1. Three big problems in Cosmology
The Horizon Problem (Isotropy Problem).
Why is the CMB temperature so close to uniform? Why are there correlations between points outside the horizon?
The Flatness Problem.
Why is Ω0 so close to 1?
The Monopole Problem.
Why are there no magnetic monopoles, no strings, no topological defects? (all exotic things which can in principle arise in the ‘primordial soup’)

2. #1: The Horizon Problem
Radiation from event A which happens at recombination has just now gotten to the Earth.
Same for an event B in the opposite direction.
The two events could not ever have been in causal contact.

3. In the first image, at T=100,000 years, the red circles are the horizon scale at that time.
The second image is at the current time. We see a larger piece of today’s universe (the big red circle). Today, our horizon has about 128,000 regions the size of the red circle in the first picture.
How is it that they all know to be at the same temperature to 1/105?

4. Even more puzzling is the fact that there is ‘correlation’ on scales bigger than the horizon at the time of recombination.
How can something this big exist,
if the horizon at that time was this big?
or this big

5. #2: The Flatness Problem
The Universe is near the critical density today. That is hard to understand because it is an unstable situation.
If we were to be a little less dense than critical, then the Universe will decelerate a little less than if we were exactly critical. Thus the density would decrease faster leading to a very low density universe today.
Any difference between the actual density and the critical density grows.
Therefore in the past the density must have been almost exactly critical for us to even be close now.

6. The matter density grows as a-3 the curvature term like a-2
The matter density grows as a-3 the curvature term like a-2. The ratio of the curvature to matter terms goes like
This ratio grows with time. If we are now 2% away from Ω0=1 then in the past the denstiy parameter must have been almost precisely one.

7. #3: The Monopole problem
Particle physics predicts that if everything was created from a hot soup at the time of the big bang, there should be at least a few magnetic monopoles around. Why are there none?
One additional thing to explain
Where did the fluctuations that seeded the CMB anisotropy and the structure we see today come from? If the Universe started completely smooth there is not enough time for the CMB fluctuations to have developed! We see acoustic peaks – what’s the source?

8. The Solution: Inflation
Inflation is the idea that the Universe underwent a short period of very fast (exponential) expansion at very early times.
This idea solves all four of the problems we have discussed.

9. 5 x 1011 dinar note. Yugoslavia, 1993
Inflation
5 x 1011 dinar note. Yugoslavia, 1993

10. How it solves the horizon problem
If there is no inflation, areas of different properties have expanded but are still within our horizon so we can see them today.

11. If there is inflation, things have expanded so that today we only see the three triangles. Everything else in the picture has expanded to much larger than our own horizon.

12. before inflation areas A and B are in causal contact

13. How it solves the flatness problem
As the universe expands manyfold, and the region within our horizon gets to be a smaller and smaller fraction of the whole Universe, the surface becomes flat over the region we can examine -- the observable Universe.
It is thought that the a expanded by a factor of >1050.

14. How it solves the monopole problem
If magnetic monopoles or other rare items get diluted as the universe expands during inflation magnetic monopoles may have diluted so much that there are none expected within our horizon

15. How it solves the problem of how to seed the fluctuations we see in the CMB
The seeds of structure are also provided by quantum mechanics! Tiny quantum fluctuations before and during the inflationary process itself are amplified by inflation and seed the acoustic oscillations that we see in the CMB

17. The Early Universe: Four Forces
Four known forces appear to explain the physics we see on scales from the entire Universe to the insides of a neutron.

18. On the largest scales gravity dominates
On large scales, only gravity and electromagnetic fields operate.
Because there are both positive and negative electric charges and they are in equal number almost everywhere, gravity is usually the dominant force at large scales

19. On atomic scales the electromagnetic force is dominant
In an atom, the positively charged nucleus attracts the negatively charged electrons. Gravity is less by ~1040.

20. Particles like protons and neutrons are NOT fundamental!
The strong force
Particles like protons and neutrons are NOT fundamental!
The are composed of quarks (there are six of these – various combinations of them make up things like protons and neutrons and others [but not electrons!])
The strong force binds quarks into the nucleons. The residual of this forces binds nucleons together into atomic nuclei.

21. The weak force
It is the weak force that causes a neutron to decay into a proton, and an electron and an antineutrino. It is very short range and very weak.
The weak force is involved in exotic interactions at the subatomic level. Some types of particles – such as neutrinos – interact only via gravity and the weak force. The hypothesized particle(s) that make up dark matter are thought to be of this type but much more massive, and are often generically referred to as WIMPs (Weakly Interacting Massive Particles)

22. Forces and the exchange of particles
The1940s gave rise to the idea that the forces are actually carried by exchanging ‘virtual’ particles. In the case of the electromagnetic forces, the exchange particles are photons. Photons are mass-less and EM forces have an infinite range.
In the case of the weak force the exchange particles are ‘intermediate vector bosons’ whose rest mass is non- zero. This is the reason that the weak force has a finite range.
The strong force is the exchange of gluons, also with mass and a finite range.
Gravitation is the exchange of gravitons – mass-less particles postulated to exist but not directly observed.
Many of these concepts are complex and challenging to grasp, and as before analogies give us at least a little sense of the underlying physics:
Virtual Force Carriers =The Pillow Fight in Space!
two people throwing pillows at each other get pushed apart...
...but extending this to attractive forces is a bit more difficult. Perhaps they are fighting over one pillow? 

23. The unification of forces
‘Spontaneous Symmetry Breaking’: WTF?
Analogies to the rescue (again!)
The snowflake: Both hydrogen and oxygen atoms are rather symmetric when they are isolated. The electric force which governs their actions as atoms is also a symmetrically acting force. But when their temperature is lowered and they form a water molecule, the symmetry of the individual atoms is broken as they form a molecule with 105 degrees between the hydrogen-oxygen bonds. When they freeze to form a snowflake, they form another type of symmetry (typically a 6-sided hexagonal symmetry at 60 degrees) and the symmetry of the original atoms has been lost. Since this loss of symmetry occurs without any external intervention, we say that it has undergone spontaneous symmetry breaking.
For very high energy interactions, above 100 GeV, weak and electromagnetic forces become indistinguishable. This happens because at these energies the force-carrying virtual particles for the weak force lose their mass and behave like photons.
When this happens the forces are said to be unified into the electroweak force. When this unification happens we say that “the symmetry is restored.”
In the 1970s it was proposed that the same should happen with the strong force at energies above 1014 GeV. This idea suggest that all 3 forces (weak, strong, electromagnetic) can be described by a ‘grand unified theory’ (GUT).
Perhaps all four forces are unified above 1019 GeV...or so some theories suggest.

24. Unification of forces

25. The Early Universe
When the universe was less than seconds old, the temperature was so high that interactions were happening at above 1019 GeV. All four forces were unified.
At seconds gravity was frozen out with a spontaneous symmetry breaking.
Further expansion cooled the Universe to 1014 GeV at seconds. At this time a second spontaneous symmetry breaking took place when the strong force was frozen out.
The inflationary period is thought to have began at the time when the strong force froze out.

26. False vacuum
It is perhaps easiest to think of this period of inflation as a phase change in the energy state of the early universe.
WaterIce is a phase change for example
but a better analogy is perhaps freezing rain:
in this state the rain is already well below freezing in temperature but is still liquid, and only turns to ice upon impact. The impact triggers the transition ; one might say the water is ‘falsely’ in a liquid state at the start
As the universe transitions from a high energy ‘false vacuum’ state to a lower energy state, the liberated energy goes into particle creation and heating... (we’ll see how in a moment)
Before the strong force decouples the Universe may have been in an unstable state called a “false vacuum.” There may have been an energy associated with the ‘inflaton’ field which had a non-zero value.
The universe settles into the “true vacuum, oscillating back and forth and generating particles and heating.
first at high energy state “false vacuum”
then into the transition expansion over 10^-32 second to the true vacuum state
may have cooled down to as low a 3K
then as the universe settled in it was reheated to 10^27K
As the universe expands exponentially, it cools
False Vacuum
Inflation begins

27. The end of inflation
At the end of inflation, the Universe was reheated to 1027K at t=10-32 seconds.
By seconds the Universe had cooled to 1015K or 100 GeV followed by a final spontaneous symmetry breaking and a freeze out separating the weak from the electromagnetic force.

28. The Heisenberg Uncertainty Principle
At very small scales, quantum mechanics takes over from normal ‘Newtonian” physics.
One of the predictions of quantum mechanics is the Heisenberg Uncertainty Principle which states that there is an intrinsic uncertainty in the energy of a system if looked at for a short time so that:
This is not a failing of instruments or an oversight, it is a fundamental reality.

29. using Einstein’s relation between mass and energy we can convert this to
This means that during short intervals of time, the amount of matter in a system is not defined to smaller than a given amount.
Therefore for a brief interval a particle and it’s antiparticle can spontaneously appear and disappear!

30. For an electron:
this is the time an electron and positron can “exist” spontaneously. A proton is 2000 times heavier so the time is 1/2000 as long.
Virtual pairs are happening all the time and the effects of this phenomenon has been experimentally measured. Really!

31. Energy of the Vacuum and Virtual Particles
The idea of the spontaneous creation of particle- antiparticles pairs is fundamental to modern quantum mechanics, and also fundamental to the theory of inflation and indeed to our entire description of the early universe (as we shall see shortly). Because it is rooted in quantum mechanics, this idea is directly testable in laboratory work (unlike inflation!) Here are two lines of evidence in support of this idea...

32. The Lamb Shift
If the vacuum is filled with virtual particle-antiparticle pairs then what happens to a ‘real’ object – a hydrogen atom say – when it is in vacuum? According to modern quantum theory, the interaction between the actual electron in the hydrogen atom, and the virtual particles in the vacuum should cause a ‘splitting’ of energy levels in the atom. This was experimentally verified in the late 1940s by Willis Lamb and collaborators; it is known as the Lamb shift.

33. The Casimir Effect
Also in the late 1940s, Hendrik Casimir predicted that two parallel plates held very close together in a vacuum should experience an attractive force. The basic idea is that the confined region between the plates limits the number of available oscillation modes in the virtual particles in the vacuum. Virtual particles outside the plates are not similarly limited; the net effect is a subtle imbalance of forces between the gap region and the outside, which pulls the plates together. This effect was not measured with precision until the 1990s. Again data matches predictions – the seething sea of virtual particles in the vacuum is real!

34. Particle - antiparticles are being created and annihilated
all the time

35. Two photons with enough energy can produce real electron-positron pairs. The gamma rays effectively pay back the energy deficit created by the virtual particles, and the gamma rays are removed instead of the virtual particles, which become real! The reverse of this interaction annihilates particles and their antiparticles.

36. During inflation virtual particles can become real particles.

37. Right after inflation
At the end of inflationary epoch (10-32 seconds) , the inflation process left the Universe hot and full of particle-antiparticle pairs and high energy photons (gamma, i.e. γ, rays) .
At this point particle-antiparticle pairs would annihilate, generating γ-rays which in turn regenerated particle-antiparticle pairs. Because of the many interactions, the matter and radiation was initially in equilibrium and at the same temperature.

38. Right after inflation
This could go on except that as the universe expanded, the radiation energy was dropping. The drop in the radiation energy is due to redshifting: the energy of a photon is inversely proportional to its wavelength, so as the wavelengths get larger the energies get smaller. The very close interactions between particles and photons at this time keeps everything at the same temperature – and so as the photon energy drops the whole Universe is cooling off...

39. Threshold Temperature
Each particle in a particle-antiparticle pair has a certain mass, and hence corresponds to a certain energy. If the total mass is M=M1+M2 the minimum total energy of the two γ-rays must be E=Mc2 in order for pair production to happen!
For each type of particle, a temperature would be reached where the photons could no longer generate particle-antiparticle pairs. This is the threshold temperature. The more massive particles have a higher threshold temperature, since more mass = more energy.

40. Baryogenesis and Leptogenesis
After t=10-6 second the temperature was 1013 K and collision energy of about 1 GeV. This point is the threshold for forming protons and neutrons (baryons, a.k.a. nucleons).
No new nucleons are produced but proton-antiproton pairs and neutron-antineutron pairs continue to annihilate. This reduces the number of baryons and increases the numbers of γ-rays.
When the universe is 1 second old, the temperature is 6×109 K and this is the threshold for electron-positron pairs (leptons). These also mostly annihilate further adding to the total numbers of photons.

41. Particle-antiparticle asymmetry
If particles and antiparticles had been formed during inflation at exactly the same rate, nearly all the particles would have annihilated leaving only those which had not found partners, and an equal amount of matter and antimatter. Over cosmic time, the matter and antimatter would annihilate – leaving more gamma rays at later times (and not much of anything else!). This is clearly not the case...
We observe that there are roughly 109 photons for each matter particle (almost all the photons are in the CMB).
This means that the asymmetry is 1/109. Stated another way, for every 109 antiprotons, there were protons formed during inflation. Of these 109 were turned into photons and the other one is still around.

42. Particle-antiparticle asymmetry
The leading candidate explanation for the particle anti-particle asymmetry stems from something called CP violation (short for charge-parity symmetry violation). The ‘violation’ here is that certain subatomic particles do not behave identically under the product of parity transformation (left to right, i.e. mirror images) and charge conjugation transformations (particles to antiparticles or vice versa). This effect was verified experimentally in 1964 by UC physicist James Cronin (Nobel laureate, 1980).

43. Nucleosynthesis: Deuterium and Helium
Before the temperature fell below 6×109 K (time = 1 second), the number of neutrons and protons was within a factor a few of equal. Protons were somewhat favored because they are slightly less massive, and the ratio is readily calculable using physics verifiable in labs. Also, free neutrons tend to decay – with a half life of 10.5 minutes – but in the early universe the decay of neutrons could be replenished from collisions between protons and electrons.
But after 1 second, electron-positrons reached threshold, the number of electrons decreased and so the neutron number began to drop as neutrons decayed, and the density of all particles species is dropping through ongoing but rapidly diminishing annihilations.

44. Nucleosynthesis: Deuterium and Helium
Before all the neutrons could decay they combined with protons to form deuterium.
However, deuterium is fragile and is easily destroyed by the γ radiation. This meant that quite a few neutrons simply decayed to protons.
When the universe was 3 minutes old, the energy of a typical photon has dropped to sufficiently low levels that deuterium was no longer being destroyed; at this point the proton to neutron ratio is about 7:1.

45. Nucleosynthesis: Deuterium and Helium
As the amount of deuterium, 2H, begins to increase, collisions between deuterium and further protons and neutrons starts the assembly (through fusion) of tritium 3H and 3He and 4He. Some small amounts of lithium and beryllium are also created at this time.
These fusion reactions have all stopped by about 15 minutes; at this point temperatures and densities have dropped to levels that are too low to support any fusion reactions.

47. The Primordial Neutrino Background
A large background of primordial neutrinos must also be present. Neutrinos decouple from the other components of the Universe as leptogenesis ends. This is very much like the cosmic microwave background, but in neutrinos not photons! This background would have a temperature of 1.9K and stem from a time when the universe was 2 seconds old.
These will be very hard to detect and at the moment there are no prospects of being able to do so.
The neutrino background would be slightly cooler than the CMB, because the cooling of the photons is mitigated by ongoing electron-positron annihilations, after neutrinos decouple.

48. Gravity Waves
The predictions of big bang nucleosynthesis have been experimentally verified by measuring the ratios of 2H, 3He and 4He, and lithium and beryllium in ‘primordial’ gas in the the universe. While this verifies our theoretical understanding of the evolution of the universe after about t=1 second, earlier times are still the subject of much theoretical debate. However...
If the inflation picture is right, the same quantum fluctuations that seed the structure seen in the CMB will create gravity waves.
These gravity waves will have wavelengths spanning all scales to greater than the horizon scale.

49. The Polarization of the CMB
The measurement of the polarization of the Cosmic Microwave Background is one way to look for a predicted signal from inflation.
There are multiple possible sources of polarization – one source is primordial gravity waves! So, if we can measure CMB polarization, we should be able to experimentally constrain the epoch of inflation (10-35 seconds after the Big Bang!)

50. Limits on primordial gravity wave background

51. What does ‘polarized’ mean?
Light has electric and magnetic fields transverse to the direction of motion. These fields can are always orthogonal to each other and can be otherwise arbitrarily oriented.
However, we can always decompose the orientation of transverse waves in light into two components perpendicular to each other, e.g. an arbitrary orientation is just a mixture of horizontal and vertical

52. Polarizers only permit one polarization to pass
Reflection and scattering very often induce polarization in light.
Horizontal polarizer
Vertical polarizer
Polarizers only permit one polarization to pass

53. Reflection and scattering very often induce polarization in light.
Polarizers only permit one polarization to pass – an effect often used in glare-reducing sunglasses!

54. Why do we expect to see polarization in the CMB?
Remember the picture of a single sound wave making a temperature pattern on the sky?

55. Scattering at recombination
An electron sitting at recombination sees a pattern of hot and cold as a density wave goes by.

56. Scattering at recombination
...because the polarization is derived from the temperature variations in the material around the scattering electron, there is a correlation between the temperature variations and the polarization. Also only certain patterns of polarization are possible, and they are more complicated than the simple linear polarization shown in previous slides
In particular, the ‘B-Mode’ polarization from scattering is zero.
E-Mode
B-Mode

57. Searching for B-Mode polarization
We expect to see the E-mode pattern of polarization in the CMB and it has been seen.
If we saw B-mode polarization it would mean it came from a process different than the processes at recombination.
Gravity waves in the space between here and the CMB source can turn some of the E-mode polarization into B-mode!

58. Predicted CMB anisotropy signal10
100
1000
0.01
0.1 1
Multipole l
δT = [l(l+1)Cl/2π]1/2 [µK]

59. WMAP 22 GHz polarization

60. WMAP 90 GHz polarization

61. Polarization Signal from WMAP

62. The Quad Experiment the South Pole

63. QuAD results from last year

64. Limits on primordial gravity wave background