iSkylab 4• Two rungs of cosmic distance ladder

– First measure distance to Cepheids with parallax, also note their periods

– Establish period-luminosity relationship as slope of luminosity vs period graph (L comes from B=L/(4π d2)

– Then observe two other Cepheids in two galaxies, determine luminosity from period, distance from B=L/(4π d2)

– Redshift gives recessional velocity Hubble’s constant as slope in velocity vs distance plot

General Relativity ?! That’s easy!

(Actually, it took Prof. Einstein 10 years to come up with that!)

Rμν -1/2 gμν R = 8πG/c4 Tμν

OK, fine, but what does that mean?

Planetary Orbits

Sun Planet’s orbit

More General than Special Relativity

• General Relativity is more general in the sense that we drop the restriction that an observer not be accelerated

• The claim is that you cannot decide whether you are in a gravitational field, or just an accelerated observer

• The Einstein field equations describe the geometric properties of spacetime

The Idea behind General Relativity

– We view space and time as a whole, we call it four-dimensional space-time.

• It has an unusual geometry, as we have seen

– Space-time is warped by the presence of masses like the sun, so “Mass tells space how to bend”

– Objects (like planets) travel in “straight” lines through this curved space (we see this as orbits), so

“Space tells matter how to move”

Effects of General Relativity

Bending of starlight by the Sun's gravitational field (and other gravitational lensing effects)

Assumption: Cosmological Principle

• The Cosmological Principle: on very large scales (1000 Mpc and up) the universe is homogeneous and isotropic

• Reasonably well-supported by observation

• Means the universe has no edge and no center – the ultimate Copernican principle!

What General Relativity tells us

• The more mass there is in the universe, the more “braking” of expansion there is

• So the game is:

Mass vs. Expansion

And we can even calculate who wins!

The Fate of the Universe – determined by a single number!

• Critical density is the density required to just barely stop the expansion

• We’ll use 0 = actual density/critical density:

0 = 1 means it’s a tie 0 > 1 means the universe will recollapse (Big Crunch)

Mass wins! 0 < 1 means gravity not strong enough to halt the expansion

Expansion wins!

• And the number is: 0 < 1 (probably…)

The “size” of the Universe – depends on time!

Expansion wins!

It’s a tie!

Mass wins!

Time

The Shape of the Universe

• In the basic scenario there is a simple relation between the density and the shape of space-time:

Density Curvature 2-D example Universe Time & Space

0>1 positive sphere closed, bound finite

0=1 zero (flat) plane open, marginal infinite

0<1 negative saddle open, unbound infinite

        

                                         

Back to: Expansion of the Universe

• Either it grows forever

• Or it comes to a standstill

• Or it falls back and collapses (“Big crunch”)

• In any case: Expansion slows down!Surprise of the year 1998(Birthday of Dark Energy):

All wrong! It accelerates!

Enter: The Cosmological Constant

• Physical origin of 0

is unclear• Einstein’s biggest

blunder – or not !• Appears to be small

but not quite zero!• Particle Physics’

biggest failure

• Usually denoted 0, it represents a uniform pressure which either helps or retards the expansion (depending on its sign)

Triple evidence for Dark Energy

• Supernova data

• Large scale structure of the cosmos

• Microwave background

                                           

                                                   

Microwave Background: Signal from the Big Bang

• Heat from the Big Bang should still be around, although red-shifted by the subsequent expansion

• Predicted to be a blackbody spectrum with a characteristic temperature of 2.725 Kelvin by George Gamow (1948)

Cosmic Microwave Background Radiation (CMB)

Discovery of Cosmic Microwave Background Radiation (CMB)

• Penzias and Wilson (1964)

• Tried to “debug” their horn antenna

• Couldn’t get rid of “background noise”

Signal from Big Bang• Very, very isotropic (1

part in 100,000)

CMB: Here’s how it looks like!Peak as expected from 3 Kelvin warm object

Shape as expected from black body

Latest Results: PLANCK

• Measure fluctuations in microwave background• Expect typical size of fluctuation of ½ degree if universe

is flat• Result:

Universe is flat !

Experiment and Theory

Expect “accoustic peak” at l=200

There it is!

Supernova Data

• Type Ia Supernovae are standard candles• Can calculate distance from brightness• Can measure redshift• General relativity gives us distance as a function of redshift for a given universeSupernovae are further away than expected for any decelerating (“standard”) universe

Pie in the Sky: Content of the Universe

We know almost everything about almost nothing!

1

2

3

23%

5%

72%

Dark EnergyDark MatterSM MatterSM Matter

Properties of Dark Energy

• Should be able to explain acceleration of cosmic expansion acts like a negative pressure

• Must not mess up structure formation or nucleosynthesis

• Does not dilute as the universe expands will be different % of content of universe as time goes by

Threefold Evidence

Three independent measurements agree:

•Universe is flat•28 % Matter•72 % dark energy

Cosmic Inflation• Size of the universe suddenly increased

exponentially

Consequences

• Fluctuations at a tiny

• fraction of a second when all parts of the universe talked to each other (to make sure everyone was at the same temperature)

• Suddenly fluctuations are enlarged

• Fluctuations become imprinted on CMB, provide seeds for large scale structure of universe (clups that grow into galaxies)

Inflation solves the Horizon Problem

• How does one side of the universe know what temperature the other side is at?

• It has no way, because light (signal velocity) is too slow

• Need inflation at larger than light speed

History of the Universe: Hot & small cold & big

before 10-43 s ?????? (“Planck Era”)

10-43 s T=1032 K gravity splits from other forces

10-43 to 10-35 s Grand Unification era

10-35 s T=1028 K Strong force splits from others. Epoch of inflation?

10-35 s to 10-10 s “Electroweak era”

10-10 s T=1015 KElectromagnetic force splits from others

10-10 to 10-4 s “Quark era”

10-4 s T=1013 K Quarks combine to form protons and neutrons

10-4 to 500,000 years Radiation era

180 s (3 minutes) T=109 K Protons and neutrons combine to form nuclei (mainly Helium,

deuterium)

500,000 years T=3,000 K Nuclei and electrons combine toform atoms – Decoupling

500,000 years to present Matter era