Related papers: The Continuum of Discrete Trajectories in Eternal …
The discovery of the string theory landscape has recently brought attention to the eternal nature of inflation. In contrast to the common belief that eternal inflation may be a generic feature of most inflationary models, in this note we…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated…
We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
Projections of finite dimensional sets and their measures are investigated in infinite-dimensional power measure spaces. The starting point is the known algebraic formula, expressing \ the $y$-projection of a finite-dimensional set $a$ as a…
We propose a new measure for eternal inflation that includes both conditions, large field fluctuations and smooth homogeneous domains, in the self reproducing probability estimate. We show that due to the increasing inhomogeneities in the…
We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an…
We propose a new measure for eternal inflation, based on search optimization and first-passage statistics. This work builds on the dynamical selection mechanism for vacua based on search optimization proposed recently by the author and…
Inflation is known to be generically eternal to the future: the false vacuum is thermalized in some regions of space, while inflation continues in other regions. Here, we address the question of whether inflation can also be eternal to the…
Eternal inflation produces pocket universes with all physically allowed vacua and histories. Some of these pocket universes might contain a phase of slow-roll inflation, some might undergo cycles of cosmological evolution and some might…
Stochastic inflation describes the global structure of the inflationary universe by modeling the super-Hubble dynamics as a system of matter fields coupled to gravity where the sub-Hubble field fluctuations induce a stochastic force into…
It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill,…
I propose a new volume-weighted probability measure for cosmological "multiverse" scenarios involving eternal inflation. The "reheating-volume (RV) cutoff" calculates the distribution of observable quantities on a portion of the reheating…
We argue that in the context of eternal inflation in the landscape, making predictions for cosmological -- and possibly particle physics -- observables requires a measure on the possible cosmological histories as opposed to one on the vacua…
The recently proposed "reheating-volume" (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological "multiverse" scenarios involving eternal inflation. I give a detailed description of…
Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured…
We show that for entire maps of the form $z \mapsto \lambda \exp(z)$ such that the orbit of zero is bounded and such that Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This…
In the context of eternal inflation, cosmological predictions depend on the choice of measure to regulate the diverging spacetime volume. The spectrum of inflationary perturbations is no exception, as we demonstrate by comparing the…
We study the details of eternal inflation in the presence of a spectator Higgs field within the framework of the minimal Standard Model. We have recently shown that in the presence of scalar field(s) which allow inflation only within a…