No boundary amplitudes for
the landscape
By Stephen Hawking
4 dimensional Minkowski space.
M=X
Y
6/7 dimensional internal space.
V is a function on the moduli space of Y
The Landscape
Possible
vacuum states
of m-theory
Strong Energy Condition
For any timelike or null vector (Va)
Start of Inflation
Inflation begins at V0
II
V /V < 2
-½
Amplitude = exp V0
Slow roll inflation
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.
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.