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Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent…
Cosmic inflation provides a window to the highest energy densities accessible in nature, far beyond those achievable in any realistic terrestrial experiment. Theoretical insights into the inflationary era and its observational probes may…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…
In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously…
This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key…
Modern cosmology provides a connection between the physics of particles and fields and observational cosmology. Making use of this link, a wealth of new observational data can be utilized to explore and constrain theories of fundamental…
In a unified picture both inflation and present dynamical dark energy arise from the same scalar field. The history of the Universe describes a crossover from a scale invariant "past fixed point" where all particles are massless, to a…
We discuss a novel scenario for early cosmology, when the inflationary quasi-de Sitter phase dynamically originates from the initial quantum state represented by the microcanonical density matrix. This genuine quantum effect occurs as a…
We review an approach that uses binary relations as the fundamental constituents of the universe, utilizing them as building blocks for both space and matter. The model is defined by an ultraviolet continuous fixed point of a statistical…
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman's path integral for superposition…
We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without…
We extend the `topological inflation' of Linde and Vilenkin to {\em unstable} monopoles. This allows the monopole to decay; not inflating eternally, as topological inflation demands. Such a situation happens naturally in some Grand Unified…
We perform a general analysis of the cosmological viability of Geometric Inflation. We show that the evolution of the universe, from inflation to the present day, can be seen from the addition of an infinite tower of curvature invariants…
The structure of the network can be described by motifs, which are subgraphs that often repeat themselves. In order to understand the structure of network motifs, it is of great importance to study subgraphs from the perspective of…
The cosmic inflation hypothesis, its relation to fundamental theory on the beginning of the universe, and the light that both shed on how the various elements and their relative amounts came into existence. The fundamental factors…
We study cosmological solutions for the very early universe beginning at the Planck scale for a universe containing radiation, curvature and, as a simplification of a possible scalar field potential, a cosmological constant term. The…
Recently Hollands and Wald argued that inflation does not solve any of the major cosmological problems. We explain why we disagree with their arguments. They also proposed a new speculative mechanism of generation of density perturbations.…
In inflation cosmologies, cosmic structure develops through the gravitational instability of the inevitable quantum noise in primordial scalar fields. I show how the acceleration of the universe defines the shape of the primordial spectrum…
The inflationary scenario has become the paradigm of early universe cosmology, and - in conjuction with ideas from superstring theory - has led to speculations about an "inflationary multiverse". From a point of view of phenomenology, the…
Cosmological inflation remains to be a unique mechanism of generation of plausible initial conditions in the early universe. In particular, it generates the primordial quasiclassical perturbations with power spectrum determined by the…