particle collider the Bullet Cluster

E X T R A G A L A C T I C
A S T RO N O M Y
STEPHEN M. WILKINS
+ MARK SARGENT

Centaurus A The Cosmic Microwave

Background
 particle collider the Bullet Cluster

LECTURE 4
THE EARLY UNIVERSE

Centaurus A The Cosmic Microwave

Background
 LAST TIME

✦ We solved the Friedmann equation(s) for dust, radiation,

and constant density.

✦ We discussed the historical debate between those who

believed in the steady state theory and those who
supported a hot big bang.

✦ We discussed Olbers’ paradox and its resolution.

 Monday Lecture Tuesday Lecture

Observational Cosmology
The Friedmann Equations
Introduction, the Contents of Galaxies and - Newtonian Derivation of the Friedmann
Week 1
the Expansion of the Universe Equation
- Hubble’s law (again)

Simple Cosmological Models

- Solutions to the Friedmann Equations The Early Universe in the HBBT
Week 2 - Dust Solution - The Cosmic Microwave Background Radiation
- Big Bang vs. Steady State - Formation of the light elements
- Radiation Solution

Dark Energy
Observational Cosmology
Week 3 The discovery of something wrong
- Distances in Cosmology
- The ultimate fate of the Universe
 LEARNING OUTCOMES

In this lecture you will learn about some of the evidence

supporting the big bang theory over alternative models (e.g.
the steady state model).

Today, we will concentrate on two pieces of evidence:

• The Cosmic (Microwave) Background Radiation

(CBR/CMB/CMBR)
• The observed abundances of light elements

Next week we will also discuss to other pieces of

evidence:

✦ The properties (number density) of galaxies

✦ The distribution of galaxies (and AGN)
 LEARNING OUTCOMES

In this lecture you will learn about some of the evidence

supporting the big bang theory over alternative models (e.g.
the steady state model).

Specifically you should be able:

✦ Outline the formation of the Cosmic Background

Radiation (CBR) and explain why it is strong
supporting evidence for the hot big bang theory.
✦ Outline the history of discovery and study of the CBR.
✦ Outline the formation of the light elements.
BARYON TO PHOTON RATIO

In the previous lecture I made the fairly reasonable claim that the
Universe contains at least radiation and (normal) matter. Most of the
energy density of the latter will be Baryons.

It’s useful to ask how the relative contributions of each component

compare today.
BARYON TO PHOTON RATIO

Observations of the background

radiation suggest,

Observations of the number density of

baryons has been found to be,
BARYON TO PHOTON RATIO

Observations of the background

radiation suggest,

Observations of the number density of

baryons has been found to be,

The baryon-to-photon ratio is then,

Technically this is not constant as additional photons are created by stars and
other physical processes. However, by number the contribution is very small
compared to the number of background photons.
We are now going to investigate what happens as we wind back
time in a Universe containing just matter (dust) and radiation.
 THE EARLY UNIVERSE

In the last two lectures we saw, by solving the fluid equation, how the
density in matter and radiation evolve:

We also saw that we can combine these equations to reveal how the
ratio of the densities varies with the expansion,
 THE EARLY UNIVERSE

For now lets assume* that the radiation component of the Universe is
distributed as a black-body.
*We will justify this assumption shortly.

You may/should remember that the energy density of a black-body

distribution is,
 THE EARLY UNIVERSE

Using, and

We can then write,

The temperature of radiation increases as we go back into the early

Universe.
 THE EARLY UNIVERSE

As we go back in time we then expect that the mean energy of

photons will increase.

[Assuming the Universe is currently composed of neutral hydrogen and

radiation with a temperature ~3K what do you think will happen as we
go back in time?]
 THE EARLY UNIVERSE

As we go back in time we then expect that the mean energy of

photons will increase.

[Assuming the Universe is currently composed of neutral hydrogen and

radiation with a temperature ~3K what do you think will happen as we
go back in time?]

Eventually the photons will be sufficiently energetic to ionise the

neutral hydrogen in the Universe.

[Assume that the background radiation forms a continuous distribution

(of photons) up to some maximum energy (minimum wavelength). What
maximum energy is required so that the background radiation can ionise
hydrogen?]
 THE EARLY UNIVERSE

[Assume that the background radiation forms a continuous distribution

(of photons) up to some maximum energy (minimum wavelength). What
maximum energy is required so that the background radiation can ionise
hydrogen?]

For an electron in the ground state we need 13.6 eV to ionise it.

However, we could ionise it by first raising the electron to the first
excited state (10.2 eV) after which we’d need an additional 3.4 eV to
ionise it. So the lowest maximum energy required is 10.2 eV NOT 13.6
eV.
THE EARLY UNIVERSE

A sufficiently dense ionised Universe is

effectively opaque; photons can not travel
far without interacting with (scattering off) a
charged particle. This is Thomson
scattering.

This is analogous to being surrounded by

fog.
THE EARLY UNIVERSE

In the early Universe photons will frequently interact with

protons and electrons leaving them thermally distributed.

Classic XKCD.
 THE EARLY UNIVERSE

Thinking about it the other way round, in an expanding Universe the

early Universe was sufficiently hot (and dense) that no neutral atoms
could form. During this time the Universe was effectively opaque to
radiation.
 THE EARLY UNIVERSE

Thinking about it the other way round, in an expanding Universe the

early Universe was sufficiently hot (and dense) that no neutral atoms
could form. During this time the Universe was effectively opaque to
radiation.

As the Universe expanded it cooled, eventually the temperature was

low enough that neutral atoms could form; this is the epoch of
recombination.

After recombination photons could travel (mostly) unimpeded and

should be observable today.
 COSMIC BACKGROUND
RADIATION

We will now look at the conditions required for recombination.

 COSMIC BACKGROUND
RADIATION

We will now look at the conditions required for recombination.

The simplest estimate we can make involves equating the photon energy to the
hydrogen ionisation energy.

The mean energy of a photon in a black-body distribution is,

so,

[why is likely an overestimate?]

 COSMIC BACKGROUND
RADIATION

[why is likely an overestimate?]

Not only do we not need 13.6

eV, as we noted earlier there
are ~109 more photons than
baryons. Thus, even when the
mean energy of photons has
fallen below 13.6 eV there are
still enough photons in the
high-energy tail to keep the
Universe ionised.
 COSMIC BACKGROUND
RADIATION

An accurate calculation of the decoupling temperature is beyond the

scope of this module. The actual value is ~3000K.
 COSMIC BACKGROUND
RADIATION

An accurate calculation of the decoupling temperature is beyond the

scope of this module. The actual value is ~3000K.

If we have an estimate of the current age of the Universe (for example

using the present day value of Hubble’s parameter) we can estimate the
present day temperature of this radiation.

Based on current constraints on the present day Hubble Parameter and

assuming our simple flat matter+radiation Universe this turns out to be,
 COSMIC BACKGROUND
RADIATION

We can also determine the age of the Universe when the CBR was
released. You will do this in the workshop and should obtain an answer of
the order of a few hundred thousands years*.

*~380,000 years based on current cosmological parameters/model.

 COSMIC BACKGROUND
RADIATION
[Is the existence of this background radiation a unique prediction of
the HBB model?]
 COSMIC BACKGROUND
RADIATION
[Is the existence of this background radiation a unique prediction of
the HBB model?]

NO! Most other models (including a naive steady state) will predict some
form of background radiation, for example made of integrated and
(redshifted) starlight. The difference is that you wouldn’t expect this
radiation to be thermally distributed.

Thus, the discovery of a thermally distributed background radiation (at

roughly the temperature expected) is a unique prediction of the HBB
model.
 COSMIC BACKGROUND
RADIATION
FIRST MEASUREMENTS

Working at Bell Labs in New Jersey,

U.S., in 1964, Arno Penzias and
Robert Wilson were experimenting
with an extremely sensitive antenna
originally built to detect radio
waves bounced off Echo balloon
satellites.

To measure the faint radio sources

they had to remove all the
recognisable effects of interference
from the receiver.
 COSMIC BACKGROUND
RADIATION
FIRST MEASUREMENTS

When they analysed their data they

found a low, steady mysterious
noise that persisted.

This noise was was 100 times more

intense than they had expected
and was evenly spread over the sky
suggesting its was extragalactic in
nature.
 COSMIC BACKGROUND
RADIATION
FIRST MEASUREMENTS

At the same time, Robert Dicke, Jim Peebles, and David Wilkinson, were
preparing to search the background radiation that was predicted to occur if
the Big Bang model was correct.
 COSMIC BACKGROUND
RADIATION
FIRST MEASUREMENTS
Penzias and Wilson found out about plans of Dicke et al. and
contacted the group. They both agreed to publish their results
at the same time.
 COSMIC BACKGROUND
RADIATION
FIRST MEASUREMENTS
Penzias and Wilson found out about plans of Dicke et al. and
contacted the group. They both agreed to publish their results
at the same time.

Penzias and Wilson ultimately

won a Noble prize for their
(somewhat accidental) role in
discovering the cosmic
background radiation.
 COSMIC BACKGROUND
RADIATION
FIRST MEASUREMENTS

In addition to its existence Dicke, Peebles, and Wilkinson (and others) predicted
that the CBR contained a lot more information offering the ability to constrain
the composition (and distribution) of matter/radiation in the early Universe.
COSMIC BACKGROUND
RADIATION
COBE

In 1989 NASA launched the Cosmic

Background Explorer (COBE).

COBE was designed to measure

both the black-body curve of the
CBR and map how the CBR
changes across the sky.
 COSMIC BACKGROUND
RADIATION
COBE

COBE revealed the CBR was

distributed consistent with a perfect
black-body.
 COSMIC BACKGROUND
RADIATION
COBE
Perhaps more importantly though, COBE revealed that the CBR was not uniform.
This is essentially an image of the Universe at recombination (~380,000 years ABB).

These areas are cooler than the average

These area are hotter than
the average
 COSMIC BACKGROUND
RADIATION
COBE
The differences in temperature are actually telling you about the
density, hotter areas have a higher density of material.

These areas are colder than the average

These area are hotter than
the average
 COSMIC BACKGROUND
RADIATION
COBE
Importantly the baryons are not spread uniformly! We will discuss
this more in Lecture 7 as it has implications for structure
formation.
These areas are colder than the average
These area are hotter than
the average
COSMIC BACKGROUND
RADIATION
WMAP AND PLANCK

COBE was followed, in 2001, by NASA’s

Wilkinson Microwave Anisotropy Probe
(WMAP) and in 2009 by ESA’s Planck
Satellite.

The facilities have also been

complemented by a range of ground-
based experiments, these are useful for
getting higher-resolution images of
small patches of the sky.
COSMIC BACKGROUND
RADIATION
WMAP

WMAP
COSMIC BACKGROUND
RADIATION
COBE

COBE
COSMIC BACKGROUND
RADIATION
PLANCK

PLANCK
COSMIC BACKGROUND
RADIATION
COSMIC BACKGROUND
RADIATION
FLUCTUATIONS

The main thing the fluctuations tell us is that the early

Universe was not entirely smooth.

If the Universe was smooth, structures (galaxies, stars,

planets, us) would never have formed.
 COSMIC BACKGROUND
RADIATION
FLUCTUATIONS

By doing a more detailed

analysis of the anisotropies it
is possible to extract a lot of
information from
observations the CMBR.

[Those taking the Introduction to

Cosmology and Early Universe
modules in Y4 will learn about
the anisotropies in more detail.]
 COSMIC BACKGROUND
RADIATION
FLUCTUATIONS

This information includes: the baryon-to-

photon ratio, the baryon-to-matter ratio,
and the geometry of the Universe.

[Those taking the Introduction to

Cosmology and Early Universe
modules in Y4 will learn about
the anisotropies in more detail.]
 COSMIC BACKGROUND
RADIATION
FLUCTUATIONS

However, it actually turns out that the

fluctuations in the CBR can’t be fully
explained by our simple model Universe
containing just matter and radiation (and
no curvature).

We will talk about this problem and its

resolution in Lecture 6.

[Those taking the Introduction to

Cosmology and Early Universe
modules in Y4 will learn about
the anisotropies in more detail.]
THE ORIGIN OF THE LIGHT ELEMENTS

If we roll back time beyond recombination the Universe will

correspondingly get hotter and denser.

Going beyond recombination the Universe’s temperature will

eventually be so high that atomic nuclei can not form.
THE ORIGIN OF THE LIGHT ELEMENTS

At this point the Universe will contain free protons, neutrons, electrons
and other subatomic particles. As the Universe cools at some point
these are able to bind into nuclei allowing the formation of the light
elements. This is big bang nucleosynthesis and is responsible for the
formation of light elements.
THE ORIGIN OF THE LIGHT ELEMENTS

To understand the formation of nuclei we first need to understand the

formation of neutrons. Neutrons have several import properties:

• Protons are (slightly) lighter than neutrons.

• Free neutrons are unstable and decay into protons [and what
else?].
• There exist stable isotopes of light elements, and neutrons
bound into them do not decay.
THE ORIGIN OF THE LIGHT ELEMENTS
NEUTRON FREEZOUT

At early times the number of particles (either protons or neutrons) will

be in thermal equilibrium and should satisfy a Maxwell-Boltzmann
distribution, in which the number density N is given by:
THE ORIGIN OF THE LIGHT ELEMENTS
NEUTRON FREEZOUT

The relative densities of neutrons and protons will then be,

Given how close they are in mass this will be approximately unity as
long as the temperature is much greater than the mass difference,
THE ORIGIN OF THE LIGHT ELEMENTS
NEUTRON FREEZOUT

The reactions converting neutrons to protons and vice versa are:

Assuming the temperature is high enough these reactions proceed in

equilibrium.
THE ORIGIN OF THE LIGHT ELEMENTS
NEUTRON FREEZOUT

When the temperature reaches*,

the rate becomes longer than the age of the Universe. At this
temperature the relative abundances of protons and neutrons became
fixed.

*The determination of this factor is beyond the scope of

this module.
THE ORIGIN OF THE LIGHT ELEMENTS

As the Universe cooled it becomes possible for light elements to be

created via nuclear fusion.

However, between neutron freeze-out and

these reactions taking place some fraction
of neutrons decay. This reduces the
neutron fraction.
THE ORIGIN OF THE LIGHT ELEMENTS

As the Universe cooled it becomes possible for light elements to be

created via nuclear fusion.

However, between neutron freeze-out and

these reactions taking place some fraction
of neutrons decay. This reduces the
neutron fraction.

[This forms the basis of one of the questions in the first

assessed problem set, albeit assuming a different value for
the neutron half-life.]
THE ORIGIN OF THE LIGHT ELEMENTS

If we assume all the remaining neutrons

get locked up in Helium the number
density of helium-4 will be,

We also know that the mass of helium is about four proton masses, so
the fraction of the total mass in helium-4 is,
THE ORIGIN OF THE LIGHT ELEMENTS

In reality, a range of light elements are

created (including various isotopes) in this
process (though overwhelmingly most of
the mass is in helium and hydrogen).

The big bang theory allows us to calculate

predictions for the abundances of these
elements.

These abundances can be measured

observationally providing a very strong test
of the BBH.
 THE ORIGIN OF THE LIGHT ELEMENTS

In fact, they don’t just give evidence

the for the BBH they actually allow us
to constrain the cosmology.
Specifically, they allow to us to
constrain baryon-to-photon ratio.

Measurements of these abundances

agree exactly with predictions based
on the baryon-to-photon ratio
measurement from the CBR.

This superb agreement can not be

explained by steady state theories.
THE ORIGIN OF THE LIGHT ELEMENTS
 SUMMARY

So far, we have talked about the formation of the Cosmic Background

Radiation. This is essentially a signature of the Universe when it was
only a few hundred thousands years old. We then talked about the
historical discovery of the Cosmic Background Radiation.

We also talked about the formation of the light elements and how the
abundances predicted by the hot big bang model match observations.