the big bang. olbers’s paradox why is the sky dark at night? if the universe is infinite, then...

The Big Bang

Olbers’s Paradox

Why is the sky dark at night?

If the universe is infinite, then every line of sight should end

on a star

Finite, and no edge

The Expanding Universethe galaxies are NOT moving through space.

Space is expanding, carrying the galaxies along!

Things that are smaller than galaxy clusters are not expanding!

QuickTime™ and a decompressor

are needed to see this picture.

Hubble’s data (1929) Riess et al (1996)

Georges LeMaitreGeorge Gamow

Ralph Alpher

Predictions of Big Bang Theory

• The Universe is homogeneous and isotropic (very smooth)

• But not too smooth…• The ratio of H/He (about 75% H, 25% He)• Trace abundances of D, 3He, Li, Be• The cosmic microwave background radiation

The Universe is Homogeneous and Isotropic

Homogeneous: looks the same at all locationsNot isotropic

Isotropic: looks the same in all directionsNot homogeneous

On the largest scales, Univese is homogeneous and isotropic!



Interactions among elementary particles of the Standard Model

Matter particles

Carriers of forces

The very early Universe:

< 10-43 seconds after Big Bang singularity: The Planck EpochAll for fundamental forces unified into one forcerealm of GR, string theory, and ???

10-43 to 10-36 seconds: Grand Unification epoch gravitation separates from unified electroweak and strong force

10-36 to 10-32 seconds (???): Inflationary epoch universe expands faster than speed of lightlarge-scale structure is established

10-36 to 10-12 seconds: electroweak epoch Universe cools off to 1028 Kstrong and electroweak forces separatetriggers inflationary epoch (?)

10-12 to 10-6 seconds: quark epoch quark-gluon plasma

10-6 to 1 second: hadron epoch

quark-gluon plasma cools until hadrons (protons, neutrons) form

T = 1 GeV

hadrons and antihadrons annihilate each other (mostly)

1 to 10 seconds: lepton epoch

leptons and antileptons annihilate each other

T = 1 MeV

10 seconds to 380,000 years: the photon epoch

Photons and electrons exist, continually recombining

Universe still sufficiently hot to ionize H atoms

3-20 minutes: Nucleosynthesis

380,000 years: Recombination

380,000 to 150 million years: Dark ages

150 million years: Reionization

Big Bang Theory

Expansion & Cooling

The First DayThe First Day

10-8 10-6 10-4 10-2 1 102 104

LEPTON ERA RADIATION ERAHADRONQUARK

boundfree

3q 2qq q

qq p,n,π….

Matter: 109 + 1 (p)Anti-matter: 109 (p)

(e±,μ±,γ….)

qq ↔ E¯ pp ↔ E¯

pp → 2γ¯

prot

on f

reez

e-ou

t

p, n : 1e±, γ : 109

e+e− ↔ E

elec

tron

fre

ezou

t

Time (s)

e+e− → 2γ

e+, e−, photons

2p2n

→ H

e4

Photons dominate

p, e− 1:1p, He4 12:1 (3:1)p, γ 1:109

1 day

H f

usi

on

p:n → 1:1 7:1

ν d

ecou

ple

Temperature (K)1012 1010 1081014

¯ n d

ecay

The First Three Minutes: The Nucleus-building Era

At t=3 minutes, T=1 billion K:

Fusion of protons and the remaining free neutrons:

* Formation of 2H (Deuterium) & 4He * End up with ~92% 1H, 8% 4He * Also end up with traces of 2H, 3He, Li, Be, B

This is what the oldest stars are observed to be made of!

Free neutrons decay into protons + electrons in about 10 minutes => p + e-

379,000 years old: First light escapes; Universe already has structure (light still arriving today)

Early fluctuations become denser condensations of matter

First stars form after ~150 million years (“reionization”)

Galaxies and galaxy clusters form, according to the floorplan laid out at 379,000 years

The Universe today: lots of stars and galaxies!

Observations of the UniverseObservations of the Universe

• 4He is extremely common: ~25% everywhere• even oldest stars have ~24% He• far too much to come from stars alone

It was made in the Big Bang, before stars existed!

High temp & density lower temp & density

Like the core of a star

Radiated light like a star

Expanding, cooling

The Universe cooled down to the temperature at which nuclei exist & nuclear fusion occurs!



Up to 1 second, thermal equilibrium:After 1 sec, expansion is faster than reaction: freeze-out of p/n = 6/1

1-600 seconds: n decay:QuickTime™ and a

decompressorare needed to see this picture.


are needed to see this picture.At about 100 seconds:Neutrons are safe in a nucleus: D formation, p/n = 7/1



3-20 minutes: nucleosynthesis


are needed to see this picture.Net result leaves very little D (part in ~105)

Calculations based on binding energies

10-6 sec < t < 1 sec

Pair-production of e+ + e-, high energies (kT) maintain equilibrium:

n + e+ p + e

p + e- n + e

As T drops:

(Average) photon below 2me = 1.02 MeV @ 1.1x1010 K

e+-e- annihilate, too few left to drive n-p conversion

n,p can’t be maintained in equilibrium for T 1010 K

~

Using 1010 K as “characteristic” T when equilibrium ends…

Nn / Np = e-1.3 MeV / kT = e-1.5 0.22

So:

Nn = .22/(1 + .22) = 0.18 and Np = 1/(1 + .22) = 0.82

i.e., 18 n’s for every 82 p’s when p-n ratio “set” (@ t = 1

sec) 1 sec < t < 250 sec

Enough high E photons (E > 2.2 MeV) to disintegrate deuterons

baryons only between t 3-20 minutes

4 min < t < 10-20 min

n + p 2H + (“stabilizes” n’s)

Then: 2H + (n,p) 3H, 3He 4He

BUT: 4He wont accept more n, p as n , p = 0

Won’t work anyway: No stable nuclei with A = 5

Can we build on 4He nuclei with larger nuclei than n, p?

2H + 4He 6Li + and 6Li + n 7Li +

and 3H + 4He 7Li +

but 7Li + n 8Li + 8Be + - + e

8Be 2 4He in 10-15 sec!

How about …

~

3He + 4He 7Be +

but 7Be + n 8Be

and then 8Be 2 4He (in 10-15 sec!)

or 7Be + p 8B + 8Be + + + e (in 0.5 sec)

but then 8Be 2 4He (in 10-15 sec!)

or 4He + 4He 8Be +

but then 8Be 2 4He (in 10-15 sec!)

Or …

BB nucleosynthesis “stops” at 4He

(& tiny amounts of others)

Problems: Must somehow “jump over” A = 5 and 8

(Thank you, stars!)

What is the composition of the universe at t = 20min?

Complication: free n’s aren’t stable

n p + - + e with T½ = 10.3 min

So: 110 n’s & 690 p’s 55 4He’s + 580 p’s

% 4He by mass = (4 x 55)/(4x55 + 1x580) = .275

i.e., the BB made universe 73% H and 27% He (by mass)

As nucleosynthesis didn’t start until 4m, some of the n’s “set” at t = 1 sec didn’t survive to be fused into 4He

Nn(at 4m) = Nn(at 1s) e- t ln2 / T½ = 18 e- 4(.693)/10.3 = 13.75

Synthesis starts with 13.75 n’s for every 82 + 4.25 = 86.25 p’s

~

379,000 years later…

• Universe cooled enough to have H atoms = recombination of protons and electrons

• Atoms DO NOT absorb photons: light escapes!

• Space is expanding: optical wavelength photons redshifted to microwave

• Predicted by Gamow and Alpher• Discovered by Penzias and Wilson (1968)• Nobel went to P & W

Looking Back in Time: the Early Universe

The more distant the objects we observe, the further back into the past we are looking.

we see a glowing

wall of bright fog

Prediction: The universe once glowed like a star.The early glow of the Universe should still be visible!

expansion

cooling

BigBigBangBang

densehot NowNow

thincool

atomic transparent

us

hot glowing fogPhotons keep getting absorbed

redshiftz = 1000 microwaves

orangelight

3000 K

380 ,000 yr

Ionized,foggy

The Cosmic Background Radiation

R. Wilson & A. Penzias

The radiation from the very early phase of the universe is still detectable today

discovered in mid-1960s

Blackbody radiation with a temperature of T = 2.73 K

The Cosmic Background Radiation (2)After recombination, photons can travel freely through space.

Their wavelength is only stretched (red shifted) by cosmic expansion.

Recombination:

z = 1000; T = 3000 K

This is what we can observe today as the cosmic background radiation!

Extremely uniform!!!

Our galaxy is here

3 billion light years

(~20% to “the edge”)

Sloan Digital Sky Survey: Univese is clumpy!

1990: Anisotropy discovered

1990 2003

The Universe’s Baby Picture: WMAP(Wilkinson Microwave Anisotropy Probe)

Photons that were emitted when Universe was 379,000 years old.

Fluctuations in the temperature (= structure) of the Universe appeared when it was very young

Many waves ofdifferent sizes,Directions & phases,all “superposed”

Sound waves :red/blue = high/lowgas & light pressure

Water waves :high/low level ofwater surface

Temperature and density fluctuations are minimal:

BUT IMPORTANT!

Very uniform and smooth: no stars or galaxies yet! (379,000 years)Smooth to 1/100,000Patchiness due to not perfectly smooth distribution of matter (“sound waves”)

The History of the Universe

Universe expands as time passes

Un

ive

rse

coo

ls d

own

as

time

pa

sse

s

P+

e=at

oms

Light can escape!



transparent

Universe is ionized (still today) but transparent because it is very diffuse

ReionizationAfter less than ~ 1 billion years, the first stars form.

Formation of the first stars

Ultraviolet radiation from the first stars re-ionizes gas in the early universe

Reionization



Lyman-alpha and cosmology





Quasars all have similar power spectra

HI cloud near quasar - safely assume that the light being absorbed is 1216A

Many clouds between us and the quasar leads to a “forest” of Ly-alpha lines

Lyman-alpha Forest



But what if there is so much HI that it blocks it completely?Extremely dense HI is only present in very early universe. This can only happen at very high redshift!

Gunn-Peterson Trough

• One of the few examples of a real prediction in astrophysics!! (1965,2001)

• Many clouds of HI between us and quasar at z = 6 or so

• Ly-alpha absorption causes a “forest” of lines

• “trough” predicted for when H is very dense (at very high redshift)



Gunn-Peterson Trough

The discovery of the trough in a z = 6.28 quasar, and the absence of the trough in quasars detected at redshifts just below z = 6 presented strong evidence for the hydrogen in the universe having undergone a transition from neutral to ionized around z = 6.



From SDSS: Quasar spectra. Note the height of the spectral lines on the left side of the spectrum. The bottom image shows the first Gunn-Peterson trough ever discovered.

Further away

Why is this cool?

• How much HI is out there, and how is it distributed?

• Ly-alpha regions trace out dark matter, because the H atoms are concentrated by DM’s gravity

The Cosmological Principle

1) Homogeneous: On the largest scales, the universe should have the same physical properties throughout

Every region has the same density, expansion rate, luminous vs. dark matter

2) Isotropic: On the largest scales, the universe looks the same in any direction that one observes.

You should see the same large-scale structure in any direction.

3) Universality: The laws of physics are the same everywhere in the universe.

the big bang. olbers’s paradox why is the sky dark at night? if the universe is infinite, then...

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