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

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

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

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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

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 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

Our Universe

Is

Cool

T 1/size

Life-supporting Space is….

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)

A New Part of Gravity

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)]

Einstein’s Static Universe

(1917)

Λ = ΛE =4Gρ/c2

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

1888-1925

1922,1924

The Vacuum Energy Density

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)

Dark Energy Dominates the Universe

Will the Universe

Expand Forever???

The Violent End of the Solar System

A Bio-friendly UniverseBig and OldDark and ColdBut 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/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 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

……

..

.