## Covid-19 and PhD Places

It’s been quite a while since I’ve written anything on here, the world has become a very strange place since the last time I did. Although the obvious reason would supposedly be the inconvenience that is Covid-19, the reason for my online absence has less to do with that, and much more to do with the more exciting fact that I devoted the majority of my time over the last few months applying to PhD positions. It is my pleasure to confirm that this endeavour has been a successful one, and that in September 2020 I will begin my PhD studies in Early Universe Inflationary Physics! I’m extremely excited to get started, and I’m especially thrilled that I’ll be researching and learning more about our understanding of the very first moments of our universe!

In light of this, I thought that an interesting thing to write about would be a recent problem that has arisen in the field of cosmology. This problem is known as the Hubble Tension, and there’s currently a big debate over whether the problem is just a result of making inaccurate measurements, or a fundamental issue in contemporary cosmology, calling for new physics to explain it.

# The Hubble Tension

## The Hubble Constant

The Hubble tension revolves around the value of a constant in cosmology called the Hubble Constant, which can be thought of as a measure of how quickly the universe is expanding. It’s an extremely important quantity that characterises fundamental features of the universe such as its age, and the size of the observable universe. Being such an informative number, it’s important that we have an accurate value for it if we want to understand the universe’s history, and its future.

The historical way of measuring its value is by observing distant galaxies and calculating how quickly they’re receding from us. Since the universe is expanding outward, we can work out how quickly various galaxies are moving away from us and then determine a rate of expansion of space. If we gather a large amount of data, then we can glean an accurate estimate for the Hubble Constant.

A problem began to arise however when cosmologists found an independent method for calculating the value of the Hubble Constant. Instead of observing the motions of celestial bodies in the universe today, we can look at the Cosmic Microwave Background (CMB). The CMB is the very first light in the universe – produced around 300,000 years after the Big Bang. It was at this point in time that the universe was cool enough for matter as we know it to form, and for light to propagate freely, unobstructed through the universe. We can use the CMB to obtain a value for the Hubble Constant in the very early universe, and then simulate the universe from that point to obtain the expected value for the constant today.

The Hubble Tension arises because these two methods of measuring the Hubble Constant produce different values! When we use the motions of galaxies today to calculate it, we end up with a value of 73kms^{-1}Mpc^{-1}. If we use the CMB however, we end up with a smaller value of around 67kms^{-1}Mpc^{-1}.

This might not seem like a huge discrepancy, there are certainly much more embarrassing contradictions between theory and experiment in the history of Physics! The reason that there is so much literature about the Hubble Tension now is because very recently a new, more accurate survey of the motions of nearby galaxies was published, and the error bars around 73kms^{-1}Mpc^{-1} were reduced. This latest reduction in the error means that the discrepancy in the values has passed the “Holy Grail” of statistical milestones in science known as the “5-sigma” significance level. In normal-speak this means that there is now roughly a 1 in 3.5million chance that the difference in these values is a fluke. In other words, the evidence is overwhelming that something’s gone wrong.

But what? Is the disagreement merely due to some systematic error in our measurements? Or is there something wrong with our theories? Does this require a new physical theory to explain?

## Measuring the Hubble Constant

The Hubble Tension has arisen from two independent ways of measuring the constant:

- Use the motions of celestial objects in our universe today
- Use the CMB to work out the constant in the past and use our current model of cosmology (known as Lambda-CDM) to predict what the value should be today.

Since the two values produced disagree, then we must either conclude that our measurements of celestial objects in the universe today are inaccurate, or that something about our current model of cosmology is wrong. There is very little consensus in the current community which of these options is correct! Here’s a little overview of how both the estimates for the Hubble Constant are derived, and where mistakes may have crept in.

### Cepheid Variables and Type Ia Supernovae

Finding out how quickly distant galaxies are moving away from us is by no means easy. Distant galaxies are, by definition, very far away from us, making it difficult to work out both how far away they actually are, and how quickly they’re moving. Virtually the only data we have about distant celestial objects are how bright they appear to our telescopes. Fortunately there are kinds of stars and supernovae that have predictable luminosities, and so if we observe how bright they are then we can work out there distance away from us!

The first step is to use the geometrical phenomenon “parallax” to determine how far away stars known as a Cepheid Variables are. Cepheid variables are named because their brightness oscillates over time, and this oscillation is related to the intrinsic luminosity (how bright they really are) of the star. If we observe how these stars pulsate, we can find out how luminous they are. Comparing this luminosity to the brightness we actually observe (light gets less bright the further away it is) we can work out how far away the star is!

This technique is useful to work out the distances to Cepheid Variables located within our own supercluster of galaxies. Outside our supercluster, we can use a brighter, more magnificent standard candle to gauge our distances – the Type Ia Supernova. This kind of supernova has a predictable “peak brightness”. If we observe how the supernova’s brightness changes as the star explodes, we can determine what the “peak” of this brightness is. From this we can work out the true brightness of the supernova, and hence how far away it is from us.

Once we have established distances to various celestial light sources in the universe, we have a “cosmic distance ladder” with which we have a “map” of the observable universe. With the distance ladder, we can plot the velocities (found using redshifts) of galaxies against how far away from us they are and the gradient of the plot gives us an estimate for the Hubble Constant.

These calculations have historically been ridden with errors, the original estimate for the Hubble Constant, calculated by Mr Hubble himself, was about 500kms^{-1}Mpc^{-1} far larger than the value of 73kms^{-1}Mpc^{-1} which we’ve settled on today. Some cosmologists argue that there are systematic errors in the recorded data, and that the perceived “Hubble Tension” is due to incorrect measurements of the cosmic distance ladder, not a fundamental disagreement between theory and observation.

### Lambda-CDM and the CMB

The other way we can measure the Hubble constant is to use the Cosmic Microwave Background (CMB). The CMB is the “first light” of the universe, formed when the universe was first cool enough for matter as we know it to form. This CMB radiation was key evidence in favour of the Big Bang Theory over older, discarded cosmological theories. To find the Hubble constant, we can use the CMB to give us an estimate of the constant back at the time the CMB was formed, and then simulate the evolution of the universe up until the present day. This gives us a theoretical prediction for the value of the Hubble Constant.

If our measurements of Cepheid Variables and Type Ia Supernovae are correct however, then this means that our theoretical prediction is wrong. If our prediction is wrong, then there must be a problem with the model that generated the prediction – there must be something wrong with the Big Bang model. Cosmologists are very hesitant however to tinker with the canonical cosmological model (known as the Lambda-CDM model). This is because Lambda-CDM gives astonishingly accurate predictions for other features of our universe – such as the relative abundances of the chemical elements in the universe. If we start changing our theory, the accurate predictions the model already has to its name get worse! Is there a way we can introduce new physics that preserves the good things in the Lambda-CDM model, while also solving the Hubble Tension problem?

## New Physics Suggestions

If there are no systematic errors in our measurements of the cosmic distance ladder, then we have to conclude that something in our current model of cosmology needs altering. At the same time however, we want to preserve all the predictions that Lambda-CDM actually gets right – like the relative abundances of elements in the universe. The problem is that the current options on the table that preserve the accurate predictions and the Hubble Constant are all rather strange, here’s a couple of them:

**Phantom Dark Energy**– Dark energy is a substance with “negative pressure” that pushes the universe apart and drives the expansion of the universe. We already know about one kind of dark energy, but what if there are other types? These can help solve the Hubble Tension, but these other kinds of dark energy allow for bizarre things like negative energies and matter moving faster than light!**Bimetric Gravity –**Perhaps we can alter our theory of Gravity? It turns out that there is a theory of gravity that gives us “effective” phantom dark energy – which allows us to solve the Hubble Tension without all the nasty negative energy and faster-than-light particles. Experimental evidence is strongly in favour of Einstein’s gravitational theory however.**Disappearing Dark Energy –**How about dark energy that suddenly disappears when we need it to? This would be fine if we had physical reasons to propose a model like this, but without these this proposal is just ad-hoc.

## Conclusion

To conclude, it’s unclear whether the Hubble Tension is really a problem in cosmology, or just a storm in a teacup. What is clear however is that a lot of literature has been published attempting to solve it. The physics community is going to be looking into this until there’s some kind of resolution. It’s exciting to think that this may be a new hint of physics beyond our current theories, but the current “new physics” proposals are not very convincing at the moment. Watch this expanding space!

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