Why did the Universe Inflate?

1. Why did the Universe Inflate?

2. Proceedings of the Nuffield Workshop, Cambridge, 1982

3. Old Inflation Scenario Bubble Collision Time Bubble Nucleation Space

4. New Inflation Scenario Slow roll down V Cosmological Constant φ

5. Microwave Background Radiation

6. 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?

7. No boundary amplitude y[hij, ]= Dg e-S[g] Sum over all metrics that have  a boundary and where the induced metric on  is hij.

8. δ2 δhijδhkl -Gijkl 3R(h) h½+ 2Λh½Ψ[hij] = 0 Wheeler DeWitt Equation 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.

9. Wheeler DeWitt Equation 1 ∂2 1 ∂ 2 ∂a2a2 ∂φ2 – a2 – + a4 VΨ(a, φ) = 0

10. B· C = 0 Δ Δ WKB Approximation Ψ = B eiC C· C + J = 0 Δ Δ

11. No Boundary Amplitude 1/m2N Amplitude = e Amplitude N

12. Volume Weighting Surface of present matter density Hubble Volume Time Space P( Observing a Hubble Volume ) = | Ψ|2× Number of Hubble Volumes MIIMM∞ | Ψ |2 e3N

13. Volume Weighted Probability Quadratic Potential Probability Planck Density Initial φ

14. Volume Weighted Probability Potential with a Maximum at φ = φm Probability φ = φm Initial φ

15. Why did the Universe Inflate? • Volume weighting gives a high probability of a large amount of Inflation