Hessian eigenvalue distribution in a random Gaussian landscape

Understand

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 minima.
• In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues.
• The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of $1/N$ expansion, where $N$ is the dimensionality of the landscape.