More Big Bang

• Big Bang Nucleosynthesis

• Problems with the Big Bang

Big Bang Nucleosynthesis• Around 10-9 s, quarks froze out into protons and

neutrons, note neutrons are unstable, but lifetime is long enough, 15 minutes.

• When did nuclei form? Simplest nucleus is deuterium, D, consists of p+n. Energy to dissociate D is 2.2 MeV, which is 160,000 that needed to dissociate H atom, so temperature should be 1.61053000 K = 5108 K.

• Nuclei started to form when temperature dropped below 5108 K.

Big Bang Nucleosynthesis• At this time, there were lots of p+n around, so it

was easy to make nuclei by adding one p or n at time. For example:

p+n D+, D+p 3He+, 3He+n 4He+

• No stable nuclei with atomic number 5, this mostly stops nucleosynthesis at He.

• Can make 4He+D 6Li+ and 4He+3H 7Li+ , but only small amounts because there is not much D or 3H.

Big Bang Nucleosynthesis

• Measurement of ratios H : 4He : 6Li : 7Li in environments unaffected by any stellar nucleosynthesis are important tests of the Big Bang theory.

Problems with the Big Bang

• The horizon problem

• The flatness problem

• How to fix the problems: inflation

Cosmic Microwave Background

The Universe glows at 2.7 K in every direction.

The temperature is the same to < 0.1%.

Observable Universe

We can only see the parts of the Universe from which light has had time to travel to us.

The Horizon

Horizon Problem

CMB is 0.98lhorzion away

Two antipodal points of CMB are 1.96lhorzion away from each other, but at same temperature within 10-5.

Flatness Problem• In matter and radiation dominated eras, any deviation

of from 1 grows with time.• Friedman equation

• Radiation era: a t1/2 and H t-1, so

• Matter era: a t2/3 and H t-1, so

H 2= 8πG3c2

u− κc2

a2 r c , 02

1−( t )=− κc2

a2 H 2 r c , 02

⇒∣1−∣∝a−2 H −2

∣1−∣∝ t ∝ a 2

∣1−∣∝ t 2 /3∝ a

Scale factor versus time

• Nuclei form at 3 minutes, radiation era ends at 47 kyr, flatness grows by 8109.• Matter dominated from 47 kyr to 9.8 Gyr. Deviation from flatness grows by (9.8109/47,000)2/3 = 3500.• Now universe is flat to 0.02, at 3 minutes must have been flat to 0.02/(8109 3500) = 710-16

Flatness problem

Any tiny deviation from the critical density is amplified over time.

Inflation makes the Universe flat

Inflation is expansion driven by a cosmological constant

In Λ era: a∝eH

it where H i =( 8π GuΛ

3c2 )1/ 2

Flatness: ∣1−∣∝ a−2 H −2∝ e−2H

it

If duration of inflation era is long compared to Hubble time, 1/H, during inflation, then universe exponentially expands and is driven exponentially towards flatness.

InflationSize[cm]

Time [seconds]

Whole observable universe came from a tiny region.

Inflation in GUT

• In Grand Unified Theories (GUT) there was an quantum mechanical field that caused inflation at 10-35 s and lasted for ~100 e-foldings.

• Starting with a strongly curved universe, this would drive the flatness to e-2100 ~ 10-87.

• If inflation ended at 10-33 s, then size of current CMB surface was 0.98lhora = 4 m (a = 810-27).

• At start of inflation, now visible universe had a size of (4 m)e-100 ~ 10-43 m. Horizon distance was 10-27 m, much larger.

Inflation and cosmology

• Inflation solves flatness problem by driving the Universe exponentially towards flatness.

• Inflation solves the horizon problem because the whole universe originally came from a very small area. Thus, the different parts of the CMB were causally connected before inflation began.

• Inflation can be tested by looking at the polarization of the CMB.

Polarization

Electromagnetic radiation consists of propagating electric and magnetic fields

Polarization of CMB

• Density waves produce E-mode polarization patterns.

• Gravitational waves produce B-mode polarization patterns.

BICEP2

Review questions

• Why is it surprising that the microwave background has almost exactly the same temperature in all directions on the sky?

• Why is it surprising that the geometry of the universe is so close to flat?

• What is the best explanation to date of why the Universe is uniform and flat?