The Expanding Universe And the Cosmological Constant * John D. Barrow
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Transcript of The Expanding Universe And the Cosmological Constant * John D. Barrow
The Expanding UniverseThe Expanding UniverseAnd the And the
Cosmological Constant Cosmological Constant **
John D. BarrowJohn D. Barrow
A Recipe for LifeA Recipe for Life
helium + helium helium + helium berylliumberyllium
helium + beryllium helium + beryllium carboncarbon
carbon + helium carbon + helium oxygenoxygen
Why is the Universe so Why is the Universe so
Big ?Big ?hydrogen hydrogen helium helium carboncarbon10 billion years of 10 billion years of alchemyalchemy10 billion years of 10 billion years of expansionexpansion10 billion light years of 10 billion light years of spacespace
The Universe contains The Universe contains onlyonly
1 Atom per cubic metre1 Atom per cubic metre1 Earth per (10 l–yr)1 Earth per (10 l–yr)33
1 Star per (1000 l–yr)1 Star per (1000 l–yr)33 1 Galaxy per (101 Galaxy per (1077 l–yr) l–yr)33
1 ‘universe’ per (101 ‘universe’ per (101010 l–yr) l–yr)33
Life-supporting Space is….Life-supporting Space is….
Almost emptyAlmost emptyBig and OldBig and Old
Dark and ColdDark and Cold
Pierre Simon Laplace (1749-1827)
Isaac Newton (1642-1727)
F F 1/r 1/r22 or F or F r r
F F A/r A/r22 + Br + Br
Force Laws With The Spherical PropertyForce Laws With The Spherical Property
or
A New Part of GravityA New Part of Gravity
- the ‘cosmological constant’ – does it exist?- the ‘cosmological constant’ – does it exist?
Acceleration: dAcceleration: d22a/dta/dt22 -GM/a -GM/a22 + + 1/3 1/3 cc22aa
a3 sinh sinh22[ct[ct(3(3)/2)/2]]
a3 t t22 a3 exp[ct exp[ct(3(3)])]
De Sitter’s Accelerating UniverseDe Sitter’s Accelerating Universe
Always expandingAlways expandingexponential curve R = exp[texponential curve R = exp[t((/3])/3])
No matter – only No matter – only It has no beginning and no endIt has no beginning and no end
(1917)(1917)Willem De SitterWillem De Sitter
1872-19341872-1934
The Vacuum Energy DensityThe Vacuum Energy DensitySame everywhere and in every directionSame everywhere and in every direction
++Same to all observers, no matter how they are movingSame to all observers, no matter how they are moving
11stst law of thermodynamics law of thermodynamics
0 = dE0 = dE + pdV = d( + pdV = d(VcVc22) + pdV = (d) + pdV = (d)Vc)Vc22 + ( + (cc2 2 + p)dV + p)dV
so d = 0 means
p = - p = - cc2 2 = constant = constantIs the thermodynamic state of the universal vacuumIs the thermodynamic state of the universal vacuum
H2 = (dr/dt)2/r2 = 8G/3 – k/r2 + cc22/3 /3
cc22/3 /3 8G /3(Lemaître 1933)
A Bio-friendly UniverseA Bio-friendly Universe
Big and OldBig and OldDark and ColdDark and Cold
But only Just !But only Just !
Why isn’tWhy isn’t 1010+66+66 cm cm-2-2
We observeWe observeobsobs 10 10-55-55 cm cm-2-2
????????No galaxies if > 10 > 10-54-54 cm cm-2-2
A Big Mystery
Gives Gives (1/ct (1/ctnownow))22 for the value of for the value of seen seen by observers in the universe at time tby observers in the universe at time tnownow
For tFor tnownow = 13.7 billion years this gives = 13.7 billion years this gives
1010-55-55 cm cm-2-2 as observed as observed..It also predicts that the fraction of the It also predicts that the fraction of the
universe’s energy density in the form of universe’s energy density in the form of space curvature isspace curvature is
kk = –k/H = –k/H22aa22 = -0.0055 = -0.0055 Minus sign Minus sign average positive curvature average positive curvature
1 = 1 = kk + + mattermatter + +
Testable in 2012-3 by Planck satelliteTestable in 2012-3 by Planck satelliteCurrent obsns -0.0089 ≤ Current obsns -0.0089 ≤ kk ≤ -0.0009 ≤ -0.0009
J.D. Barrow and D. Shaw, Phys. Rev. Lett. J.D. Barrow and D. Shaw, Phys. Rev. Lett.
106, 101302 (2011), Phys. Rev. D 83, 04351 106, 101302 (2011), Phys. Rev. D 83, 04351 (2010)(2010)
A New TheoryA New Theory
The Far, Far FutureThe Far, Far Future
r exp[ct exp[ct((//3)]3)]
All stars dieAll stars die
All black holes evaporateAll black holes evaporate