Wavefunction of the Universe on the
Landscape of String Theory
Laura Mersini-Houghton
UNC Chapel Hill, USA
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2. Prelude
Indications from Precision Cosmology are:
We may need new physics to explain observables


Clustering of LSS and/or CMB spectra may require non-inflationary
channels if their cross-correlation is small.
Weak lensing potential that maps LSS will provide evidence for these
claims (+ new information)
Therefore it is time we take seriously:
The cosmological implications of string theory (as thecurrent
leading candidate for new physics)
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3. String Cosmology: Virtues & Vices (a)
A well defined framework
Lots of progress
Can predict realistic cosmologies
Can address fundamental issues
BUT…
Ends up predicting too many of them, perhaps
N≈10100 – 10500 known as the Landscape of String
Theory
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4. String Cosmology: Virtues & Vices (b)
Q: Does This mean theory loses its predictive power and
becomes non-falsifiable?
The theme, over-and-over again, is:
Q: Which vacua does our universe pick?
Q: Do we need to appeal to the Anthropic principle in order to
address the vacuum selection problem???
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5. Anthropic Selection (AS)– a few
remarks
Good to have an open mind to new principles, on the condition that
they are subjected to Scientific Scrutiny
Done on the basis that the theory/principle that can be tested
I believe AS fails the above criteria since:
Relating life to the existence of structure may be incorrect. E.g: It can
be based on requiring carbon. But it may be over simplistic to derive Λ
from this effect,
because:
We are incapable of calculating a probability distribution for the
universe since both life and structure are too complex and we don’t
understand yet how they depend on the initial conditions
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6. Anthropic Selection
– a counter example
Kauffman Theory:
Given a degree of initial random complexity, life (proteins)
always arises as an Attractor Point of any initial set of
phase space, after a few cycles of evolution/trajectories in
phase space
This is an alternative theory attempting to define life. The
probability distribution would be very different if AS is applied to
this theory.
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Wheeler DeWitt (WDW) Equation
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
Minisuperspace of (non-)SUSY landscape vacua,
described by the potential V (φ) with potential wells
that sit at zero, and by the metric of spatially flat and
homogenous 3-geometries

N is a lapse function that can be set to N = 1. The
combined action, (gravity + landscape moduli):
Wheeler DeWitt Equation

Is the Hamiltonian constraint on Wave Functional Ψ

With
where
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;
The Landscape Background
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
Consider the array of vacua on the landscape to
be a ‘super-lattice’ on the configuration space of
Phi.

Model the SUSY sector of the landscape by a
periodic potential lattice with vacua sitting at zero
energy.

Model the non-SUSY sector of the landscape by a
stochastic distribution of vacua energies, namely
a randomly disordered ‘super-lattice’ ,(white noise).
Proposal For Selection Criterion
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
Place quantum cosmology on the background of the landscape of
string theory.

Allow WaveFunction of the universe to propagate on the
landscape. Choose boundary conditions and find solutions from
the Wheeler-DeWitt equation, (WDW).

Calculate the Probability Distribution for the band of solutions
obtained from WDW.

From solutions obtain the density of states (DoS) matrix, (like in
quantum mechanics). Maximum of DoS gives the most probable
universe.
The Selection Criterion for the
Landscape Vacua
Is thus a dynamic selection based on the
Proposal:
To allow the WaveFunction of the Universe to
propagate on the Landscape background and, by
using Quantum Cosmology Framework, to
calculate the Most Probable Solution.
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Proposal Applied to SUSY Sector
Solutions obtained from WDW eqution for
SUSY sector are ‘standing wave’, extended
over the whole landscape. (Similar to Thetavacua).
The most probable solution is the lowest energy
state. Note it is lifted from zero, due to an induced
mass gap:
Solutions is separated by a finite energy.
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Applied to non-SUSY Sector
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
Solution for the wavefunction of the
universe for the non-SUSY sector are
‘Anderson’-localized:

Probability distribution, obtained from
Density of States rho, is peaked around the
universe with zero vacuum energy:
15. Remarks:
Landscape is rich in phenomenology
Top Down: explore the structure
Bottom-up: use QC framework to calculate and predict Λ, V
(higgs) etc.
Decoherence can be addressed from quantum mechanical
solutions (tunneling among vacua not crucial, any short range VI
equally good for allowing propagation through sites. )
Likely that any QG structure may be a discrete set of vacua. This
approach may be generic
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Extension to Higgs/SM degrees of freedom for the vacua can
relate V(higgs)/Λ through scaling. An N-body multi-scattering
problem…work in progress.