29.04.2024

Knowledge

How old is the universe?

We know exactly how old the Science Olympiad umbrella association is: this year, it’s turning 20! An anniversary worth celebrating. But when is the universe’s anniversary? And how many candles should we put on space’s birthday cake? In this article, Physics Olympiad volunteer Yuta explains in five steps why approximately 13.772 billion candles should do.

Intensity of radiation from a black body as a function of its wavelength for different

temperatures. Source: Wikimedia Commons. © Wikimedia

 

Step One: The Big Bang

The leading scientific theory about the creation of the universe is the Big Bang theory. Even though it was the subject of much debate throughout the past century, it ended up being recognized the “standard cosmological model” in 2005. Its idea is that the origin of the universe was an explosion, shortly after which the universe began to expand exponentially, and kept expanding ever since.

Step Two: Black bodies

A black body is a body that absorbs all radiation. Such absorption is due to the thermal agitation which takes place in the body in question and causes the emission of thermal radiation. In other words: the particles which the black body consists of keep moving and interacting, not just with each other but also with incoming radiation particles. They get drawn in and consequently absorbed into a sequence of atomic reactions. Those reactions in turn free particles, which constitute the radiation emitted by the surface of the black body. The famous physicist Max Planck has shown a law describing this radiation, called spectral energy radiance:

where v is the radiation’s frequency, T the temperature, c the speed of the light (300’000 km/s) and kB Boltzmann’s constant (1,38 · 10-23 J/K). The intensity of the radiation emitted by a black body is therefore different for each frequency.

Step Three: The universe as a black body

At the beginning of its existence, the universe was a black body. Indeed, right after the Big Bang, it was extremely dense and, in consequence, had an extremely high temperature and energy level. The temperature of a body is defined by the amount of interactions between its particles. Therefore, a high energy level is also caused by the agitation of the particles that constitute the body, in this case, these particles are simply elementary particles, such as protons, electrons, neutrons, photons, etc.

As a result of the universe being a high-energetic black body, photons, the light particles, weren’t able to move around properly: indeed, they were always getting “trapped” in interactions between other elementary particles, such as atom formations and deformations. In consequence, the light wasn’t traveling freely throughout the universe, as it does in our world. What happened? We shouldn’t forget that, due to its expansion, the universe loses energy and therefore gets colder and less dense. That’s why at some point of its expansion, it stopped being a black body. Specifically, it has been calculated that the universe stopped being a black body at the temperature of 3,000 Kelvin.

 

The idea of the expansion of the universe: as it expands, it loses density and therefore energy. Source: Wikimedia images. © Wikimedia

This transformation is called the recombination. Ever since the recombination, light has been light as we know it, traveling freely at an extremely high velocity (as a reminder, the speed of light is equal to 300’000 km/s) without constantly getting tied up in atomic reactions.

Step Four: Cosmic Background Radiation and the Doppler effect

At the beginning of the 20th century, two astrophysicists, Arno Penzias and Robert Wilson, observed an abnormal background radiation while trying to detect the echo of a satellite’s radar. Turns out, this mysterious radiation background fits perfectly to the properties of the radiation produced during the recombination. In other words, as soon as photons gained the ability to move freely, they created a background of radiation that we can still see nowadays. This is what this background looks like:

Map of the CMB: the red areas are the ones with the highest temperatures and the blue ones with the lowest. Source: WikiMedia. © Wikimedia

We can observe, though, that the radiation’s temperature is not equal everywhere: indeed, some areas are way warmer than others. Some of those fluctuations are due to the fact that the universe wasn’t the same everywhere before the recombination: its density (and consequently the density of atomic reactions happening inside of it and the surface radiation) wasn’t constant. Other fluctuations are caused by the obstacles that the background radiation encounters on its way. Such obstacles can be very different, from galaxies to simple punctual electro-magnetic fields caused by stars or planets.


During one of his experiments, the Austrian physicist Christian Doppler observed a really interesting phenomenon: when the source of a sound is moving, the pitch of the sound emitted changes. It has later been shown that it’s the case not only for sound waves, but for any kind of radiation, including light. Described in a formula, the spectral shift z is given by:

where lobs is the observable wavelength and l0 is the original wavelength.

Step Five: The age of the universe

The background radiation emitted during the recombination should, just like any other radiation, be submitted to Doppler’s effect, as its source, the universe, is in permanent expansion and thus moving! According to experimental measurements, the properties of the CMB perfectly fit the radiation of a temperature of 2,728 K emitted by a black body.

Knowing that the temperature of the universe during the recombination was around 3’000 K, it is possible to determine the spectral shift of the CMB using Doppler’s formula. Knowing the shift, we can approximate the distance that the CMB particles have run and therefore, knowing the speed of light, the lifetime of the CMB (as a reminder, it’s is made out of “light particles”, photons). This lifetime is equal to the age of the universe ever since the recombination.

Now the lingering question is how much time passed between the Big Bang itself and the recombination? In comparison to the timespan after the recombination, that era was pretty short. However, based on experimental data, assumptions about the composition and consequently the density of the universe back before the recombination, astrophysicists managed to calculate that the recombination happened approximately 380,000 after the Big Bang. Everything taken together, the universe is approximately 13.772 billion years old (you can, indeed, see that compared to this huge number 380,000 years are nothing)!

About the author: Yuta Mikhalkin volunteers for Physics in the Science Olympiad media team and studies mathematics in the University of Geneva. She wrote her matura thesis on the history of the universe.

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