The ! AS1001:Extra-Galactic Astronomy! • is the study of the . • Once upon a time, … (<1600) most Western science was done by the Church, influenced by dogma, Scripture. Lecture 7: The Development of Cosmology • Church’s (Aristotle’s) cosmological model: at centre, Moon, , 5 planets (MVMJS), fixed stars on 8 rotating spheres. • Copernicus, Galileo and Kepler challenged the Church’s authority, placing the Sun at the centre, seeing comets as orbiting Sun, craters on Moon, Venus phases, moons of Jupiter, … • (Church recently apologised for persecuting Galileo to suppress his heretical views.)

The Copernican Principle! Olber’s Paradox! Modern Cosmology assumes: The idea of “permanency of the Heavens” There is nothing special about persisted. In 1826 Olber voiced a well known our location in the cosmos. paradox:

A simple but powerful concept Why is the sky dark at night? extending the Copernican Revolution: Our Sun, on outskirts of a galaxy. This question, 100 years before Einstein and Our galaxy, one of zillions. Hubble, undermines the concept of an eternal, Our view is typical, not special. unchanging, infinite Universe.

Olber’s Paradox! Olber’s Paradox! If the Universe is infinite, with a uniform • But, more distant stars are fainter. distribution of stars, every line of sight • It doesn’t matter! eventually encounters a star. WHOLE SKY AS BRIGHT AS THE SUN  • Flux ~ L / d 2 • I = Flux per square arcsec ~ (L / d 2 ) / θ2 • But θ ∼ r / d, so: I ~ L / r2 Intensity is independent of distance. • If the Universe is infinite, then the entire sky should be as bright as the surface of the sun! Olber’s Paradox: Version 2! Olber’s Paradox: Version 2! • n = density of stars • Add up flux from shells out to radius R. R 3 Integrate : [stars/pc ] F dF L n dr dr = " = " • No of stars within shell : 0 2 r R dN = n 4! r dr F = L n [r] • Flux from one star : 0 L F = L n R f = 4! r2 • Equal flux dF from each shell dR. • Flux from all stars in the shell : • If shells extend to R = infinity, L n 4" r2 ! dF = f dN = dr = L n dr the flux from the sky is infinite. 4 r2 " BUT THEN WHY IS THE NIGHT SKY DARK?

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Solutions to Olber’s Paradox! Solutions to Olber’s Paradox! • Finite size • Yes. But we would then be “at the • Finite size • Yes. But we would then be “at the centre”, a preferred location. centre”, a preferred location. • Intervening dust • Intervening dust • No. The dust would heat up and also • No. The dust would heat up and also radiate as brightly as a star radiate as brightly as a star • Finite age • Finite age • Yes. But this violates the • Yes. But this violates the “permanency of the Heavens” “permanency of the Heavens” • Expansion • Expansion light to redshifts light to longer λs • Helps. But not enough. longer λs • Helps. But not enough.

Correct Solution: Universe has a finite age

Finite age: We can see sources within a sphere whose radius is the light travel time for the age of the Universe Problems with Permanency! Light from stars outside the • Before Hubble discovered the Universal sphere has not yet reached us. Expansion (next lecture), there were already several problems: We can see the stars inside the sphere – Olber’s Paradox – Energy Conservation (to shine forever, stars would need an infinite fuel reserve) – Age of Earth rocks, meteorites.

• These all point to a Universe with a beginning Observable Universe: (or at least to a problem with permanency!) R ~ 15 billion light years Modern Cosmology! Einstein’s Special Relativity! • Laws of Physics are the same for all constant-velocity Modern Cosmology : observers. There is no absolute reference frame. 1) Einstein’s gravity theory: • Light speed (in the vacuum) is a fundamental limit. General Relativity (1916) 2) Hubble’s discovery: Expanding Universe (1929)

Together they resolve • All observers see the same photon velocity! Olber’s Paradox (1826) • Moving objects compressed in direction of motion. “ ” • Moving clocks run slower! Why is the sky dark at night ? • Counter-intuitive but extensively tested ! • e.g. Relativistic particles travel farther before decay.

The Equivalence Principle! Einstein’s Gravity: General Relativity! You cannot distinguish (by local measurements) between • In GR, Newton’s “action at a distance” gravity is acceleration and a uniform gravitational field. replaced by warping space and slowing time. i.e., gravity and inertia are indistinguishable • Space and time inextricably linked => “SPACETIME” F = G M m / r2 F = m a • GR1: Warped spacetime tells matter how to move. • GR2: Mass/energy tells spacetime how to warp. Both see the apple fall.

GR equates gravitational mass with inertial mass and explains why they are identical.

3 Classic Tests of GR! Gravitational Lensing! • 1. Precession of Mercury’s Orbit – Known to be too fast since mid-1800s. • By stars: General Relativity explains the discrepancy – The Sun Newton: 531”/century – Planet Hunting Observed: 574”/century – Dark Matter searches Precession • By galaxies: • 2. Gravitational Lensing – Time-delay => – GR predicts that a mass bends light rays. Prediction cosmological confirmed in 1919, by Eddington photography of star parameters positions during vs after solar eclipses. • By galaxy clusters: • 3. Gravitational – Mass probe – Clocks run slow in a gravitational field – Natural Telescope – Light is redshifted leaving a massive object – Seen in white dwarf spectra, also our GPS network. Abell 2218 a giant gravitational lens! Cosmology in the 1920s! • Einstein’s GR, applied to the Universe as a whole, (uniform density ρ, pressure p ) gives 2 equations:

•• R 4)G ' 3p $ Acceleration: = ! % ( + 2 " No need to R 3 & c # 2 • remember these. ' $ 2 % R " 8)G( kc For interest only Velocity: = ! 2 % R " 3 R & # • These describe a Dynamical Universe: R( t ) • Universe must be expanding or collapsing. • If ρ (density) and p (pressure) are positive, then an expanding Universe decelerates.

Einstein’s blunder: ! Summary! The Λ • Despite Olber’s paradox, etc. • Extending the Copernican principle: “ ” Einstein believed in permanency of the Heavens . – Olber’s Paradox => A finite Universe • To allow a steady-state Universe ( R = constant ), – Finite Age measures => A beginning he tweaked his equations, adding a Cosmological – General Relativity => A dynamical Universe Constant ( •• Λ): R 4#G % 3p( + = " ' $ + * + R 3 & c 2 ) 3 Don’t need to • These all point to a dynamic Universe 2 % • ( remember these. R( t ) with a beginning and a finite age. R 8#G$ kc 2 + ' * = " + ' R* 3 R2 3 Interest only & ) • Despite this, Hubble’s discovery of the • 1929: Hubble discovers Expansion of the Universe. Expansion (next lecture) was a great surprise that shocked the world. • Einstein!ʼs regret: “Λ was my Greatest Blunder”. • 1998: Λ returns as driving acceleration.