Related papers: Stationary Measure in the Multiverse
There is a deep cosmological mystery: although dependent on very different underlying physics, the timescales of structure formation, of galaxy cooling (both radiatively and against the CMB), and of vacuum domination do not differ by many…
In this paper we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type statistic, which…
Using analytical methods and Monte Carlo simulations, we analyze new statistics designed to detect isolated step-like discontinuities which are coherent over large areas of Cosmic Microwave Background (CMB) pixel maps. Such coherent…
We investigate the no-boundary measure in the context of moduli stabilization. To this end, we first show that for exponential potentials, there are no classical histories once the slope exceeds a critical value. We also investigate the…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well-defined, and…
In the context of the pre-big bang scenario the large-scale CMB anisotropy can be seeded by a primordial background of very light (or massless) axion fluctuations. In that case the slope of the temperature anisotropy spectrum, allowed by…
Upcoming cosmic microwave background (CMB) experiments are expected to detect new signals probing interaction of CMB photons with intervening large-scale structure. Among these the moving-lens effect, the CMB temperature anisotropy induced…
Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex…
We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This…
In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the…
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…
Recently a brane world perspective on the cosmological constant and the hierarchy problems was presented. Here, we elaborate on some aspects of that particular scenario and discuss the stability of the stationary brane solution and the…
Many modern cosmological scenarios feature large volumes of spacetime in a de Sitter vacuum phase. Such models are said to be faced with a "Boltzmann Brain problem" - the overwhelming majority of observers with fixed local conditions are…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
The standard $\Lambda$CDM model provides an excellent fit to current cosmological observations but suffers from a potentially serious Boltzmann Brain problem. If the universe enters a de Sitter vacuum phase that is truly eternal, there will…
This paper extends the recent investigation of the string theory landscape in hep-th/0605266, where it was found that the decay rate of dS vacua to a collapsing space with a negative vacuum energy can be quite large. The parts of space that…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…
Many cosmologists (myself included) have advocated volume weighting for the cosmological measure problem, weighting spatial hypersurfaces by their volume. However, this often leads to the Boltzmann brain problem, that almost all…
KKLT give a mechanism to generate de Sitter vacua in string theory. And recently, the scenario, {\em landscape}, is suggested to explain the problem of the cosmological constant. In this scenario, the cosmological constant is a de Sitter…