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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)

3. String Cosmology: Virtues

& Vices (a) 3 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 ≈10 100 – 10 500 known as the Landscape of String Theory

4. String Cosmology: Virtues

& Vices (b) 4 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



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 8

 With

where

;

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).

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Proposal For Selection Criterion



Place quantum cosmology on the background of the landscape of

string theory. 

Allow the WaveFunction of the universe landscape. Choose boundary conditions and find solutions from Wheeler-DeWitt equation, (WDW).

to propagate on the



Calculate the Probability Distribution obtained from WDW. for the band of solutions



From solutions obtain the density of states (DoS) matrix, (like in quantum mechanics). Maximum of DoS gives the most probable universe.

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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 .

Proposal Applied to SUSY Sector

Solutions obtained from WDW eqution for SUSY sector are ‘standing wave’, extended over the whole landscape. (Similar to Theta vacua).

The most probable solution is the lowest energy state. Note it is lifted from zero, due to an induced mass gap:

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Solutions is separated by a finite energy.

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Applied to non-SUSY Sector

 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:

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15. Remarks:

Landscape is rich in phenomenology Top Down: Bottom-up: explore the structure 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 V I equally good for allowing propagation through sites. ) Likely that any QG structure may be a discrete set of vacua. This approach may be generic 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.