Related papers: The Distribution of Vacua in Random Landscape Pote…
It is speculated that the correct theory of fundamental physics includes a large landscape of states, which can be described as a potential which is a function of N scalar fields and some number of discrete variables. The properties of such…
Random, multifield functions can set generic expectations for landscape-style cosmologies. We consider the inflationary implications of a landscape defined by a Gaussian random function, which is perhaps the simplest such scenario. Many key…
The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential…
We consider the statistical properties of vacua and inflationary trajectories associated with a random multifield potential. Our underlying motivation is the string landscape, but our calculations apply to general potentials. Using random…
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential…
We study the probability distribution P(\Lambda) of the cosmological constant \Lambda in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux…
In theories in which the cosmological constant Lambda takes a variety of values in different ``subuniverses,'' the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it.…
Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…
Using the replica method we calculate the mean spectral density of the Hessian matrix at the global minimum of a random $N \gg 1$ dimensional isotropic, translationally invariant Gaussian random landscape confined by a parabolic potential…
Finding the mean of the total number of stationary points for N-dimensional random Gaussian landscapes can be reduced to averaging the absolute value of characteristic polynomial of the corresponding Hessian. First such a reduction is…
We propose that the Standard Model is coupled to a sector with an enormous landscape of vacua, where only the dimensionful parameters--the vacuum energy and Higgs masses--are finely "scanned" from one vacuum to another, while dimensionless…
After reviewing the cosmological constant problem - why is Lambda not huge? - I outline the two basic approaches that had emerged by the late 1980s, and note that each made a clear prediction. Precision cosmological experiments now indicate…
We propose a new selection criteria for predicting the most probable wavefunction of the universe that propagates on the string landscape background, by studying its dynamics from a quantum cosmology view. Previously we applied this…
In a previous paper we found that in the context of the string theory ``discretuum'' proposed by Bousso and Polchinski, the cosmological constant probability distribution varies wildly. However, the successful anthropic predictions of the…
We consider an elastic manifold of internal dimension $d$ and length $L$ pinned in a $N$ dimensional random potential and confined by an additional parabolic potential of curvature $\mu$. We are interested in the mean spectral density…
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…
Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions however approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
If the gradient of a probability distribution on a landscape of vacua aligns with the variation of some fundamental parameter, the parameter may be likely to take some non-generic value. Such non-generic values can be associated to critical…
We suggest a novel picture of the quantum Universe -- its creation is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed state which…