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Introduction to Astrophysics

Lecture 18: Cosmology: the Hot Big Bang

In this lecture we will be studying what happens in the early stages of the Universe’s evolution.

Things to remember from the last lecture:

The Universe is currently expanding.

There are three possible types of Universe: open, critical and closed. It is not too clear which if any describes our Universe, whose expansion is apparently currently accelerating!

Nevertheless all models share a common feature, which is that the Universe started out arbitrarily small.

The Friedmann cosmologies

Closed

Critical

Open

Time

Siz

e

What happens at the early stages?

In the early stages the Universe is a very dense environment, as the material is crammed into a much smaller volume.

NB: The Universe is probably infinitely large (though because of the finite speed of light we can only ever see part of it). However just because it is infinitely big doesn’t mean it can’t change size!

What happens at the early stages?

The young Universe was also very hot. To see this we must consider what happens to photons of light in an expanding Universe.

As the Universe expands the wavelength of light is stretched, moving it towards the long wavelength part of the spectrum.

What happens at the early stages?

So, the photons in the young Universe must have had much shorter wavelengths.

This corresponds to them having a higher energy, and hence a higher characteristic temperature.

Temperature is proportional to 1/size.

When the size is very small, the temperature is very high.

What happens at the early stages?

Nowadays, the photons of light in the Universe comprise a very small part of the total mass-energy of the Universe.

But the energy of a photon is proportional to its frequency, and so the photons contributed much more energy early on.

In fact, it is believed that during the early stages the total mass-energy of the Universe is dominated by radiation rather than by normal matter (protons, electrons etc).

What is `temperature’?

The temperature of a gas is a measure of the energies of the individual particles: the higher the temperature the more energetic the particles are.

The same is true of photons of light. If the temperature is hotter that means that the typical photons are more energetic.

Convenient energy units

A Joule is not a very good unit for measuring the energy of a photon, as it is so small. Much more useful is an electron-volt (eV).

1 eV = 1.602 x 10-19 J

It is a nice unit because photons in the visible part of the electromagnetic spectrum have energies around 1 eV.

Physical processes in the early Universe

The types of physical process that can take place depend on how the energy of photons of radiation compares to characteristic physical scales of matter.

The typical binding energy of electrons in atoms is about 10 eV. For example the binding energy of the electron in a hydrogen atom is 13.6 eV.

The typical binding energy of protons and neutrons in nuclei is of order 1 MeV. For example about 7 MeV is required to smash a helium nucleus into its constituent protons and neutrons.

One MeV = one million eV

Nucleosynthesis

When typical photon energies exceed a few MeV, it is impossible for nuclei to exist in the Universe, as photons will immediately smash them.

Temperature: about 1010 Kelvin

Time: about 1 second after the Big Bang

As the Universe expands and cools, the photon energies become less, and nuclei form in the Universe for the first time.

George Gamov

Cosmic cookery

“Take a collection of protons and neutrons. Heat to 1010 Kelvin and mix well. Leave to cool for a second, then serve …”

Because protons are lighter, there are more of them than neutrons.

The most stable light nucleus is Helium-4, which has the highest binding energy. It is made up of two neutrons and two protons.

Almost all the neutrons finish up in Helium-4. The leftover protons are hydrogen nuclei. (NB a hydrogen nucleus is just a proton.)

The Big Bang predicts about 75% hydrogen and 25% helium, which is exactly what is observed. This is the primordial gas from which the first stars are made!

From nuclei to atoms

After the nuclei form, there are still no atoms in the Universe, because their binding energy is much less and the photons are still energetic enough to destroy them. But eventually the cooling is enough for atoms to form and survive.

Temperature: about 3000 Kelvin

Time: about 400,000 years after the Big Bang

The Cosmic Microwave Background

Once atoms form, the radiation can no longer interact with them. [c.f. the photoelectric effect]

The leftover radiation continues to cool and now, ten billion years or so later, we can detect it using observatories such as the COBE satellite. The radiation is mainly in the microwave region of the spectrum, corresponding to a temperature of about 3 Kelvin. It is the cosmic microwave background.

The Cosmic Microwave Background

In a very real sense, the cosmic microwave background is the left-over heat from the Hot Big Bang. Its discovery in 1965 by Penzias and Wilson was the death-knell for the Steady State theory.

Nowadays, we study the variations in temperature of the microwave background, which were first detected in 1992 by COBE. Although the variations are only tens of microKelvin in size, they are thought to be the precursors of galaxies.

The state of the art in cosmic microwave background measurements is the Wilkinson Microwave Anisotropy Probe (WMAP), a NASA mission which reported its first results in February 2003.

Microwave background

map at 94 GHz.

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The Cosmic Microwave Background

At Sussex we are involved in a European Space Agency mission, the Planck Surveyor satellite, to be launched in 2007.

It will provide by far the most accurate mapping of the cosmic microwave background ever.

The Very Early Universe

What happened within the first second?

Answer: no one knowsOne popular idea, known as inflation, is that the Universe underwent a burst of extremely rapid acceleration in its earliest stages. This can explain several otherwise puzzling features about our Universe.

Concerning the instant of the Big Bang itself, currently we have next to no idea what was going on then.

Summary

The Universe started out in a very hot dense state, though we don’t understand how.

After about one second, it was cool enough that nuclei were first able to form.

After about three hundred thousand years, the first atoms formed and the microwave background radiation is left over.

After perhaps a billion years, galaxies and stars first form and we’re on the way to life as we know it.

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And that’s it ...

You’ve learnt about:

The history of Astronomy Light and gravity Solar System properties and formation Star properties, birth, life and death Nebulae, galaxies and large-scale structure The Hot Big Bang

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