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## What is the redshift of the Cosmic Microwave Background (CMB)?

Last week, as I mentioned in this blog here, I had an article on the Cosmic Microwave Background’s accidental discovery in 1965 published in The Conversation. Here is a link to the article. As of writing this, there have been two questions/comments. One was from what I, quite frankly, refer to as a religious nutter, although that may be a bit harsh! But, the second comment/question by a Mark Robson was very interesting, so I thought I would blog the answer here.

This article on the Cosmic Microwave Background was published in The Conversation last Thursday (23rd July 2015)

Mark asked how we know the redshift of the CMB if it has no emission or absorption lines, which is the usual way to determine redshifts of e.g. stars and galaxies. I decided that the answer deserves its own blogpost – so here it is.

## How does the CMB come about

As I explain in more detail in my book on the CMB, the origin of the CMB is from the time that the Universe had cooled enough so that hydrogen atoms could form from the sea of protons and electrons that existed in the early Universe. Prior to when the CMB was “created”, the temperature was too high for hydrogen atoms to exist; electrons were prevented from combining with protons to form atoms because the energy of the photons in the Universe’s radiation (given by $E=h \nu$ where $\nu$ is the frequency) and of the thermal energy of the electrons was high enough to ionise any hydrogen atoms that did form. But, as the Universe expanded it cooled.

In fact, the relationship between the Universe’s size and its temperature is very simple; if $a(t)$ represents the size of the Universe at time $t$, then the temperature $T$ at time $t$ is just given by

$T(t) \propto \frac{ 1 }{ a(t) }$

This means that, as the Universe expands, the temperature just decreases in inverse proportion to its size. Double the size of the Universe, and the temperature will halve.

When the Universe had cooled to about 3,000K it was cool enough for the electrons to finally combine with the protons and form neutral hydrogen. At this temperature the photons were not energetic enough to ionise any hydrogen atoms, and the electrons had lost enough thermal energy that they too could not ionise electrons bound to protons. Finally, for the first time in the Universe’s history, neutral hydrogen atoms could form.

For reasons that I have never properly understood, astronomers and cosmologists tend to call this event recombination, although really it was combination, without the ‘re’ as it was happening for the first time. A term I prefer more is decoupling, it is when matter and radiation in the Universe decoupled, and the radiation was free to travel through the Universe. Before decoupling, the photons could not travel very far before they scattered off free electrons; after decoupling they were free to travel and this is the radiation we see as the CMB.

## The current temperature of the CMB

It was shown by Richard Tolman in 1934 in a book entitled Relativity, Thermodynamics, and Cosmology that a blackbody will retain its blackbody spectrum as the Universe expands; so the blackbody produced at the time of decoupling will have retained its blackbody spectrum through to the current epoch. But, because the Universe has expanded, the peak of the spectrum will have been stretched by the expansion of space (so it is not correct to think of the CMB spectrum as having cooled down, rather than space has expanded and stretched its peak emission to a lower temperature). The peak of a blackbody spectrum is related to its temperature in a very precise way, it is given by Wien’s displacement law, which I blogged about here.

In 1990 the FIRAS instrument on the NASA satellite COBE (COsmic Background Explorer) measured the spectrum of the CMB to high precision, and found it to be currently at a temperature of $2.725 \text{ Kelvin}$ (as an aside, the spectrum measured by FIRAS was the most perfect blackbody spectrum ever observed in nature).

The spectrum of the CMB as measured by the FIRAS instrument on COBE in 1990. It is the most perfect blackbody spectrum in nature ever observed. The error bars are four hundred times larger than normal, just so one can see them!

It is thus easy to calculate the current redshift of the CMB, it is given by

$z \text{ (redshift)} = \frac{3000}{2.725} = 1100$

and “voilà”, that is the redshift of the CMB.  Simples 😉

## Our most detailed view of the early Universe

Yesterday (Thursday the 21st of March 2013), the European Space Agency (ESA) released its first results from the Planck satellite. The picture is shown below.

This picture is a picture of the temperature differences in the earliest image we can obtain of the baby Universe. These temperature differences, technically called “anisotropies” are what have led to the structure we see in today’s Universe. They provide a powerful way for us to determine all kinds of things about our Universe, including its age, geometry, and what makes up our Universe.

## COBE

The first satellite to provide us with a view of these anisotropies was COBE, the Cosmic Background Explorer, a NASA satellite launched in the late 1980s. In 1992 it released this image, which caused a sensation.

The reason the image looks so “fuzzy” is because the detail with which COBE could see was limited, it only had a resolution of 7 degrees (a 7 degree patch, about 14 full Moons across, was the smallest patch it could see). The day it was released happened to be the day that Sir Arnold Wolfendale, who was then the “astronomer Royal” England, was visiting Cardiff, where I was finishing up my PhD. The press were constantly ringing the department to speak to him, and of course this was a time before mobile phones so the press kept the university’s switchboard pretty busy that day fielding calls for him.

## Onwards to WMAP

Some 10 years later, a more detailed map was provided by NASA’s WMAP satellite. WMAP (Wilkinson Microwave Anisotropy Probe) had a much better resolution that COBE, as the image below shows.

Between COBE and Planck were a number of important experiments such as BOOMERANG (a ballo-borne experiment) and DASI (based at the South Pole and led by John Carlstrom of the University of Chicago where I was based at the time) which gave some very important information, but I think it is fair to say that it was WMAP that heralded in the era of what we now call “precision observational cosmology”. Using technical analyses of the WMAP image shown above, cosmologists have been able to determine the age of the Universe (13.7 billion years), its geometry (flat), and even that only some 5% is made up of ordinary matter, with about 28% being made up of the mysterious “dark matter” and some 67% made up of the even more mysterious “dark energy”.

## Why launch Planck?

Planck was launched in March 2009 by the European Space Agency. It was actually launched on the same rocket which launched the Herschel Space Observatory which I blogged about here. Planck has a number of improvements over WMAP, and over the next few years results will be released of measurements WMAP did not have the capability to make. But, its first result is its map of the anisotropies. As this fantastic article from the New York Times explains, there are a number of confirmations of our already accepted theories in this first image, but also a number of things which will require us to re-think some things we thought we knew.

For example, initial analysis of the Planck image suggests the Universe is 13.8 billion years old, not 13.7 as calculated by the WMAP data. Also, it has determined the composition of the Universe to be 4.9% normal matter, 27 dark matter and 68% dark energy, slightly different from values determined by WMAP. The value for how quickly the Universe is expanding is also found to be different, WMAP determined a value of 67 km/s/Megaparsec and Planck determines a value of 69 km/s/Megaparsec. Some of the features in the WMAP image which some argued were an artifact of the way the image was produced are still present in the Planck image, which has been produced with an entirely different satellite and processed with an entirely different method. This suggests some of these features are, in fact, real.

A lot more analysis of even this first image will be done over the next several months, and Planck will continue to make measurements over the next several years to refine the image shown above, as well as to make measurements of things like the polarisation of the radiation coming from this earliest view of the Universe.

I will leave you with this wonderful graphic from the above mentioned New York Times article.

There has never been a more exciting time to be a cosmologist!