Lecture 15● Pick up graded quiz 4. Corrections due Thursday.● Midterm and Quiz 3 corrections will be returned

Thursday● Updated schedule on web:

– This week: cosmology, 2 lectures– Tuesday Dec 5: Quiz 5, on cosmology– Dec 5: life, connections between big and small– Dec 7: begin review. Return graded Quiz 5.– Monday Dec 11, 7-9 pm, Roessler 66: finish

review. Quiz 5 corrections due.

Hot Big Bang Cosmology

● if universe is expanding, it must have been denser and hotter in the past

● what would be the observable consequences of this?

Cosmic Microwave Background● thermal radiation left

over from era of plasma, predicted 1948

● 1950's: temperature predictions ranged from 5-50 K

● 1960's: observers began to look for it

● what wavelength should it be?

Penzias & Wilson

● stumbled into CMB in 1965 while studying galaxy

● found excess ~3 K thermal radiation in all directions (~1 mm wavelength)

● only later realized what it was

● Nobel Prize 1978

CMB SpectrumMost Perfect Thermal Emitter Ever Measured!

COBE, early 1990's

John Mather2006 Nobel Prize

CMB Fun Facts

● ~400 photons per cm3

● speed of light is large! 1013 photons per cm2 per second!

● accounts for a few percent of the TV “snow” you see between stations (for those of you without cable....)

Alternatives to Big Bang?

● Big Bang was originally a pejorative term!

● “Steady state” model hypothesized that new matter is created to maintain a constant density as universe expands

● Steady state model was unable to account for CMB!

● Creation of new matter has never been observed

Fred Hoyle 1915-2001,most ardent steady-stater(also established the principle of nucleosynthesis in stars, 1946)

Further back in time...● universe must have been hot enough for nuclear

reactions (everywhere). “The First Three Minutes”

● starting with a proton/neutron soup in a 7:1 ratio (explain why later), can form 12 H nuclei for each He nucleus

● predict 3:1 ratio by mass

● how does it change with time/vary by galaxy?

● agrees well with observations!

Big Bang Nucleosynthesis: Details

● after He formation, universe had expanded, cooled too much to fuse He

● trace amounts of intermediate stage 2H (deuterium) left over

● more 2H is used up if neutron+proton (baryon) density is higher

● similar arguments for 3He, Li

● inferred baryon density matches census of stars+gas!

Why 7:1 p/n Ratio?

● extrapolate further back in time (1st few seconds). Possible reactions:

– p + e => n (converts kinetic energy to mass)

– n => p + e (releases kinetic energy and/or photon)

● very hot universe (1011 K): reaction goes both ways

● cooling universe (~1010 K): 1st reaction cannot proceed, not enough input energy available

● end up with many more protons than neutrons!

● why not all protons?

Big Bang (so far) vs. Observations

✔ prediction of CMB: temperature and isotropy

✔ “postdiction” of He abundance

✔ matching 2H, 3He, Li abundances and census of stars/dust/gas

✔ postdiction of 7:1 proton:neutron ratio

● structure: where does it come from?

✗ horizon problem: different parts of our horizon are not in causal contact, yet have same physical conditions

✗ flatness problem

Cosmic History

Large-Scale Structure

Structure Formation Simulation(stills from the movie, cosmicweb.uchicago.edu/filament.html)

(screensavers available on same website!)

box is 140 million light-years across

But space is expanding... ● competing effects: expansion of space vs gravitational

attraction of objects in that space

● “the universe is expanding” is an approximation which works very well on large scales, less so on small scales

● observationally, the average distance between galaxies is increasing

Hubble's original data(Bennett Fig 20.20)show nearby galaxiesapproaching us)

Expanding Space in Simulations

● these movies are made in comoving coordinates: the box is expanding too

● advantages to thinking in comoving coordinates:

– portrays the same “piece of the universe”

– material does not move out of the box

– simplifies thinking about, e.g. galaxy density. We study the comoving density of galaxies.

● formation of same structure in comoving and physical coordinates: http://www-theorie.physik.unizh.ch/~diemand/clusters/

Structure Formation: Light Cone

(Virgo Collaboration)

Structure Formation:Different Models

redshift = 1 redshift = 0

Details

Galaxy Group Formation Moviecosmicweb.uchicago.edu/group.html

box is 14 million light-years, 1/10 of previous movie

Initial Conditions

● full description of a system includes physical laws and initial conditions (more generally, boundary conditions)

● the initial conditions for these simulations come from bright and dark spots in the CMB

first map of CMB fluctuations, early 1990's, COBE mission

George Smoot2006 Nobelist

Universe's Baby PicturesCosmic Microwave Background, Imaged by WMAP Satellite

Emitted at ~380,000 years old. Bright spots are only ~10-5

brighter than dark spots!

CMB Anisotropies● Reminder: CMB is 2.7 K thermal radiation, emitted at

t~300,000 years

● Anisotropy: some areas are ~10-5 K brighter, indicating denser plasma

● typical size ~1 degree (but come in a spectrum of sizes)

● after 13 billion years of gravitational contraction, these dense spots match the structure we see today!

Structure: Summary

● Evolution of structure from tiny ripples in CMB is well understood.

● Simulations produce structures much like what we see today (clusters, voids, filaments, in the right amounts and sizes.

● Amount of dark matter inferred from CMB matches the amount inferred from cluster X-rays, lensing, etc!

● Baryon density inferred from CMB matches that inferred from Big Bang nucleosynthesis!

● But still haven't explained where ripples in the CMB came from...

Big Bang (so far) vs. Observations

✔ prediction of CMB: temperature and isotropy

✔ “postdiction” of He abundance

✔ matching 2H, 3He, Li abundances and census of stars/dust/gas

✔ postdiction of 7:1 proton:neutron ratio

● structure seen in CMB: where does it come from?

✗ horizon problem: different parts of our horizon are not in causal contact, yet have same physical conditions

✗ flatness problem

Review Questions

What evidence do we have that the universe was a hot plasma (~3000 K) 13 billion years ago?

A. proton/neutron ratio

B. deuterium abundance

C. cosmic microwave background

D. the night sky is dark

E. helium abundance

Review Questions

What evidence do we have that the universe was very hot (~1010 K) in the first few seconds?

A. proton/neutron ratio

B. deuterium abundance

C. cosmic microwave background

D. the night sky is dark

E. helium abundance

Review Questions

What evidence do we have that there are too few protons and neutrons to account for most of the mass in the universe?

A. proton/neutron ratio

B. deuterium abundance

C. cosmic microwave background

D. the night sky is dark

E. helium abundance

More Evidence: Ages● oldest star clusters

(not shown here) are 13 billion years old

● how does that compare to Big Bang estimate?

Big Bang: Age Example 1

A galaxy 1 billion light-years away is receding at 24,000 km/s (Hubble's constant is 24 km/s per million ly). When was its distance zero?

● 109 light-years = 1022 km● 1022 km / 2.4x104 km/s = 4.2x1017 s or

13.2 billion years

Big Bang: Age Example 2

A galaxy 2 billion light-years away is receding at 48,000 km/s (Hubble's constant is 24 km/s per million ly). When was its distance zero?

● 2x109 light-years = 2x1022 km● 2x1022 km / 4.8x104 km/s = 4.2x1017 s or

13.2 billion years

Notice a Pattern?

● The age of the universe is just 1/H0 if the expansion has been at a constant rate.

● H0 = 24 km/sec/million ly, but 1 million ly = 1019 km, so H0 = 2.4x10-18 sec-1 or 7.6x10-11 yr-1

● 13.2 billion years, matches the ages of the oldest stars!

● But it should be decelerating due to gravitational self-attraction. Higher velocity in past implies it's younger.

● Hmm, it can't have slowed down much! (Save thought for next lecture.)

Big Bang (so far) vs. Observations

✔ prediction of CMB: temperature and isotropy

✔ “postdiction” of He abundance

✔ matching 2H, 3He, Li abundances and census of stars/dust/gas

✔ postdiction of 7:1 proton:neutron ratio

✔ age of universe slightly greater than age of oldest stars

● structure seen in CMB: where does it come from?

✗ horizon problem: different parts of our horizon are not in causal contact, yet have same physical conditions

✗ flatness problem

Possible Expansion HistoriesBig Crunch Big Chill Big Rip

Possible Expansion Histories

Deceleration Due to Gravity

● If the universe has enough mass, it will halt the expansion. “Critical density” is 4.5x10-27 kg m-3 or ~3 protons m-3!!

● Make some previous statements more quantitative:

– baryon density is 4% of critical density

– dark matter density is 23% of critical density● A universe at critical density is called “flat”. Less dense

is “open”, more dense is “closed.”

Geometry (Optional)● in a flat (Euclidean) geometry, sum of angles in a triangle

is 180 degrees and parallel lines never meet nor diverge

● on the surface of a sphere (closed geometry), triangle sums to >180 degrees and “parallel lines” (great circles) eventually intersect

● in an open geometry, triangle sums to <180 degrees and parallel lines diverge

Flatness Problem

● universe is suspiciously close to flat, even if only 27% of critical density.*

● could have been 0.0000001% of critical density or 1040 times larger than critical density

● just a coincidence??

*we will learn later that it is even closer than that!

Review Questions

How do we know the ages of the oldest stars?

A. radioactive dating of oldest elements

B. main sequence turnoff

C. inverse of Hubble constant

D. redshift

E. deuterium abundance

Review Questions

How do we know the “age of the universe” (more precisely, the time since the Big Bang)?

A. radioactive dating of oldest elements

B. main sequence turnoff

C. inverse of Hubble constant

D. redshift

E. deuterium abundance