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Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…
The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another…
Cosmological perturbation theory is a key tool to study the universe. The linear or first order theory is well understood, however, developing and applying the theory beyond linear order is at the cutting edge of current research in…
The cosmic no hair conjecture is tested for a large class of inhomogeneous cosmologies with a positive cosmological constant. Firstly, we derive a new class of exact inhomogeneous cosmological solutions whose matter content of the models is…
We describe several different regimes which are possible in inflationary cosmology. The simplest one is inflation without self-reproduction of the universe. In this scenario the universe is not stationary. The second regime, which exists in…
Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…
An introductory account is given of the modern understanding of the physics of the early Universe. Particular emphasis is placed on the paradigm of cosmological inflation, which postulates a period of accelerated expansion during the…
With the recent measurements of temperature and polarization anisotropies in the microwave background by WMAP, we have entered a new era of precision cosmology, with the cosmological parameters of a Standard Cosmological Model determined to…
Links in most real networks often change over time. Such temporality of links encodes the ordering and causality of interactions between nodes and has a profound effect on network dynamics and function. Empirical evidences have shown that…
The possibility that the multiverse corresponds to physical reality deserves serious investigation. Having three different important theories,(quantum mechanics, string theory and inflation), predict the existence of the multiverse is…
In the past decade, the importance of dissipation and fluctuation to inflationary dynamics has been realized and has led to a new picture of inflation called warm inflation. Although these phenomena are common to condensed matter systems,…
This paper investigates a scale-invariant inflationary model characterized by a scalar field non-minimally coupled to gravity and a curvature term quadratic in the Ricci scalar. The model's dynamic is analyzed using a full numerical…
The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by…
In this paper we review Penrose's Weyl curvature conjecture which states that the concept of gravitational entropy and the Weyl tensor is somehow linked, at least in a cosmological setting. We give a description of a certain entity…
Primordial perturbations in our universe are believed to have a quantum origin, and can be described by the wavefunction of the universe (or equivalently, cosmological correlators). It follows that these observables must carry the imprint…
These four lectures cover four topics in modern cosmology: the cosmological constant, the cosmic microwave background, inflation, and cosmology as a probe of physics at the Planck scale. The underlying theme is that cosmology gives us a…
Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background…
The large-scale structure of the universe suggests that the physics underlying its early evolution is scale-free. This was the historic motivation for the Harrison-Zel'dovich-Peebles spectrum and for inflation. Based on a hydrodynamical…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
Cosmological production of scalar, non-minimally coupled dark matter depends on the specifics of the inflationary model under consideration. We analyze both Starobinsky inflation and a quadratic potential, solve the full background…