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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

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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

The Expanding Universe

And the

Cosmological Constant

*

John D. Barrow


The expanding universe and the cosmological constant john d barrow

Determining accurate distances: a longstanding challenge


The expanding universe and the cosmological constant john d barrow

A Hubble puzzle that you should follow!


The expanding universe and the cosmological constant john d barrow

There is no centre

and

there is no edge


The expanding universe and the cosmological constant john d barrow

Why is the Universe so old?


The expanding universe and the cosmological constant john d barrow

A Recipe for Life

helium + helium  beryllium

helium + beryllium  carbon

carbon + helium  oxygen


The expanding universe and the cosmological constant john d barrow

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 expanding universe and the cosmological constant john d barrow

The Universe is Almost Empty


The expanding universe and the cosmological constant john d barrow

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


The expanding universe and the cosmological constant john d barrow

Our Universe

Is

Cool

T 1/size


The expanding universe and the cosmological constant john d barrow

Life-supporting Space is….

Almost emptyBig and OldDark and Cold


The expanding universe and the cosmological constant john d barrow

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)


The expanding universe and the cosmological constant john d barrow

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)]


The expanding universe and the cosmological constant john d barrow

Einstein’s Static Universe

(1917)

Λ = ΛE =4Gρ/c2

R = ΛE-1/2


The expanding universe and the cosmological constant john d barrow

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


The expanding universe and the cosmological constant john d barrow

Friedmann’s universes

1888-1925

1922,1924


The expanding universe and the cosmological constant john d barrow

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 = 8G/3 – k/r2 + c2/3

c2/3  8G /3

(Lemaître 1933)


The expanding universe and the cosmological constant john d barrow

Dark Energy Dominates the Universe


The expanding universe and the cosmological constant john d barrow

Will the Universe

Expand Forever???


The expanding universe and the cosmological constant john d barrow

The Violent End of the Solar System


The expanding universe and the cosmological constant john d barrow

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


The expanding universe and the cosmological constant john d barrow

A Big Mystery

Why isn’t

  10+66 cm-2

We observe

obs  10-55 cm-2

????

No galaxies if  > 10-54 cm-2


The expanding universe and the cosmological constant john d barrow

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 expanding universe and the cosmological constant john d barrow

The Far, Far Future

r  exp[ct(/3)]

All stars die

All black holes evaporate


The expanding universe and the cosmological constant john d barrow

After 100 billion yrs

The last vestige of the expanding universe

Disappears from our view forever

……

..

.


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