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 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
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)]
Einstein’s Static Universe (1917)
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
Friedmann’s 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 (Lemaître 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 isn’t 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 universe’s 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 ……...