The six numbers that define the entire Universe

In this edited extract from The Little Book of Cosmology, physicist Prof Lyman Page explains how our model of the Universe relies on just six parameters.

By Prof Lyman Page

Published: Friday, 24 March 2023 at 12:00 am

How do we study the Universe as a whole?

My work focuses on the cosmic microwave background (CMB) – the faint energy remnants of the Big Bang – and how measuring it can guide our path to understanding the Universe. But there are many other ways to study the cosmos, and the physicists who study it specialise in everything from General Relativity, to thermodynamics, to elementary particle theory.

We make observations in nearly every wavelength regime accessible to measurement and with state-of-the-art particle detectors. The observations come from nearby and from the farthest reaches of space. All of this evidence and theory can be put together into a surprisingly simple standard model of cosmology, which has just six parameters. These are the numbers that define our entire Universe.

The contents of the Universe

The first three parameters tell us about the contents of the Universe. We describe them as fractions of a total matter and energy budget, like the components of a pie chart. The first parameter describes the amount of normal matter, or atoms, in the Universe, and it says that atoms account for just 5 per cent of the Universe.

The second parameter describes dark matter, some type of new fundamental particle that we do not yet understand, which accounts for 25 per cent of the Universe.

Remarkably, the amount of dark matter, which we can derive from our measurements of the minute temperature fluctuations in the cosmic microwave background radiation, agrees with the value deduced from observations of the motions of stars and galaxies. However, the value we derive from the CMB measurements is much more precise.

Our measurements also tell us something else. Because the CMB comes to us from the decoupling era – when the early Universe had cooled enough to set photons free from the hot plasma that had bound them for several hundred thousand years after the Big Bang, causing the Universe became transparent – we can see that dark matter clearly existed in the early Universe. What’s more, we can see that atoms, the stuff of which we are made, accounts for just one-sixth of the total mass in the Universe.

The third parameter is the cosmological constant, the mysterious dark energy that is at the root of the accelerating expansion of the Universe. This accounts for 70 per cent of the Universe’s total matter and energy budget. We do not know what this dark energy is either, but we know it exists, because we have directly measured its presence through the cosmic acceleration.

Forming stars and galaxies

The fourth parameter is the optical depth, or how opaque the Universe was to the photons travelling through it. This is the most astrophysical of all the parameters of the standard model of cosmology. By this, we mean that it captures our rather scant knowledge of the entire complex process of the formation and subsequent explosion of the first stars and the formation of the first galaxies in the Universe.

The intense light from these early stars and galaxies broke apart the hydrogen that was prevalent in the cosmos into its constituent protons and electrons, causing the reionisation of the Universe. In this process, about 5-8 per cent of the CMB photons – the photons that had been released at the time of decoupling — were rescattered.

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To use an analogy, considering that the Universe had been transparent before, it is as though a bit of fog rolled in. Not too much – you could still see a distant shore – but the visibility was reduced. Interestingly, to determine the optical depth of the Universe, it takes a measurement of the polarisation of the CMB.

Polarisation, along with intensity and wavelength, is one of the three characteristics of a light wave. The polarisation specifies the direction in which a light wave is oscillating. For example, light reflected off the hood of your car is horizontally polarised. That is, the light wave oscillates back and forth horizontally. Polarised sunglasses block this oscillation direction and its associated reflected glare.

Similarly, the electrons freed by the process of reionisation scattered and polarised the CMB photons. If you could look at the CMB with or without polarised “sunglasses”, you would see that it looks slightly different.

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An all-sky map of the cosmic microwave background © NASA / WMAP Science Team

Quantum fluctuations

The last two parameters describe the seeds of the minute fluctuations that gave rise to all the structure we observe today in the Universe. If we had a complete model of the Universe – one that began with tiny quantum fluctuations and successfully predicted what the fluctuations of matter in spheres measuring 25 million light-years in diameter would be – we could eliminate one of these two parameters.

Unfortunately, while we have a very successful framework for understanding how the Universe evolved, we do not yet know all the connections, and so we require it as a parameter.

It is called the primordial power spectrum and it describes the fluctuations in the density of the Universe in three-dimensional space. In the very early Universe, these fluctuations were small, but as the Universe expanded, these density variations were writ large across the cosmos.

Where there were slightly denser areas in the primordial cosmos, matter continued to clump together, and we can now see galaxies or clusters of galaxies; in others, where there was less density, we see almost nothing.

The remaining parameter, called the scalar spectral index, is the most challenging to understand – but it is also our best window into the birth of the Universe. It tells us how the primordial fluctuations, the tiny energy variations that were present in the infant Universe, depend on angular scale.

To better grasp this, let’s use a musical analogy. This final cosmological parameter allows us to distinguish between “white noise” and, say, “pink noise”, in which bass notes (analogous to large angular scales) have a somewhat greater loudness than treble notes (analogous to small angular scales).

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Using the CMB, we find that the primordial fluctuations were ever so slightly larger in amplitude at large angular scales than they were at smaller ones. Put another way, the primordial cosmic noise is slightly pink.

With these six parameters in hand, we can compute the characteristics not only of the CMB but of any cosmological measurement we’d like to make. We can, for example, compute the age of the Universe: 13.8 billion years (give or take 40 million years).

The single most constraining observation is that of the CMB anisotropy – the minute fluctuations in temperature. However, the standard model of cosmology is consistent with all measurements, from all walks of physics and astronomy.

In short, no matter how we look at the cosmos – with galaxy surveys, through exploding stars, through the abundance of the light elements, through the speeds of galaxies, or through the CMB – we need only the six parameters given above, and known physical processes, to describe the Universe we observe.

What does it mean to be able to describe something so simply and quantitatively? It means that we understand how the pieces of the Universe fit together to form a whole. We understand some deep connections in nature.

It means we can be proved wrong – not by different arguments, but by a better quantitative model that describes more aspects of nature. There are few systems studied by scientists that can be described so simply, completely, and with such high accuracy. We are fortunate that the observable Universe is one of them.

The Little Book of Cosmology by Lyman Page is out now (£16.99, Princeton University Press).

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