No boundary amplitudes for the landscape

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No boundary amplitudes for the landscape By
Stephen Hawking
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4 dimensional Minkowski space.
M X Y
6/7 dimensional internal space.
V is a function on the moduli space of Y
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The Landscape
Possible vacuum states of m-theory
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Strong Energy Condition
For any timelike or null vector (Va)
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Start of Inflation
Inflation begins at V0
VII/V lt 2 Amplitude exp V0-½
Slow roll inflation
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Conclusions
1. Universe is always in the semi-classical 4
dimensional general relativity regime.
2. The whole universe is in a homogeneous
landscape, not a mosaic.
3. No primordial topological defects.
4. Amplitudes will be non zero for some but not
all landscape states.
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Eternal Inflation Scenario
Quantum fluctuations in a scalar field are
supposed to drive the potential up to the Planck
value.
Widely separated regions were supposed to fall
into different local minima of the potential
which would give the universe a mosaic structure.