The Expanding UniverseThe Expanding UniverseAnd the And the

Cosmological Constant Cosmological Constant **

John D. BarrowJohn D. Barrow

Determining accurate distances: a longstanding challenge

A Hubble puzzle that you should follow!A Hubble puzzle that you should follow!

There is no centreThere is no centre

and and there is no edgethere is no edge

Why is the Why is the Universe Universe

so oldso old??

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 The Universe is is

Almost EmptyAlmost Empty

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

Our Our

UniverseUniverseIsIs

CoolCool

T 1/size

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)])]

Einstein’s Static UniverseEinstein’s Static Universe

(1917)(1917)

Λ = ΛE = 4Gρ/c2

R = ΛE-1/2

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

Friedmann’s universesFriedmann’s universes

1922,19241888-1925

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)

Dark Energy Dominates the UniverseDark Energy Dominates the Universe

Will the Universe Will the Universe Expand Expand ForeverForever

??????

The Violent End of the Solar SystemThe Violent End of the Solar System

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

After 100 billion yrsThe last vestige of the expanding universe

Disappears from our view forever……

...