• Cosmic Microwave Background

• Primodial Nucleosynthesis

• The Early Universe

SPECIAL END OF SEMESTER LECTURE

The Cosmic Microwave Background (CMB)

Observational discovery of the CMBThe hot big bang modelWhat can we learn from the CMB?

Penzias & Wilson (Bell-Labs)

I : THE OBSERVATIONAL DISCOVERY OF THE COSMIC MICROWAVE BACKGROUND

Arno Penzias & Robert Wilson (1964) Attempted to study radio emissions from our

Galaxy using sensitive antenna built at Bell-Labs

Needed to characterize and eliminate all sources of noise

They never could get rid of a certain noise source… noise had a characteristic temperature of about 3 K.

They figured out that the noise was coming from the sky, and was approximately the same in all directions…

II : THE HOT BIG BANG MODEL

Penzias & Wilson had discovered radiation left over from the early universe…The hot big bang model… Developed by George Gamov He suggested that the universe started off in

an extremely hot state. As the Universe expands, the energy within

the universe is spread over in increasing volume of space…

Thus the Universe cools down as it expands

From Black Body Radiation Eq. (4.5) Energy Density ~T4

But =(# photons/L3)h =(# photons/L3)(hcR4

T~1/R

T(t)=T(to) [R(to)/R(t)] = T(to) (1+z)

If T= 2.7 K today at z=1 it was 5.4 K

Why did they suggest this model? If the early Universe was hot (full of energy), a

lot of features of the current universe could be explained…

Could explain where the matter that we see around us came from (baryogenesis occurred well within first second)

Could explain the observed ratio of elements (nucleosynthesis occurred within first few minutes)

Predicted that there should be left over radiation in the present Universe…

A brief look at the stages of the Universe’s life…

Most crude description… t=0: The Big Bang For first 400,000ys,

universe is an expanding “soup” of tightly coupled radiation and matter

After 400,000yrs, radiation and matter “decouple”. They are free to flow and expand independently of each other.

This is the left over radiation that we see now as the CMB…

III : THE COSMIC BACKGROUND EXPLORER (COBE)

The COBE mission Built by NASA-Goddard Space Flight Center Launched Nov. 1989 Purpose was to survey infra-red and microwave

emission across the whole sky. Primary purpose – to characterize the CMB.

Had a number of instruments on it: FIRAS (Fair infra-red absolute

spectrophotometer) DMR (Differential Microwave Radiometer) DIRBE (Diffuse Infrared background Experiment)

Our Galaxy observed by the DIRBE instrument on COBE

Back to the CMB: DMR map of the microwave sky…

Map of the microwave sky (frequency of 50GHz)… We’re looking at the CMB The map is very uniform. Means that the CMB is extremely isotropic (i.e.

the same in every direction we look) Supports the idea that the Universe is isotropic

(one of the basic cosmological principles). In fact, if we measure the universe to be

isotropic, and we’re not located at a special place in the Universe, we can also deduce that the Universe is homogeneous!

The spectrum of the CMB (FIRAS)

Spectrum has precisely the shape predicted by the theory… So-called “Blackbody” spectrum Characteristic temperature of 2.728K

FLUCTUATIONS

Left with a random pattern of fluctuations in the CMB… correspond to temperature differences of 30 millionths of a Kelvin

What are these fluctuations… The early universe was very close to being

perfectly homogeneous But, there were small deviations from

homogeneity… some regions were a tiny bit colder and some were a tiny bit hotter.

When matter and radiation decoupled, this pattern of fluctuations was frozen into the radiation field.

We see this nowadays as fluctuations in the CMB.

Why are the fluctuations important? Before decoupling, fluctuations in the radiation

field also meant fluctuations in the mass density

After decoupling, these small fluctuations in density can get amplified (slightly dense regions get denser and denser due to gravity).

These growing fluctuations eventually collapse to give galaxies and galaxy clusters.

So, by studying these fluctuations, we are looking at the “seeds” that grow to become galaxies, stars, planets, people, dogs, cats etc.

The geometry of the Universe…

From the cosmic microwave background…We know how far apart these “blobs” should be on average.Can use this knowledge to make a giant triangle.

us

Distance todecouping epoch

Result: The universe is flat In terms of density, =1 to better than

1% How do we reconcile this with our

direct measurement of the density?

Primordial Nucleosynthesis

The structure of “normal” matterNucleosynthesis and the hot big bangThe density of baryonic matter in the Universe, B

III : The accelerating Universe

Huge clue came from observations of Type-1a Supernovae (SN1a) Very good “standard candles” Can use them to measure relative

distances very accurately

Type 1A Supernovae

What produces a SN1a? Start off with a binary star system One star comes to end of its life – forms a

“white dwarf” (made of helium, or carbon/oxygen)

White Dwarf starts to pull matter off other star… this adds to mass of white dwarf (accretion)

White dwarfs have a maximum possible mass… the Chandrasekar Mass (1.4 MSun)

If accretion pushes White Dwarf over the Chandrasekar Mass, it starts to collapse.

The results…

This program gives most accurate value for Hubble’s constant H=65 km/s/Mpc

Find acceleration, not deceleration! Very subtle, but really

is there in the data! Profound result!

Dark Energy

There is an “energy” in the Universe that is making it accelerate Call this “Dark Energy” This makes up the rest of the gravitating

energy in the Universe, and causes it to be flat! Completely distinct from “Dark Matter”

Remember Einstein’s cosmological constant…? Dark Energy has precisely the same effect as

Einstein’s cosmological constant So, he was probably right all along!

I : SOME BACKGROUND: THE STRUCTURE OF MATTER

Atom is made up of… Nucleus (very tiny but contains most off

mass) Electrons (orbit around the nucleus)

Atom held together by attraction between positively-charged nucleus and negatively-charged electrons.

The nucleus is itself made up of: Protons, p (positively charged) Neutrons, n (neutral; no charge) Collectively, these particles are known as baryons p is slightly less massive than n (0.1% difference) Protons and neutrons bound together by the strong

nuclear force (exchange of “gluons”)

Number of protons determines element: Hydrogen – 1 proton Helium – 2 protons Lithium – 3 protons Beryllium – 4 protons Boron – 5 protons Carbon – 6 proton …

Number of neutrons determines the isotope… e.g., for hydrogen (1 proton), there are three isotopes

Normal Hydrogen (H or p) – no neutrons Deuterium (d) – 1 neutron Tritium (t) – 2 neutrons

There’s one more level of complexity… not needed for this discussion, but generally useful to know:

Protons & Neutrons are made up of trios of quarks Up quarks & Down quarks Proton = 2 up quarks + 1 down quark Neutron = 1 up quark + 2 down quarks

There are other kinds of quarks (strange, charm, top, bottom quarks) that make up more exotic types of particles…

II : NUCLEOSYNTHESIS IN THE EARLY UNIVERSE

Nucleosynthesis: the production of different elements via nuclear reactionsConsider universe at t=180s i.e. 3 minutes after big bang Universe has cooled down to 1 billion K Filled with

Photons (i.e. parcels of electromagnetic radiation) Protons (p) Neutrons (n) Electrons (e) [also Neutrinos, ghostly photon-like particles]

Protons and Neutrons can fuse together to form deuterium (d)

p+n->d

But, deuterium is quite fragile…

The first three minutes…

Before t=180s, Universe is hotter than 1 billion degrees. High-T means that photons carry a lot of energy Deuterium is destroyed by energetic photons as

soon as it forms

After the first 3 minutes…

But, after t=180s, Universe has cooled to the point where deuterium can surviveDeuterium formation is the first step in a whole sequence of nuclear reactions: Helium-4 (4He) formation:

pHedt

ptdd

4

An alternative pathway to Helium…

This last series of reactions also produces traces of left over “light” helium (3He)

pHedHe

nHedd

43

3

Further reactions can give Lithium (Li)

Reactions cannot proceed beyond Lithium due to the “stability gap”

LitHe 74

If this were all there was to it, then the final mixture of hydrogen & helium would be determined by initial number of p and n. If equal number of p and n, everything would

basically turn to 4He… Pairs of protons and pairs of neutrons would team up into stable Helium nuclei.

Would have small traces of other species But we know that most of the universe is

hydrogen… clearly there is something more interesting going on.

Neutron decay

Free neutrons (i.e., neutrons that are not bound to anything else) are unstable! Neutrons spontaneously and randomly turn

in to protons

Half life for this occurrence is 15 mins (i.e., take a bunch of free neutrons… half of them will have decayed after 15 mins).

epn

While the nuclear reactions are proceeding, supply of “free” neutrons is decaying away.So, speed at which nuclear reactions occur is crucial to final mix of elementsWhat factors determine the speed of nuclear reactions? Density (affects chance of p/n hitting each

other) Temperature (affects how hard they hit) Expansion rate of early universe (affects how

quickly everything is cooling off).

Full calculations are complex. We need to: Work through all relevant nuclear reactions Take account of decreasing density and

decreasing temperature as Universe expands Take account of neutron decay

Feed this into a computer… Turns out that relative elemental abundances

depend upon the quantity BH2

Here, B is the density of the baryons relative to the critical density.

crit

BB

Bh2

Mpcskm

Hh

//1000

From M.White’s webpage, UC Berkeley

So, by measuring the abundance of H, D, 3He, 4He, and 7Li, we can Test the consistency of the big bang model Use the results to measure the quantity Bh2

We can use the spectra of stars and nebulae to measure abundances.Why is it not straightforward to then use these measurement to test the big bang theory and measure Bh2 ?

Bh2

Results

All things considered, we have Bh20.015.

If H0=65km/s/Mpc, h=0.65 B0.036

036.0B

III : WHERE DO THE OTHER ELEMENTS COME FROM?

Big Bang Nucleosynthesis produces most of the hydrogen & helium observed today.But what about other elements? There are naturally occurring elements as

heavy as Uranium Some elements (e.g., Carbon, Nitrogen,

Oxygen) are rather plentiful (1 atom in every 105 atoms)

We believe that these elements were formed in the cores of stars (long after the big bang happened).

In the normal life of a star (main sequence)…

nuclear fusion turns Hydrogen into Helium

In the late stages of the life of a massive star…

Helium converted into heavier elements (carbon, oxygen, …, iron)

At end of star’s life, get an orion-like structure (see picture to right)

What’s special about iron? Iron has the most stable nucleus Fusing hydrogen to (eventually) iron

releases energy (thus powers the star) Further fusion of iron to give heavier

elements requires energy to be put in… Can only happen in the energetic

environment of a supernova explosion So, all heavier elements are created during

supernova explosions

The Early Universe

What happened before nucleosynthesis?

I : SOME TERMINOLOGY

Our terminology… Very Early Universe: from BB to t=10-35s Early Universe: from t=10-35s to t=3mins

The study of the early universe: No observations to constrain theories… .. but, the basic physics governing the universe is well

understood and tested in laboratories on Earth (particle accelerators).

The study of the very early universe: Still no observations to constrain theories… … and the basic physics gets less and less certain as

one considers times closer and closer to the big bang.

II : THE TEMPERATURE OF THE UNIVERSE

Recap – the universe started off very hot and cooled as it expanded.In fact, the temperature in inversely proportional to the scale factor

The temperature is crucial in determining what goes on in the early universe

RT

1

At a given temperature, each particle or photon has the same average energy:

kB is called “Boltzmann’s constant” (has the value of kB=1.3810-23 J/K)

As the Universe cools down, the average energy per particle/photon decreases.

TkE B2

3

Particle production…

Now, suppose two photons collideIf they have sufficient combined energy, a particle/anti-particle pair can be formed.

So, we define Threshold Temperature: the temperature above which particle and anti-particle pairs can be created.

Different particles have different threshold temperatures (since masses differ) Protons : T1013K Electrons : T 5109K

Bthres k

mcT

3

2 2

Above the threshold temperature… Continual creation/destruction of

particles and anti-particles (equilibrium)

Below threshold temperature… Can no longer create pairs Particles and anti-particles annihilate Small residual of particles (matter)

left over

III : MATTER AND FORCES

We also need to discuss the structure of matter and the nature of forces in a little more detail.Firstly, matter:

Two types of matter particles… Those based on quarks, and those that are not!

Forces: There are four fundamental forces in the Universe Each has an associated “force particle” (a “boson”)

Electromagnetic force (mediated by photons) Electric & Magnetic fields are familiar in everyday life!

Strong nuclear force (mediated by gluons) Holds the nuclei of atoms together (i.e., binds quarks

together)

Weak nuclear force (mediated by W and Z particles)

Responsible for neutron decay

Gravitational force (mediated by gravitons) Gravitons have never been detected… still theoretical

In the high-temperature early universe, these forces were all unified (in the same way that electricity and magnetism are unified today).As universe cooled down, they started to “decouple” from each other.

When forces “decouple”

IV : TIMELINE FOR THE BIG BANG

The Big Bang! (t=0)

The “Planck” Epoch (t<10-43s) Particle Horizon is c t<10-35m All fundamental forces are coupled Very difficult to describe the universe at this

time – something completely outside of our experience.

Full theory of Quantum Cosmology needed to describe this period of the Universe’s life

Such a theory doesn’t yet exist…

End of the Planck Epoch (t=10-43s) Gravity decouples from other forces Classical General Relativity starts to describe

gravity very well Gravitons cease their interactions with other

particles… start free streaming through space

Produces a background of gravitational waves (almost completely redshifted away in present day)

The Unified Epoch (t=10-43 - 10-35s) Two forces operate

Gravity (described by GR) All other forces (described by so-called Grand Unified

Theories; GUT) Baryogenesis

Slight asymmetry between particle & antiparticle Get more matter than antimatter by 1 part in 109

Same as ratio of number of baryons to CMB photons today

This produces the matter dominance that we have today! At end of epoch, GUT force splits into Strong and

Electroweak force.

The quark epoch (10-35 –10-6 s)Universe consists of soup of Quarks Gluons Electroweak forces particles Photons Other more exotic particles

Electroweak force splits at about t=10-11sQuark epoch ends with “quark-hadron phase transition” quarks pull themselves together into particles

called hadrons (baryons are a subclass of this).

Hadron Epoch (t=10-6 – 10-4 s) Particle horizon D=102 – 104 m Soup of protons, neutrons, photons, W &

Z particles + exotics Matter/anti-matter asymmetry from GUT

era gives baryon/anti-baryon asymmetry. End of epoch given when temperature

falls below proton threshold temperature

Lepton Epoch (t=10-4 – 15 s) Abundant production of electron/positron pairs Equilibrium between protons and neutrons

Epoch ended when temperature falls below electron threshold temperature.

Proton/Neutron ratio frozen in at this point.

And this takes us up to Nucleosynthesis, which you know all about!!

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