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# Cosmology

In 1964, American astronomers Robert Wilson and Arno Penzias were analyzing radio telescope data when they came across what appeared to be persistent background noise that they could not get rid of. What they had found was not "noise", but rather one of the most important discoveries in the history of cosmology. It was dubbed the Cosmic Microwave Background (CMB)—low-frequency radiation that seems to come from the universe itself.

Image Credit: NASA/WMAP

Further analysis revealed that the CMB had a peak wavelength of $$\SI{1.06}{\milli\meter}.$$ If this radiation is coming from the universe all around us, use Wien's law to estimate its temperature (in $$\si{\kelvin}$$).

Details

• Wien's law is $$\lambda_\text{max} T = \SI{0.0029}{\meter\cdot\kelvin}.$$

It appears as if the cosmic microwave background radiation is emitted by a very cold object, just above absolute zero. Often, you hear astrophysicists refer loosely to the temperature you just calculated as the temperature of the universe itself. Let's explore what they mean.

Several missions staged over the past several decades have collected successively higher-resolution CMB data. For example, in the early 21st century, Wilkinson Microwave Anisotropy Probe (WMAP) collected data from an orbit near Lagrange point L2, $$1.5$$ million kilometers from Earth, away from any human or atmospheric disturbances. It pointed its sensors across the sky, collecting an emission spectrum from points in every direction with an angular resolution of $$0.3^\circ$$.

Here is WMAP's result displayed using a Mollweide projection, which incidentally, is a common projection used to display the surface of the Earth:

When you look at this WMAP image of the CMB, how much of the sky are you observing?

The CMB radiation is not in the visible part of the spectrum. To create an image of the CMB, color is assigned to the peak wavelength of each measurement—blue areas are colder; red areas are warmer than average.

After processing, we can see the contrast in the image corresponding to small temperature variation from point to point. The temperature difference between a blue pixel and a red pixel is $$\SI{10^{-6}}{\kelvin}.$$

Given how small the temperature variation is, what does this image tell us about the universe?

Although the images of the CMB are constructed by detecting microwaves in the present day, we know that light that travels from distant places in the universe to form images of objects in the past. In later quizzes we will take on the issue of CMB anisotropies; in this quiz, we want to work out when (approximately) and from what the CMB photons were emitted.

To understand the origin of this radiation we will first consider something we already understand—the Sun. The Sun consists of a hot plasma—gas that is so hot the electrons in it have separated from their nuclei, so that negative electrons and positive nuclei can move independently from one another.

In the Sun, the gas is hydrogen, so the nuclei are just single protons. Electrons and protons may meet and recombine, but often separate as the energy fluctuates.

Which state of hydrogen has the greater potential energy?

The Sun's energy arrives on the Earth as a stream of photons.

Where have the photons we see come from?

Hydrogen gas is transparent; however, plasma is opaque to light. In the plasma, Hydrogen nuclei and free electrons block radiation by absorbing it and re-emitting it in a random direction.

Imagine what would happen if we took a section of the Sun and cooled it down. What would happen to the ratio of plasma to Hydrogen atoms?

We know that the Sun's plasma contains a lot of photons that are constantly being absorbed and re-emitted. If the Sun were to instantaneously cool down so that the plasma quickly turned to Hydrogen gas, all the photons trapped inside would be able to escape.

The total energy carried by all of this radiation is immense. Lucky for us, this is not likely to happen. However, something like it did happen once.

Let's come back to the universe as a whole and assume that the Cosmic Microwave Background radiation we detect today was produced by some large, luminous object in the early universe.

Thinking back to Hubble's Law, what happens to radiation emitted by an object in the early universe before it can reach us today?

The universe is expanding, so all of the matter we see today was contained within a much smaller volume in the early universe. As a result, it was denser and hotter. In fact, we now believe it was filled with a plasma much like the Sun's—opaque to photons. As the universe cooled below about $$\SI{3000}{\kelvin},$$ protons captured electrons to form Hydrogen, and the universe quickly became transparent.

This process, called recombination, is accompanied by the release of a large amount of radiation trapped in the opaque plasma. Let's consider whether Cosmic Microwave Background we see today could be drastically red-shifted radiation released during this transition.

Find difference $$\Delta \lambda$$ between the peak wavelength of radiation emitted from a universe-filling plasma at $$\SI{3000}{\kelvin},$$ and the peak wavelength of cosmic microwave background today.

Details

• The CMB today has a wavelength of around $$\SI{1.06}{\milli\meter}.$$
• Express your answer as a ratio $z = \frac{\Delta \lambda}{\lambda_0}$ where $$\lambda_0$$ is the original wavelength emitted at recombination. You may recall that this ratio $$z$$ is simply called the redshift and appears in the Doppler shift formula.

Astronomers use $$z$$-values as a measurement of time. The light we collect today from highly redshifted, distant objects was emitted billions of years ago; thus, high redshifts correspond to much earlier times. The $$z$$-value you just calculated corresponds to a time just $$380000$$ years after the big bang.

In a homogeneous universe, recombination occurs nearly simultaneously everywhere in the Universe. This would explain why the CMB radiation is not localized in one direction, but instead appears to come from every direction. Cosmological models similarly predict a redshift of photons emitted during recombination close to your estimate in this quiz. This is our current theory of the origin of the CMB.

The big bang occurred $$13.7$$ billion years ago, so the cosmic microwave background is a tool for peering into the very early universe. In the remainder of this chapter, we will periodically return to observations of the CMB to help us assess the amount of matter it contains and uncover its ultimate fate.

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