The expanding universe
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The Expanding Universe. Except for a few nearby galaxies (like Andromeda), all the galaxies are seen to be moving away from us

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The Expanding Universe

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The expanding universe

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 universe1

The Expanding Universe

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

Milky Way


The expanding universe2

The Expanding Universe

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

Milky Way


Twice as far away,

so moves twice as fast

The expanding universe3


The Expanding Universe

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


A while later:



The expanding universe4

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:

The expanding universe5

The Expanding Universe

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

The expanding universe6

The Expanding Universe

  • 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)

Cosmological red shift

Cosmological Red-Shift

Not really a Doppler effect

Space itself is being stretched between galaxies

Conclusions from our observations

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 expandsnow, 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

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


  • “To understand the very big

    we have to understand the

    very small”

How does the expansion work

How does the expansion work?

Like an explosion (hot, dense matter in the beginning), but space itselfexpands!

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

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

Do pumpkins fall faster than apples?

The expanding universe


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

The idea behind general relativity

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

Planetary Orbits


Planet’s orbit

Effects of general relativity

Effects of General Relativity

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

The dynamics of the universe

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

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



It’s a tie!

Mass wins!


The fate of the universe

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

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

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 noedge and nocenter – the ultimate Copernican principle!

The fate of the universe determined by a single number

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 > 1means the universe will recollapse (Big Crunch) Mass wins!

0 < 1means gravity not strong enough to halt the expansion Expansion wins!

And the number is: 0 < 1 (probably…)

The shape of the universe

The Shape of the Universe

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

DensityCurvature2-D exampleUniverseTime & Space

0>1 positive sphere closed, bound finite

0=1 zero (flat) planeopen, marginal infinite

0<1 negative saddleopen, unbound infinite

So how much mass is in the universe

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

“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

First evidence for dark matter: The missing mass problem

  • Showed up when measuring rotation curves of galaxies

Is dark matter real

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

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

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

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

Enter: The Cosmological Constant

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

  • Physical origin of 0is unclear

  • Einstein’s biggest blunder – or not !

  • Appears to be small but not quite zero!

  • Particle Physics’ biggest failure

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