Related papers: Topos Many-Node Theory: Roots, Foundations and Pre…
We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein…
The hypothesis that the Universe underwent a period of exponential expansion at very early times has become the most popular theory of the early Universe. Not only does it solve some of the problems of standard big bang cosmology, but it…
This review article aims at presenting the theory of inflation. We first describe the background spacetime behavior during the slow-roll phase and analyze how inflation ends and the Universe reheats. Then, we present the theory of…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. I describe the quantum origin of density perturbations, giving a heuristic derivation of…
Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a ``steady-state''…
Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance…
Topologically protected sheet-like surfaces, called domain walls, form when the potential of a field has a discrete symmetry that is spontaneously broken. Since this condition is commonplace in field theory, it is plausible that many of…
A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as $\O$-regions. We argue…
Inflationary cosmology leads to the picture of a "multiverse," involving an infinite number of (spatially infinite) post-inflationary thermalized regions, called pocket universes. In the context of theories with many vacua, such as the…
We develop our recent suggestion that inflation may be made past eternal, so that there is no initial cosmological singularity or "beginning of time". Inflation with multiple vacua generically approaches a steady-state statistical…
The standard model of cosmology is based on the hot Big Bang theory and the inflationary paradigm. Recent precise observations of the temperature and polarization anisotropies in the cosmic microwave background and the matter distribution…
Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models,…
The established cosmological theory which describes the history of the Universe since shortly after the "Big Bang" until today is remarkably successful. Thanks to the increasing precision of available observational data, we are now able to…
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of…
In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possible physical relevance of this scheme for inflationary…
The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of…
Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when…
Motifs are thought to be some fundamental components of social face-to-face interaction temporal networks. However, the motifs previously considered are either limited to a handful of nodes and edges, or do not include triangles, which are…
After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt equation, boundary conditions, interpretation of $\psi$), I discuss how these ideas can be tested observationally. Observational predictions differ for different choices…
The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an…