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The Expanding Universe And the Cosmological Constant * John D. BarrowPowerPoint Presentation

The Expanding Universe And the Cosmological Constant * John D. Barrow

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Why is the Universe so old?

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 only1 Atom per cubic metre1 Earth per (10 l–yr)31 Star per (1000 l–yr)31 Galaxy per (107 l–yr)31 ‘universe’ per (1010 l–yr)3

Almost emptyBig and OldDark and Cold

Force Laws With The Spherical Property

o

F 1/r2 or F r

r

Isaac Newton (1642-1727)

F A/r2 + Br

Pierre Simon Laplace (1749-1827)

Acceleration: d2a/dt2 -GM/a2 + 1/3 c2a

- the ‘cosmological constant’ – does it exist?

a3 sinh2[ct(3)/2]

a3 t2

a3 exp[ct(3)]

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

Same everywhere and in every direction

+

Same to all observers, no matter how they are moving

1st law of thermodynamics

0 = dE + pdV = d(Vc2) + pdV = (d)Vc2 + (c2 + p)dV

so d = 0 means

p = - c2 = constant

Is the thermodynamic state of the universal vacuum

H2 = (dr/dt)2/r2 = 8G/3 – k/r2 + c2/3

c2/3 8G /3

(Lemaître 1933)

Expand Forever???

A Bio-friendly UniverseBig and OldDark and ColdBut only Just !

Why isn’t

10+66 cm-2

We observe

obs 10-55 cm-2

????

No galaxies if > 10-54 cm-2

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/H2a2 = -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 last vestige of the expanding universe

Disappears from our view forever

……

..

.

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