, a closed Universe might provide us with more lensing than we might otherwise expect. However, as mentioned before, this is a rather controversial opinion – cosmologists are Flat Universers based on a number of different observations which all confirm that the Universe is flat. For one, if we relax the assumption of flatness, Planck will produce cosmological parameter values that are in disagreement with galaxy clustering. In addition to this, the amplitude of the galaxy weak lensing signal predicted by Planck in a curved Universe is even higher than in the flat case, further exaggerating the disagreement between CMB and weak lensing.
Most of Planck’s results are, nevertheless, robust against the assumptions on the amount of lensing of its temperature measurements. There are also additional features of cosmic microwave radiation that may be measured and that show agreement with the standard model. It is, therefore, up to you to decide, how much you trust this witness – I do not want you to lose faith! The main lesson here is to take everything with just a pinch of salt. If you want to take a look at an example of how sometimes adjusting analysis methods does not necessarily change the main conclusion significantly, follow “Comparing apples to galaxies”. If, instead, you’d prefer to learn more about Planck and other assumptions we make when analysing its data, go ahead (with care!) towards the “The dark expansion”. If the long journey has tired you, we do not judge – feel free to proceed towards the end and see if you can find success at “Closing the case?”.
The dark expansion
Before we delved into Planck’s point of view, we learned that, in order to use its measurements to describe the Universe today, we must use some evolution rules, some model. This is because the picture of the Universe carried by cosmic radiation is a very old one and you might rightfully wonder, how much the final results depend on the model that we use.
The greatest challenge we face here concerns our assumptions about dark energy – the mysterious component that causes our Universe to expand in an accelerated manner. In the infancy of the Universe, the time of CMB, the amount of dark energy was negligible, but it has steadily grown ever since to become important just before the formation of Earth. It is, therefore, incredibly lucky that we are able to conduct this investigation – had we lived in an earlier epoch, we might have never known that dark energy existed!
As we do not know what dark energy actually is, we usually assume a simple form of how the amount of dark energy in the Universe evolves by setting its density to a constant value. Remarkably, our observations fit this model very well and we’re yet to see any deviations from it. Assuming constant dark energy density also makes things much easier for Planck. As it probes the Universe long before dark energy became important, Planck does not know much about dark energy properties. Therefore, telling it exactly what they are, allows us to obtain very precise constraints regardless.
We may, nevertheless, consider a case where the dark energy density is not constant but evolves at some rate, which we might try to determine from our measurements. Unfortunately, for Planck, that means that the expansion rate of the Universe may not be determined anymore, as it has no information on what this rate of dark energy evolution might be and, therefore, how much dark energy there is today. We can get by with a little help from our friends – clustering or weak lensing measurements which are based on galaxies in the late Universe where dark energy is the dominant component and who can, therefore, provide additional constraining power. However, if we want to talk to Planck on its own, there will be few answers to be had.
You might then wonder where this leaves us with the standard model and the weak lensing amplitude tension. If you read about “Comparing apples to galaxies”, you will know that this tension relates to the amount of structure in the Universe. However, it is impossible to describe the amount of structure without defining a scale at which you want to measure it. You can understand this if you’ve ever seen a lake from a distance – on a calm evening, the surface may look so smooth you might be tempted to think it is a mirror. Come a little closer though and you will see the little waves and ripples dancing in the setting sun. Similarly, the smoothness of the Universe depends on the scale at which you look. This scale dependence may be a problem for Planck if you were to express distances relative to the (poorly measured) expansion rate of the Universe without assuming constant dark energy density. For reasons that we will have to skip here, such a definition of distances is actually a pretty common practice and, as a result, up until very recently we thought that Planck knew very little about the amount of structure in these less well-defined cases.
However, it turns out that, as long as we tell Planck exactly what scale we want the amount of structure measured at (i.e. without using the units relative to the unknown expansion rate), it will be able to determine this quantity perfectly fine, no matter what assumptions we make about the evolution of dark energy. This might seem counter-intuitive since I already told you that cosmic microwave background radiation comes from times before dark energy dominance. Nevertheless, this doesn’t mean that any dark energy model at all will be able to reproduce Planck’s observations. It turns out that only certain combinations of the amount of dark energy today and the rate at which it evolves are allowed and they all lead to the same amount of structure today.
Despite this success, the bad news is that the amount of structure these models lead to is actually higher than what we see when assuming the standard model, suggesting that relaxing our standard assumptions does not solve our case. Another commonly adopted assumption is that of a flat Universe – if you haven’t checked that out yet, go to “Planck against Flat Universers” to read more! Otherwise, there are a couple of last words I want to say to encourage you at the end of this case – if you’re ready to hear them, please go to “Closing the case?”.
Closing the Case?
As we reach the end of this investigation, you may feel like we have not come any closer to figuring out what is going on. In fact, looking at different assumptions and different observations sometimes made us feel further from a solution than when we started. However, I do hope you learned something along the way! It is perhaps a little difficult to appreciate these lessons when we have not even figured out if the murder did indeed happen – if there is something not quite right with our standard model, our understanding of the Universe, but I urge you to not despair.
Ultimately, this experience is very close to what being a researcher is actually like: the majority of roads don’t seem to lead anywhere, but, as cheesy as it sounds, it is the journey that leads us to a better understanding of our models and our data and allows us to take a more critical look at the established way of doing things, the ways of thinking that we have gotten so used to. Hopefully, you are not too discouraged by the long travels and are able to appreciate all the twists and turns with an open mind. And, who knows, one day all of these puzzle pieces that made no sense might just fit together to reveal something new and beautiful about the Universe around us. But in the meantime, I will need some very special kind of dark energy – another coffee!