1. The Expanding Universe The Expanding Universe And the Cosmological Constant * John D. Barrow

2. Determining accurate distances: a longstanding challenge

4. A Hubble puzzle that you should follow!

5. There is no centre and and there is no edge

9. Why is the Universe so old ?

10. A Recipe for Life helium + helium  beryllium helium + beryllium  carbon carbon + helium  oxygen

11. Why is the Universe so Big ? hydrogen  helium  carbon 10 billion years of alchemy 10 billion years of expansion 10 billion light years of space

12. The Universe is Almost Empty

13. The Universe contains only 1 Atom per cubic metre 1 Earth per (10 l–yr) 3 1 Star per (1000 l–yr) 3 1 Galaxy per (10 7 l–yr) 3 1 ‘universe’ per (10 10 l–yr) 3

14. Our Universe IsCool T  1/size

15. Life-supporting Space is…. Almost empty Big and Old Dark and Cold

16. Pierre Simon Laplace (1749-1827) Isaac Newton (1642-1727) F  1/r 2 or F  r F  A/r 2 + Br Force Laws With The Spherical Property o r

17. A New Part of Gravity  - the ‘cosmological constant’ – does it exist? Acceleration: d 2 a/dt 2  -GM/a 2 + 1/3  c 2 a  sinh 2 [ct (3)/2 ] a 3  sinh 2 [ct (3)/2 ]  t2a3  t2 t2a3  t2  exp[ct(3)] a 3  exp[ct(3)]

18. Einstein’s Static Universe (1917)

19. 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

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

25. The Vacuum Energy Density Same everywhere and in every direction + Same to all observers, no matter how they are moving 1 st law of thermodynamics  0 = dE + pdV = d(Vc 2 ) + pdV = (d)Vc 2 + (c 2 + p)dV so d = 0 means p = - c 2 = constant p = - c 2 = constant Is the thermodynamic state of the universal vacuum c 2 /3 H 2 = (dr/dt) 2 /r 2 = 8G/3 – k/r 2 + c 2 /3 c 2 /3 c 2 /3  8G  /3 (Lemaître 1933)

26. Dark Energy Dominates the Universe

27. Will the Universe Expand Forever ???

28. The Violent End of the Solar System

30. A Bio-friendly Universe Big and Old Dark and Cold But only Just !

32. Why isn’t   10 +66 cm -2 We observe  obs  10 -55 cm -2 ????  > 10 -54 cm -2 No galaxies if  > 10 -54 cm -2 A Big Mystery

33. Gives   (1/ct now ) 2 for the value of  seen by observers in the universe at time t now For t now = 13.7 billion years this gives   10 -55 cm -2 as observed.   10 -55 cm -2 as observed. It also predicts that the fraction of the universe’s energy density in the form of space curvature is  k = –k/H 2 a 2 = -0.0055 Minus sign  average positive curvature Minus sign  average positive curvature 1 =  k +  matter +   Testable in 2012-3 by Planck satellite Current obsns -0.0089 ≤  k ≤ -0.0009 J.D. Barrow and D. Shaw, Phys. Rev. Lett. 106, 101302 (2011), Phys. Rev. D 83, 04351 (2010) A New Theory

34. The Far, Far Future  exp[ct( / 3)] r  exp[ct( / 3)] All stars die All black holes evaporate

35. After 100 billion yrs The last vestige of the expanding universe Disappears from our view forever ……...