AS1001:Extra-Galactic Astronomy

1. AS1001:Extra-Galactic Astronomy Lecture 7: The Development of Cosmology Kenneth Wood 316 kw25@st-andrews.ac.uk http://www-star.st-and.ac.uk/~kw25

2. The Copernican Revolution • 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: • This simple statement led to the Copernican Revolution. Science was liberated from the power of the Church to address all questions. There is nothing special about the location of the Earth in the cosmos

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

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

6. A B Olber’s Paradox • The fact that some stars are more distant is irrelevant: • Flux from A:~ L/d 2 • Flux per square arcsec from A: ~(L/d 2)/q2 • As q ~ 1/d, this implies: Flux per square arcsec independent of distance • If the Universe is infinite then the entire sky should be as bright as the surface of the sun!

7. dr r Olber’s Paradox: Formally • Let n = the density of stars [number/m3] with intrinsic luminosity L uniformly distributed to infinity • No of sources within shell is: • Flux of each source is: • Total light from shell is:

8. Olber’s Paradox • Integrating gives: • i.e., We get equal contributions from each shell, if the shells extend to infinity we must get an infinitely bright sky: BUT THE SKY AT NIGHT IS DARK

9. Intervening dust Finite age to Stars/Universe Light redshifted to longer ls The dust would heat up and also radiate as brightly as a star Violates the permanency of the Heavens Universe expanding: not static. Universal Expansion does not noticeably effect darkness of night sky Solutions to Olber’s Paradox

10. Intervening dust Finite age to Stars/Universe Light redshifted to longer ls The dust would heat up and also radiate as brightly as a star Violates the permanency of the Heavens Universe expanding: not static. Universal Expansion does not noticeably effect darkness of night sky Solutions to Olber’s Paradox Correct Solution: Universe has a finite age

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

12. Problems with Permanency • Prior to Hubble’s discovery of the Universal Expansion (next lecture) there were some problems: • Olber’s Paradox • Energy Conservation (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) Einstein’s theory of relativity (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 Relativity • 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-intuitive but has been tested exhaustively!

15. The Equivalence Principle • This states that you cannot distinguish between being at rest in a gravitational field and acceleration. i.e., gravity and inertia are indistinguishable • GR equates inertial mass with gravitational mass and explains why they are identical

16. Spacetime • In GR the concept of Newtonian gravity was replaced by the concept of inertial mass deforming space and slowing time. • Hence space and time must be combined together => SPACETIME

17. Precession Confirmation of GR • The Precession of Mercury’s Orbit • Known to be too fast since mid-1800s. General Relativity explains the discrepancy perfectly • Gravitational Lensing • GR predicts that a mass can bend light and the first confirmation of GR came in 1919 from occultation times of stars behind solar eclipses • Gravitational Redshift • Light is redshifted leaving a massive object Newton: 531”/century Observed: 574”/century

18. Gravitational Lensing • By a star • The Sun • Planet Hunting • Dark Matter searches • By a galaxy • Time-delay => cosmological parameters • By a cluster • Mass probe • Natural Telescope

19. Abel 2218 a giant gravitational lens

20. Cosmology in the 1920s • Einstein applied GR to the Universe as a whole and found the following two equations: • These describe the dynamics (acceleration and velocity) of the Universe as a whole • As r (density of matter) and p (pressure of radiation) are always positive they imply a decelerating universe expanding/contracting universe. Don’t need to remember these. Interest only

21. Einstein’s blunder • Despite Olber’s paradox and the conservation of energy, Einstein believed in the “permancy of the Heavens” and tweaked his equations by adding a Cosmological Constant (L): • In 1929 the Expansion of the Universe was discovered by Hubble (Next Lecture) • “L was my Greatest Blunder”, Einstein 1929 Don’t need to remember these. Interest only

22. Summary • From the Copernican principle: • Olber’s Paradox => A finite Universe • Finite Age measures => A beginning • General Relativity => 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 was a great surprise to the world