The Expanding Universe The Expanding Universe And the Cosmological Constant * John D. Barrow Determining accurate distances: a longstanding challenge A Hubble puzzle that you should follow! There is no centre and and there is no edge Why is the Universe so old ? A Recipe for Life helium + helium beryllium helium + beryllium carbon carbon + helium oxygen 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 The Universe is Almost Empty The Universe contains only 1 Atom per cubic metre 1 Earth per (10 lyr) 3 1 Star per (1000 lyr) 3 1 Galaxy per (10 7 lyr) 3 1 universe per (10 10 lyr) 3 Our Universe IsCool T 1/size Life-supporting Space is. Almost empty Big and Old Dark and Cold Pierre Simon Laplace ( ) Isaac Newton ( ) F 1/r 2 or F r F A/r 2 + Br Force Laws With The Spherical Property o r 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)] Einsteins Static Universe (1917) De Sitters Accelerating Universe Always expanding exponential curve R = exp[t ( /3]) No matter only It has no beginning and no end (1917) Willem De Sitter Friedmanns universes 1922, 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 = 8G/3 k/r 2 + c 2 /3 c 2 /3 c 2 /3 8G /3 (Lematre 1933) Dark Energy Dominates the Universe Will the Universe Expand Forever ??? The Violent End of the Solar System A Bio-friendly Universe Big and Old Dark and Cold But only Just ! Why isnt cm -2 We observe obs cm -2 ???? > cm -2 No galaxies if > cm -2 A Big Mystery 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 cm -2 as observed. cm -2 as observed. It also predicts that the fraction of the universes energy density in the form of space curvature is k = k/H 2 a 2 = Minus sign average positive curvature Minus sign average positive curvature 1 = k + matter + Testable in by Planck satellite Current obsns k J.D. Barrow and D. Shaw, Phys. Rev. Lett. 106, (2011), Phys. Rev. D 83, (2010) A New Theory The Far, Far Future exp[ct( / 3)] r exp[ct( / 3)] All stars die All black holes evaporate After 100 billion yrs The last vestige of the expanding universe Disappears from our view forever ...
