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John D Barrow

The Maths Of Whole Universes. John D Barrow. A New Piece of Gravity.  - the ‘cosmological constant’ – does it exist?. G ab + g ab = T ab where  = 8G N /c 4 Geometry = mass-energy. Einstein’s Static Universe. (1917). De Sitter’s Accelerating Universe. Always expanding

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John D Barrow

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  1. The Maths Of Whole Universes John D Barrow

  2. A New Piece of Gravity  - the ‘cosmological constant’ – does it exist? Gab + gab = Tab where  = 8GN/c4 Geometry = mass-energy

  3. Einstein’s Static Universe (1917)

  4. De Sitter’s Accelerating Universe Always expanding exponential curve R = exp[t/3] No matter – only  It has no beginning and no end (1917) Willem De Sitter 1872-1934

  5. Friedmann’s universes 1888-1925 1922,1924

  6. Georges Lemaître (1894-1966) Einstein’s Static Universe is unstable Einstein: ‘the biggest blunder of my life’

  7. Lemaître's Universe 1927 The best description of the visible universetoday  > 0

  8. Tolman’s Oscillating Universe Richard Tolman and Einstein at Cal Tech 1932

  9. Tolman includes the 2nd Law of thermodynamics: Oscillations grow (1932) JDB + Dabrowski include the cosmological constant: Oscillations always end (1995)

  10. Kasner’s Anisotropic Universe Volume  abc  time 1921 Edward Kasner (1878-1955) (a,b,c) = (tp, tq, tr) p + q + r = 1 and p2 + q2 + r2 = 1 -1/3  p  0  q  2/3  r  1

  11. How Kasner Gave Us Google Kasner’s 9-yr old nephew Milton Sirotta invented the names Googol = 10100 Googolplex = 10Googol In 1996 Larry Page and Sergey Brin called their new internet search engine ‘BackRub’. Sean Anderson suggested Googolplex. Shortened it to Googol but Anderson mistyped Google.com when he searched to see if Googol.com was available. It was, Brin liked it better, so Google.com was registered on 15 Sept 1997 The Googleplex HQ

  12. expansion shear rotation

  13. The Ten Universes Of Bianchi and Taub Shear Distortion Rotation Gravitational Waves But Everyone sees the same history Spatially homogeneous Ordinary Differential Equations time space

  14. The End of a closed Universe will not be Simultaneous

  15. Misner’s Mixmaster Universe y = x sin(1/x) An infinite number of things happen in a finite time as t  0 x 1/x - [1/x] : 0 < x < 1 continued fraction map 1969

  16. Gauss’s Probability Distribution xn+1 = 1/xn – [1/xn] As n   the probability of outcome x tends to p(x) = 1/[(1+x)ln2] : 01 p(x)dx = 1 Error is < (0.7)n after n iterations p(x) In a Letter to Laplace 30th Jan 1812 ‘a curious problem’ that had occupied him for 12 years Distribution of the fractional parts x

  17. xn+1 = 1/xn – [1/xn] = T(xn) T(x) T(x) =1/x – k (1-k)-1<x<k-1 k integer ldT/dxl = 1/x2 > 1 as 0 < x < 1 x n steps = initial  exp[ht]: where h = 2/[6(ln2)2]  3.45

  18. Gödel's Rotating Universe Allows time travel to occur ! 1949

  19. The Big Bang Universes

  20. The Evidence of a Hot Early History

  21. The Inflationary Universe A temporary lambda 1981

  22. Even Smaller Beginnings

  23. Chaotic Inflation Geography is more complicated than we thought

  24. Eternal Inflation 1077 More than 10 by-universes from our patch alone

  25. What is the Probability of some ‘universe’ arising in the Multiverse? N(A)/N(B) = / Or – maybe you could take the limit? - But…. Fraction of even numbers in 1,2,3,4,5,6,7,8,…  1/2 Fraction of even numbers in 1,3,2,5,7,4,9,11,…  1/3 Answer depends on how you count the universes The Probability Measure Problem

  26. Any Beginning in a Quantum Universe?

  27. The Universe is Accelerating Again  > 0 Lemaître's universe describes our visible universe to high precision

  28. Dark Energy Dominates the Universe The Return of Einstein’s Lambda ?

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