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