Post on 01-Apr-2015
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