E4 Cosmology

Newton’s Universe

• Infinite (in space and time)•Static

Olbers paradox

• If Newton’s ideas were correct, the sky should never be dark!

• Imagine an infinite Universe containing an infinite number of stars more or less uniformly distributed in space

Mathematically

• Let n be the number of stars per unit volume of space

Mathematically

• Let n be the number of stars per unit volume of space

• At a distance d from a star of luminosity L, the received energy per area per second (apparent brightness) is given by b = L/(4πd2)

Mathematically

• Imagine a thin shell of stars, thickness t, at a distance d from an observer.

Mathematically

d

• The number of stars in this shell = number density x volume = 4πr2nt

Mathematically

d

• The energy received per second per unit area from all the stars in the shell is thus L/(4πd2) x 4πr2nt = Lnt

Mathematically

d

• Since Lnt is constant (doesn’t depend on d) and there are an infinite number of thin shells surrounding the observer, the total energy received must be infinite!

Mathematically

d

• Since the sky is not infinitely bright this cannot be true, and this is Olber’s paradox.

Mathematically

d

• # of stars in shell increases with d2

• Intensity of the stars decreases with 1/d2

• Brightness of shells is constant, and there are an infinite number of them!

In other words

d

• The Universe has a finite age and the speed of light is finite, so light has not arrived from some stars

• Stars have a finite age and there are a finite number of stars

In summary

The Big Bang

Red-shift

• Light from distant galaxies is Doppler red-shifted. Meaning they are moving away from us. The further they are away, the more the red-shift so the faster they are moving away.

Penzias and Wilson• They worked on ultra-sensitive cryogenic microwave receiver, intended

for radio astronomy observations. In 1964 the pair encountered radio noise which they could not explain. It was far less energetic than the radiation given off by the Milky Way, and it was isotropic, so they assumed their instrument was subject to interference by terrestrial sources. They tried, and then rejected, the hypothesis that the radio noise emanated from New York City. An examination of the microwave horn antenna showed it was full of pigeon droppings . After the pair removed the guano buildup, and the pigeons were shot (each physicist says the other ordered the deed), the noise remained. Having rejected all sources of interference, the pair published a paper announcing their findings. This was later identified by Robert Dicke as the cosmic microwave background radiation (CMB), the radio remnant of the Big Bang. This allowed astronomers to confirm the Big Bang, and to correct many of their previous assumptions about it. Penzias and Wilson received the 1978 Nobel Prize

• http://en.wikipedia.org/wiki/Arno_Allan_Penzias 6/8/2010 11.31 am

CMB – Cosmic microwave background

The Universe is bathed in microwave radiation, at a wavelength indicating a blackbody temperature of about 3 K. This is the remnants of the energy produced by the Big Bang

• The Universe has a finite age and the speed of light is finite, so light has not arrived from some stars

• Stars have a finite age and there are a finite number of stars

Big Bang and Olber’s paradox

• Space and time originated with the Big Bang

• The Universe is NOT expanding into a void

Important!

“A day without a yesterday”Lemaître

What next?

What next?

• Open Universe – Will continue expanding forever if not dense enough to halt the expansion

• Flat Universe – Will continue expanding but the rate of expansion decreases (approaching zero) if at critical density

• Closed Universe – The Universe will stop expanding and will start to contract – leading to the Big crunch! If there is sufficient density

Density of Universe

Problems in finding Density of Universe

• Not enough mass is visible to account for observations

• Must be “dark mass”• Neutrino masses not yet determined• WIMPS – Weakly interacting massive particles –

Neutrinos and other particles predicted by theoretical Physics

• MACHOS – Massive compact halo objects – Brown and Black dwarfs

Expansion increasing!

• We believe that the mass of the Universe is at the critical value (mainly “dark mass”), however, since 1998 we have known that the rate of expansion is actually increasing!

• It appears that the universe is filled with an all-permeating vacuum energy called “dark energy” which creates a kind of repulsive force

Strange–times!

Questions!

Page 520 Questions 3, 4, 5, 6, 7, 10.