Related papers: Probabilities in the landscape
We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of…
We show that density fluctuations in standard inflationary scenarios may take the most general non-Gaussian distribution if the wave function of the Universe is not in the ground state. We adopt the Schr\"odinger picture to find a…
With present and future observations becoming of higher and higher quality, it is timely and necessary to investigate the most significant theoretical uncertainties in the predictions of inflation. We show that our ignorance of the entire…
This study reviews the advances made in inflationary theory, especially regarding the seeming disparity between inflation energy and dark energy, and their significance to cosmic evolution as a whole. I attempt to connect the two sources of…
Based on comments made at the 23rd Solvay Conference, December 2005, Brussels.
In this thesis, we show how the structure of the landscape potential of the primordial Universe may be probed through the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the…
In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a…
In this review I focus on a few selected topics, where recent theoretical and/or observational progress has been made and important developments are expected in the future. They include: 1) Evolution of isotopic ratios, 2) Mixing processes…
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
The evolution of the inflaton field fluctuations from gauge-invariant metric fluctuations is discused. In particular, the case of a symmetric $\phi_c$-exponential potential is analyzed.
Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the…
Inflation has been the driving idea in cosmology for two decades and is a pillar of the New Cosmology. The inflationary paradigm has now passed its first round of significant tests, with two of its three basics predictions confirmed at…
Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the…
We investigate the inflationary implications of extensions of Poincare symmetry. The simplest constructions with local scale invariance lead to universal predictions: the spectral index is $n_s = 1-2/N$, in excellent agreement with Planck…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
It is conjectured that inflation, taking account of quantum gravity, leads to a discrete spectrum of cosmological perturbations, instead of the continuous Gaussian spectrum predicted by standard field theory in an unquantized background.…
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…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
In order to overcome the limitations of the original expression of the probability distribution appearing in literature of Incomplete Statistics, a new expression of the probability distribution is derived, where the Lagrange multiplier %B%…