The Big Bang

• The Big Bang

• Tempature and density history of the Universe

• Cosmic Background Radiation

• Contents of the Universe

Big Bang

• Our conclusion that the Universe actually began at some point in time is based on extrapolating back the observed Hubble expansion of galaxies

• Is there any other evidence?

Big BangIf the Universe was smaller in the past, but had roughly the same amount of matter and energy, then the density of matter and energy must have been higher in the past.

The Universe was hotter in the past

• Temperature is proportional to the average kinetic energy per molecule

lower T higher T

kTmvK2

3

2

1 2 k = Boltzmann constant = 1.3810-23 J/K = 8.6210-5 eV/K

Big Bang

Big Bang

Big Bang

Big Bang

First protons and neutrons at about 1 second.Helium nuclei formed at about 100 seconds.Observed ratio of Helium/Hydrogen matches Big Bang prediction.Universe is opaque.

Opaque

Big Bang

At one million years, electrons combine with nuclei and atoms form.Universe becomes transparent.

Transparent

Transition occurs at around T = 3740 K.

Cosmic Microwave Background

The Universe glows at 2.7 K in every direction.

CMBDiscovered by Arno Penzias and Robert Wilson in 1960-65 while employed by AT&T’s Bell Labs and attempting to find the source of noise in an antenna used to bounce telephone signals bounced off metallic balloons high in the atmosphere.

They won the Nobel prize in 1978.

CMB

Radiation is a blackbody spectrum originally emitted at 3000 K but red shifted by a factor of 1000.

Three pieces of evidence for the Big Bang model

• Hubble expansion: galaxies are moving away from us with speed proportional to distance.

• The cosmic microwave background: a 2.7 K glow seen in all directions.

• The ratio of Helium to Hydrogen in gas clouds unaffected by stars.

Cosmic Microwave Background

Small fluctuations are due to sound waves at recombination.

• Properties of the CMB are set by physics of ionized plasma at ~4000 K – well known physics.

• Temperature variations in the Cosmic Microwave Background (CMB) are observed to be about 0.0003 K, agrees with calculations of sound waves propagating through plasma.

• The expected physical size of the hot/cold regions can be calculated. What can we do with this?

Fluctuations in CMB

• We can draw triangles!

• Angles in triangles in curve space do not equal 180°.

• This affects the angular size

Angular size in curved space

d

D

d

D

RdR

D

)/sin(

d

D

RdR

D

)/(sinh

• In positively curved Universe, fluctuations appear larger than calculated

• In negatively curved Universe, fluctuations appear smaller

• In flat Universe, fluctuations appear at expected size

Angular size of CMB fluctuations

Curvature of the Universe

The curvature of the Universe is determined by the density parameter 0

C0

Measurement of CMB fluctuations gives

02.002.10

0 < 1 negative curvature

0 > 1 positive curvature

Contents of the Universe

• Normal matter – Stars– hot gas– anything made of atoms

• Total is 4% of C

Rotation curve of Milky Way

Mass of the Milky Way

Dark Matter

• Dark – it doesn’t produce light (any kind)

• Does have mass, produces gravity

• Nature is unknown

• Most likely it is elementary particles

Contents of the Universe

• Normal matter is 4% of C

• Dark matter is 23% of C

• Total of normal and dark matter is M = 0.3

• But, we need 100% of C since Universe is flat

• Remainder, 73%, is “Cosmological constant” or “dark energy” = 0.7

Contents of the Universe

Why can't we see radiation produced during the first 300,000 years after the Big Bang?

1. It was absorbed soon after it was emitted.

2. It hasn't reached us yet.

3. It has been deflected by black holes.

4. It passed by our part of the universe a few billion years ago.

Review Questions

• Give three pieces of evidence for the Big Bang model.

• What will happen to the Universe if the density is less than the critical density?

• A few seconds after the big bang did hydrogen atoms exists? Why or why not?