The Expanding Universe• Except for a few nearby galaxies (like Andromeda), all the

galaxies are seen to be moving away from us

• Generally, the recession speed of a galaxy is proportional to its distance from us; that is, a galaxy that’s twice as far away is moving twice as fast (aside from local motions within galaxy clusters)

The Expanding Universe

This expansion pattern (speed proportional to distance) actually implies that galaxies are all moving away from each other

ExpansionMilky Way

The Expanding Universe

This expansion pattern (speed proportional to distance) actually implies that galaxies are all moving away from each other

ExpansionMilky Way

Twice as far away, so moves twice as fast

The Expanding Universe

This expansion pattern (speed proportional to distance) actually implies that galaxies are all moving away from each other

A while later:

d

Start:

d 2d

The Expanding Universe

• Each galaxy sees the others moving away with the same pattern (further → faster)

• As though the galaxies ride on a rubber band that is being stretched!

A while later:

Start:

The Expanding Universe

In three dimensions, imagine the galaxies are raisins in an expanding loaf of bread

• Appears the universe “exploded” from a state in which matter was extremely dense and hot – the Big Bang

• Where did the expansion begin? Everywhere!• Every galaxy sees the others receding from it – there is no

special point (center)

The Expanding Universe

Cosmological Red-Shift

• Not really a Doppler effect• Space itself is being stretched between

galaxies

Conclusions from our Observations• The Universe has a finite age, so light from very

distant galaxies has not had time to reach us, therefore the night sky is dark.

• The universe expands now, so looking back in

time it actually shrinks until…?

Big Bang model: The universe is born out of a hot dense medium

13.7 billion years ago.

Big Bang

• The “start” of the universe, a primordial fireball the early universe was very hot and dense

intimate connection between cosmology and nuclear/particle physics

“To understand the very big we have to understand the very small”

How does the expansion work?• Like an explosion (hot, dense matter in the

beginning), but space itself expands!

• Slowed down by gravitational attraction

• Attraction is the stronger, the more mass there is in the universe

• Scientifically described by Einstein’s General theory of Relativity (1915)

More General

• 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

Do pumpkins fall faster than apples?

No!

Galileo: In the absence of air, all objects experience the same acceleration (change in motion) near Earth’s surface

http://www.youtube.com/watch?v=5C5_dOEyAfk

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”

Planetary Orbits

Sun Planet’s orbit

Effects of General RelativityBending of starlight by the Sun's gravitational field (and other gravitational lensing effects)

The Dynamics of the Universe

• There is a competition between Hubble expansion and gravity, which attempts to pull things together

• The ultimate fate of the universe depends on how fast it is expanding and how much mass is in it– More mass means more slowing of the expansion

• If there is too little mass the expansion “wins” and the universe will expand for ever – “unbound” universe

• If there is enough mass gravity “wins” and the universe will eventually re-collapse (Big Crunch) – a “bound” universe

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

Expansion wins!

It’s a tie!

Mass wins!

Time

The Fate of the Universe

• The Hubble constant H0 tells us how fast the universe is expanding• We also need to know the density of matter in the universe• “Critical” density is the density required to just barely stop the

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

0 = 1 is then the critical density 0 > 1 means the universe will re-collapse (Big Crunch) 0 < 1 means gravity is not strong enough to halt the expansion

• And the number is: 0 = 1 ± 0.02

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!

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!

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 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

    

                                             

So, how much mass is in the Universe?

• Can count all stars, galaxies etc. this gives the mass of all “bright”

objects

• But: there is also DARK MATTER

“Bright” Matter

• All normal or “bright” matter can be “seen” in some way– Stars emit light, or other forms of

electromagnetic radiation– All macroscopic matter emits EM radiation

characteristic for its temperature– Microscopic matter (particles) interact via the

Standard Model forces and can be detected this way

First evidence for dark matter: The missing mass problem

• Showed up when measuring rotation curves of galaxies

Is Dark Matter real?

• It is real in the sense that it has specific properties

• The universe as a whole and its parts behave differently when different amounts of the “dark stuff” is in it

• Good news: it still behaves like mass, so Einstein’s cosmology still works!

Properties of Dark Matter• Dark Matter is dark at all wavelengths, not

just visible light• We can’t see it (can’t detect it)• Only effect is has: it acts gravitationally like

an additional mass• Found in galaxies, galaxies clusters, large

scale structure of the universe• Necessary to explain structure formation in

the universe at large scales

What is Dark Matter?

• i.e. what does Dark matter consist of?– Brown dwarfs?– Black dwarfs?– Black holes?– Neutrinos?– Other exotic subatomic particles?

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)