why did the universe inflate?. proceedings of the nuffield workshop, cambridge, 1982

Why did the Universe Inflate?

Proceedings of the Nuffield Workshop, Cambridge, 1982

Old Inflation Scenario

Time

Space

Bubble Nucleation

Bubble Collision

New Inflation Scenario

φ

Slow

roll downCosmological Constant

V

Microwave Background Radiation

Why did the Universe Inflate?

Why did the scalar field start with a high value of the potential, and run down to a minimum?

Why didn’t it just start at the minimum?

No boundary amplitude

[hij, ]= Dg e-S[g]

Sum over all metrics that have a boundary andwhere the induced metric on is hij.

Wheeler DeWitt Equation

-Gijkl

δ2

δhij δhkl

3R(h) h½ + 2Λh½ Ψ [hij] = 0

Where Gijkl is the metric on superspace,Gijkl = ½ h -½ (hikhjl + hilhjk – hijhkl)

and 3R is the scalar curvature of the intrinsic geometry of the three-surface.

1 ∂2 1 ∂

2 ∂a2 a2 ∂φ2 – a2 – + a4 V Ψ(a, φ) = 0

Wheeler DeWitt Equation

WKB Approximation

Ψ = B eiCΔ

C·

Δ

C + J = 0Δ

B·

Δ

C = 0

No Boundary Amplitude

N

Am

plitu

de

Amplitude = e 1/m2N

Volume WeightingSurface of present

matter densityHubble Volume

P( Observing a Hubble Volume ) = | Ψ |2 × Number of Hubble Volumes

MIIMM∞ | Ψ |2 e3N

Time

Space

Volume Weighted Probability

Initial φ

Pro

babi

lity

Planck Density

Quadratic Potential

Volume Weighted Probability

Initial φ

Pro

babi

lity

φ = φm

Potential with a Maximum at φ = φm

Why did the Universe Inflate?

• Volume weighting gives a high probability of a large amount of Inflation