Copernican revolu5on Copernican principle Olber s paradox Permenancy

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Robyn Dorsey
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1 Cosmology Backdrop Copernican revolu5on Copernican principle Olber s paradox Permenancy Modern Cosmology Rela5vity The cosmological constant Hubble s discovery An expanding Universe The age of the Universe Turtles all the way down

2 The Copernican Revolu5on Cosmology is the study of the Universe Most science was conducted by the church Earth at centre of an eternal, unchanging Universe Galileo, Copernicus, and Kepler challenged the church s authority by displacing the Earth from the centre of the Solar System

3 The Copernican Principle Modern Cosmology begins with the following simple axiom: There is nothing special about the loca5on of the Earth in the cosmos This simple statement led to the Copernican Revolu5on. Science was liberated from the power of the Church to address all ques5ons.

4 Olber s Paradox The idea of permanency of the Heavens persisted. In 1826 Olber voiced a well known paradox: Why is the sky dark at night? This ques5on pre- empts Einstein and Hubble by no5ng the impossibility of an infinitely old and infinitely large universe

5 Olber s Paradox If the Universe is infinitely big with a uniform distribu5on of stars every line of sight will eventually intercept a star

6 Olber s Paradox The fact that some stars are more distant is irrelevant: A B Flux from A: ~ L/d 2 Flux per square arcsec from A: ~ (L/d 2 )/θ 2 As θ 1/d, this implies: Flux per square arcsec independent of distance If the Universe is infinite then the en5re sky should be as bright as the surface of the sun!

7 Olber s Paradox: Formally Let n = the density of stars [number/m 3 ] with intrinsic luminosity L uniformly distributed to infinity No of sources within shell is: dn = n 4! r 2 dr r dr Flux of each source is: f = L 4! r Total light from shell is: 2 2 Ln4! r di = f dn = dr = 2 4! r Lndr

8 Olber s Paradox Integra5ng gives: I = # " 0 " di = Lndr I = Ln[ r] # 0 I = # i.e., We get equal contribu5ons from each shell, if the shells extend to infinity we must get an infinitely bright sky: BUT THE SKY AT NIGHT IS DARK

9 Solu5ons to Olber s Paradox Intervening dust Finite age to Stars/Universe Light redshiged to longer λs The dust would heat up and also radiate as brightly as a star Violates the permanency of the Heavens Universe expanding: not sta5c. Universal Expansion does not no5ceably effect darkness of night sky

10 Solu5ons to Olber s Paradox Intervening dust Finite age to Stars/Universe Light redshiged to longer λs The dust would heat up and also radiate as brightly as a star Violates the permanency of the Heavens Universe expanding: not sta5c. Universal Expansion does not no5ceably effect darkness of night sky Correct Solu5on: Universe has a finite age

11 Finite age: We can see light sources within a sphere whose radius is the light travel /me for the age of the Universe Cannot see light from Sources outside this sphere Can see light from these sources Observable Universe: R ~ 15 billion light years

12 Problems with Permanency Prior to Hubble s discovery of the Universal Expansion there were some problems: Olber s Paradox Energy Conserva5on (for stars to shine indefinitely they would require an infinite fuel reserve) Ages of Earth, meteorites and stars These all point toward a Universe with a beginning (or at least to a problem with permanency!)

13 Modern Cosmology Modern Cosmology began at the turn of the century from: 1) Einsteins theory of rela5vity (1916) 2) Hubble s discovery of the expansion of the Universe (1929) Together they resolved Olber s Paradox (1826) Why is the sky dark at night?

14 Einstein s Theory of Rela5vity The laws of Physics are the same to all observers, i.e., there is no fundamental reference frame. The speed- of- light represents a fundamental limit and the velocity of a photon is measured to be the same to all observers Counter- intui5ve but has been tested exhaus5vely!

15 The Equivalence Principle This states that you cannot dis5nguish between being at rest in a gravita5onal field and accelera5on. i.e., gravity and iner5a are indis5nguishable GR equates iner5al mass with gravita5onal mass and explains why they are iden5cal

16 Space5me In GR the concept of Newtonian gravity was replaced by the concept of iner5al mass deforming space and slowing 5me. Hence space and 5me must be combined together => SPACETIME

17 Confirma5on of GR The Precession of Mercury s Orbit Known to be too fast since mid- 1800s. General Rela5vity explains the discrepancy perfectly Newton: 531 /century Observed: 574 /century Precession Gravita5onal Lensing GR predicts that a mass can bend light and the first confirma5on of GR came in 1919 from occulta5on 5mes of stars behind solar eclipses Gravita5onal Redshig Light is redshiged leaving a massive object

18 By a star The Sun Planet Hun5ng Dark Marer searches By a galaxy Time- delay => cosmological parameters By a cluster Mass probe Natural Telescope Gravita5onal Lensing

19 Abel 2218 a giant gravita5onal lens

20 Cosmology in the 1920s Einstein applied GR to the Universe as a whole and found the following two equa5ons: R R 2 ' $ % R " % R " & # 4) G =! 3 ' % & 3p ( + 2 c 8) G( =! 3 Don t need to remember these. Interest only These describe the dynamics (accelera5on and velocity) of the Universe as a whole As ρ (density of marer) and p (pressure of radia5on) are always posi5ve they imply a decelera5ng universe, an expanding/contrac5ng universe. kc R 2 2 $ " #

21 Einstein s blunder Despite Olber s paradox and the conserva5on of energy, Einstein believed in the permanency of the Heavens and tweaked his equa5ons by adding a Cosmological Constant (Λ): R R 2 ( % & R # & R # ' $ 4* G =! 3 ( & ' ) + 8* G) = + 3 3p 2 c "! 3 % # + $ kc R " Don t need to remember these. Interest only In 1929 the Expansion of the Universe was discovered by Hubble Λ was my Greatest Blunder, Einstein 1929

22 Hubble s Discovery From the Copernican principle: Olber s Paradox => A finite Universe Finite Age measures => A beginning General Rela5vity => A dynamical Universe These all point towards a dynamic Universe which has a beginning and a finite age. Despite this the discovery of the Expansion came as a great surprise to the world

23 Hubble s Discovery Having proved that M31 was external to our galaxy, Hubble collected images and spectra for many more galaxies From photographic images he es5mated distances using the brightest stars (NB: the fainter galaxies were too distant to find and measure Cepheid stars) For nearby galaxies he showed that the brightest star methods works as a distance indicator and calibrated it to Andromeda From spectra he calculated the radial veloci5es of these galaxies Plosng distance versus velocity he found:

24 Cepheid variable stars Pulsa5ng stars (mechanism understood) Pulsa5o nperiod propor5onal to flux Measuring pulsa5on is like reading the warage on the light bulb

25 Andromeda: The nearest spiral Cepheids found here. Measure Cepheid Period Infer True flux from P- L rela5on Measure apparent flux Apply inverse square law to get distance

26 v d= Ho

27 Most galaxies recede More distant galaxies recede faster There is a linear rela5onship between velocity and distance: v = H o d v = velocity (km/s) d = distance (Mpc) H 0 = The Hubble constant (km/s/ Mpc) Hubble s Law

28 Universal Expansion Hubble s law appears to violate the Copernican Principle as it seems to place us at a special loca5on: Milky Way Everything is moving away from us?

29 Universal Expansion Q) What is so special about our loca5on? A) Nothing! Me You Consider: According to Hubble s Law: I see: v v 2v 3v But if we jump to your loca5on, you see: 3v 2v v v

30 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 contrac5on can produce a centre- less but dynamic Universe.

31 An Expanding Universe Hubble s observa5ons resolved Olber s Paradox and allowed Einstein to remove the fudge from his equa5ons. It overturned the idea of permanency and replaced it with an approximate age for our Universe. Why? For any object we can calculate the 5me at which it would have been located at our posi5on. From Hubble s Law this will be the same for all galaxies. t Age d1 = d v d2 d = V V1 d V 1 2 = = H o V2

32 The Hubble Constant The exact value of the Hubble Constant has been the focus of heated debate since its discovery. Ini/ally Hubble measured it to be 500km/s/Mpc However he had mistaken RR Lyraes for Cepheids in most of his galaxies. When corrected, the Hubble Constant changed to 100km/s/Mpc For most of the past few decades measurements have come in in the range km/s/mpc The Hubble Space Telescope was named ager Hubble and its primary aim was to measure H 0

33 The HST Key Program The Hubble Space Telescope enables us to measure Cepeheids in the distant Virgo cluster and thereby obtain our most accurate value for H 0 H o km / s / Mpc = 75 ±15

34 The Age of the Universe From 1/H 0 we can calculate an approximate age for the Universe: t t t t t Age Age Age Age Age = = = 1 H o 1 75 = 4" 10 = 1.267" 10! 13Gyrs 1 75 s. Mpc / 6 ( 10 " 3" 10 " & 3 ' " ( & ' yrs km 4" " 24" 60" % # $ = 17 s % # $ yrs

Observational Cosmology

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