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