The Expanding Universe And the Cosmological Constant John

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 there is no edge

Why is the Universe so old ?

A Recipe for Life helium + helium beryllium helium + beryllium 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 7 3 1 Galaxy per (10 l–yr) 1 ‘universe’ per (1010 l–yr)3

Our Universe Is Cool T 1/size

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

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

A New Part of Gravity Acceleration: d 2 a/dt 2 -GM/a 2 + 1/3 c 2 a - the ‘cosmological constant’ – does it exist? a 3 sinh 2[ct (3 )/2] a 3 t 2 a 3 exp[ct (3 )]

Einstein’s Static Universe (1917) Λ = ΛE = 4 Gρ/c 2 R = ΛE-1/2

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

Friedmann’s universes 1922, 1924 1888 -1925

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 = d. E + pd. V = d( Vc 2) + pd. V = (d )Vc 2 + ( c 2 + p)d. V so d = 0 means p = - c 2 = constant Is thermodynamic state of the universal vacuum H 2 = (dr/dt)2/r 2 = 8 G /3 – k/r 2 + c 2/3 8 G /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 !

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

A New Theory Gives (1/ctnow)2 for the value of seen by observers in the universe at time tnow For tnow = 13. 7 billion years this gives 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 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)

The Far, Far Future 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 ……. . .