Observational Cosmology Prof Simon Driver Simon.Driver@icrar.org 1. An Expanding Universe 2. The Hot Big Bang 3. The Microwave Background 4. Building a model geometry 5. Building a model dynamics 6. The Einstein de Sitter & Milne Universes 7. Dark Energy 8. Inflation 9. Loose ends and future directions Course Text: Introduction to Modern Cosmology by A.Liddle
Lecture 1: The Expanding Universe 1. The Copernican Principle 2. Olber s Paradox 3. The idea of Permanency 4. The discovery of the expansion 5. Hubble s law 6. The age of the Universe, Earth and Stars 7. The Big Bang and its three pillars: - Big Bang Nucleosynthesis - The Cosmic Microwave Background - The age of the Universe 8. An Adiabatic Expansion 9. Equations of State 10. How density of matter and radiation scale with expansion Course Text: Chapters 1 & 2 Wikipedia: Copernican Principle, Olber s Paradox, Hubble s Law
The Copernican Revolution Cosmology is the study of the Universe Pre-1593 world view was laid down by the Church Earth at centre of an eternal, unchanging Universe 1473-1543 Galileo, Copernicus, and Kepler challenged this authority by displacing the Earth from the centre of the Solar System 1543 Copernicus publishes... so began the Scientific revolution
The Copernican Principle Modern Cosmology begins with the following axiom: There is nothing special about the location of the Earth in the cosmos This comments on space but not on time. Universe still perceived as eternal and unchanging. The sense of Permanency was an entrenched known from pre-1543 But everything starts and ends?
Olber s Paradox In 1826 Olber voiced a well known paradox: Why is the sky dark at night? This question pre-empts Einstein and Hubble by noting the impossibility of an infinitely old and infinitely large universe If the Universe is infinitely big with a uniform distribution of stars every line of sight will eventually intercept a star
Olber s Paradox The fact that some stars are more distant is irrelevant: A B Flux from A: ~ L/d 2 Flux per unit solid angle from A: ~ (L/d 2 )/θ 2 As θ 1/d, this implies flux per unit solid angle constant If the Universe is infinite then the entire sky should be as bright as the surface of the sun!
Olber s Paradox: Formally Let n = the density of stars with intrinsic luminosity L uniformly distributed to infinity No of sources within shell is: dn = n 4" r 2 dr Flux of each source is: f = L 4" r 2 r dr Total light from all shells is: I = " di = " f dn = Ln4# r 2 $ " dr = " Lndr = Ln r 4# r 2 0 [ ] 0 $ = $ But it is dark at night
Solutions to Olber s Paradox Intervening dust - But dust will heat and reradiate An edge to the stars - Violates Copernican Principle Finite age to Stars/Universe - Violates permanency Contractions/expansions - No noticeable effect unless extreme Can see light from sources Cannot see light from sources outside sphere Correct Solution: Universe has a finite age
Problems with Permanency Prior to the discovery of the Universal Expansion scientists were already aware of problems: Olber s Paradox Energy Conservation (for stars to shine indefinitely they would require an infinite fuel reserve) Ages of Earth, meteorites, and stars All of above point toward a Universe with a beginning (or at least to a problem with the notion of permanency!) Even Einstein missed his chance as he added a Cosmological Constant to GR to keep the Universe static. Everything has to have a start and an end Kalagan, age 7, Feb, 2011 Nedlands Primary School
Hubble s Discovery Proved that M31 was external to our galaxy. Hubble collected many galaxy images and spectra Measured brightest stars and Cepheid variables to get distances Measured offset of common spectral features to get velocity Plotting distance v velocity he found: Hubble s Law: H 0 = v d A linear relation between a galaxy s distance (d) and recession velocity (v) Today: H o =72 km/s/mpc ß UNITS!!
Hubble s Data For these 5 bright ellipticals in nearby clusters we see that fainter galaxies have their Ca H & K lines redshifted further Simply by assuming that the brightest elliptical in a cluster is of comparable absolute magnitude we see Hubble s law for
Shifting spectral features SAME GALAXY PLACED AT DIFFERENT DISTANCES, LIGHT IS STRETCH DURING TRAVEL
Universal Expansion Hubble s law appears to violate the Copernican Principle as it seems to place us at a special location: Milky Way Everything is moving away from us?
Universal Expansion Q) What is so special about our location? A) Nothing! Consider: Me You According to Hubble s Law: v v 2v 3v I see: But if we jump to your location, you see: 3v 2v v v
The Universal Expansion A vector jump to another galaxy will result in that galaxy seeing all others moving away from it. Only an expansion or contraction can produce a centre-less but dynamic Universe.
The Age of the Universe If we extrapolate back at constant velocity every galaxy was coincident at a time of d/v=1/h o So from 1/H 0 we can calculate an approximate age for the Universe: t Age = 1 H o = 1 75 s.mpc /km t Age = 1 75 " # 106 " 3"10 16 & % ( = 4 "10 17 s $ 10 3 ' # 1 & t Age = 4 "10 17 "% ( yrs $ 365.25 " 24 " 60 " 60' t Age =1.267 "10 10 yrs t Age )13Gyrs
Big Bang v Steady-State GR without the Cosmological Constant provided a basis for the expansion But a model has to make predictions to gain credibility Big Bang provided one explanation and one prediction: Big Bang Nucleosynthesis --- explained the 4 He and other light element abundances (1948) The Cosmic Microwave Background --- predicted the ubiquitous background radiation (1948) Unlike the expansion the CMB was predicted before its discovery Big Bang model adopted over Steady State following CMB Both follow from the idea that as the Universe expands it cools
Abundances in the Solar System Very high Helium abundance not expected via stellar nucleosynthesis
Yield from SN
Data v prediction (400σ errorbars)
Adiabatic Expansion If U self-contained it must expand without losing energy: (1 st law of thermodynamics) Can use E=mc 2 and rewrite with m= ρ(4πr 3 /3) where r is some physical radius for expanding region of density ρ. de dt = d(4"r3 #c 2 3) dt de = "pdv = 4 3 "r3 c 2 d# dt + #4"r2 c 2 dr dt = $4"pr2 dr dt = $pdv [Uses: Chain rule + d(x 3 )=3x 2 d Use dot notation: i.e., dx dt = x 4 3 "r3 c 2 # + 4"r 2 c 2 # r = $4"r 2 p r Rearrange to get the Fluid Equation: " + 3 r r (" + p c 2 ) = 0
Equations of State We have an expression for how the density of U depends on the density and pressure of its contents. We know about two kinds of stuff: Matter - uniform diluted stationary matter exerts no pressure, p=0 Radiation - photons exert radiation pressure given by, p=ρc 2 /3 [From Thermodynamics, see also Problem 4.2] This can be generalised into an equation of state: p = w"c 2 w=0 for normal matter, 1/3 for photons (and -1 for dark energy).
How radiation and matter scale Matter: Subbing w=0 into EoS and then Fluid Eqn gives: " + 3" r r = 0, 1 r 3 d dt ("r3 ) = 0, i.e., " M # r $3 Radiation: Subbing w=1/3 into EoS and then Fluid Eqn gives: " + 4" r r = 0, 1 r 4 d dt ("r4 ) = 0, i.e., " R # r $4 In an adiabatically expanding Universe matter dilutes with length cubed and radiation with length to the fourth. This means radiation dominates over matter in the very early Universe with serious implications
Early Universe radiation dominated Figure Credit: Pearson Education Inc. Pearson Addison-Wesley
Lecture 1: The Expanding Universe 1. The Copernican Principle 2. Olber s Paradox 3. The idea of Permanency 4. The discovery of the expansion 5. Hubble s law 6. The age of the Universe, Earth and Stars 7. The Big Bang and its three pillars: - Big Bang Nucleosynthesis - The Cosmic Microwave Background - The age of the Universe 8. An Adiabatic Expansion 9. Equations of State 10. How density of matter and radiation scales with expansion Course Text: Chapters 1 & 2 Wikipedia: Copernican Principle, Olber s Paradox, Hubble s Law