We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that within the stochastic framework they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the $Delta N$ form
alism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would of course be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization group invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.
We present a new method to study the Nernst effect and diamagetism of an extreme type-II superconductor dominated by phase fluctuations. We work directly with vortex variables and our method allows us to tune vortex parameters (e.g., core energy and
number of vortex species). We find that diamagnetic response and transverse thermoelectric conductivity ($alpha_{xy}$) persist well above the Kosterlitz-Thouless transition temperature, and become more pronounced as the vortex core energy is increased. However, they textit{weaken} as the number of internal vortex states are increased. We find that $alpha_{xy}$ closely tracks the magnetization $(-M/T)$ over a wide range of parameters.
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 $tto infty$.
We discuss generic properties of classical and quantum theories of gravity with a scalar field which are revealed at the vicinity of the cosmological singularity. When the potential of the scalar field is exponential and unbounded from below, the gen
eral solution of the Einstein equations has quasi-isotropic asymptotics near the singularity instead of the usual anisotropic Belinskii - Khalatnikov - Lifshitz (BKL) asymptotics. Depending on the strength of scalar field potential, there exist two phases of quantum gravity with scalar field: one with essentially anisotropic behavior of field correlation functions near the cosmological singularity, and another with quasi-isotropic behavior. The ``phase transition between the two phases is interpreted as the condensation of gravitons.
