Related papers: Towards a gauge invariant volume-weighted probabil…
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…
I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
We define a Gaussian invariant measure for the two-dimensional averaged-Euler equation and show the existence of its solution with initial conditions on the support of the measure. An invariant surface measure on the level sets of the…
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 basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are…
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and…
It has been suggested that the no boundary proposal would predict little or no slow roll inflation leading to an empty deSitter universe. However it is argued that the probability for the whole universe should be multiplied by a zero mode…
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…
Presently, the optical selection rules for excitons under circularly-polarized light are manifestly gauge-dependent. Recently, Fernando et al. introduced a gauge-invariant, quantized interband index. This index may improve the topological…
We examine the amount of parameter tuning to make slow-roll inflation marginally eternal by considering an R-invariant chaotic inflation as an example of one-parameter tuning in supergravity. The primordial inflation turns out to be…
I describe reasons to think we are living in an eternally inflating multiverse where the observable "constants" of nature vary from place to place. The major obstacle to making predictions in this context is that we must regulate the…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
The Hubble tension cast a blight on the standard cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain…
For slow-roll inflation we study the phase transition to the eternal regime. Starting from a finite inflationary volume, we consider the volume of the universe at reheating as order parameter. We show that there exists a critical value for…
We argue that inflationary dynamics may support a scenario where significant matter-antimatter asymmetry is generated from initially small-scale quantum fluctuations that are subsequently stretched out over large scales. This scenario can…
We derive a general expression for the gauge invariant mass (m_G) for an Abelian gauge field, as induced by vacuum polarization, in 1+1 dimensions. From its relation to the chiral anomaly, we show that m_G has to satisfy a certain…
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…
We argue that all the necessary ingredients for successful inflation are present in the flat directions of the Minimally Supersymmetric Standard Model. We show that out of many gauge invariant combinations of squarks, sleptons and Higgses,…