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Eternal inflation and localization on the landscape · Around

2007

Eternal inflation and localization on the landscape

Podolsky, D., Enqvist, K.

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We model the essential features of eternal inflation on the landscape of a dense discretuum of vacua by the potential $V(\phi)=V_{0}+\delta V(\phi)$, where $|\delta V(\phi)|\ll V_{0}$ is random.

We find that the diffusion of the distribution function $\rho(\phi,t)$ of the inflaton expectation value in different Hubble patches may be suppressed due to the effect analogous to the Anderson localization in disordered quantum systems.
At $t \to \infty$ only the localized part of the distribution function $\rho (\phi, t)$ survives which leads to dynamical selection principle on the landscape.
The probability to measure any but a small value of the cosmological constant in a given Hubble patch on the landscape is exponentially suppressed at $t\to \infty$.

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The volume of the literature regarding this subject is extremely large. The original publications, where the effect of Anderson localization was introduced, include P.W. Anderson, Phys. Rev. 109
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A.A. Starobinsky, in Field Theory, Quantum Gravity and Strings , edited by H.J. de Vega and N. Sanchez (Springer-Verlag, 1986), p. 107
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K. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, 1999)
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