Related papers: Topos Many-Node Theory: Roots, Foundations and Pre…
Inflationary cosmology has, in the last few years,received a strong dose of support from observations. The fact that the fluctuation spectrum can be extracted from the inflationary scenario through an analysis that involves quantum field…
We show that it is possible to combine an early phase of String Gas Cosmology which can explain the origin of the observed structures on cosmological scales with a short later period of power law inflation which creates spatial flatness.…
In this paper we present an approach to determine the smallest possible number of neurons in a layer of a neural network in such a way that the topology of the input space can be learned sufficiently well. We introduce a general procedure…
Starting from pure multidimensional gravity with curvature-nonlinear terms but no matter fields in the initial action, we obtain a cosmological model with two effective scalar fields related to the size of two extra factor spaces. The model…
These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe.
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained…
There is something missing in our understanding of the origin of the seeds of Cosmic Structuture. The fact that the fluctuation spectrum can be extracted from the inflationary scenario through an analysis that involves quantum field theory…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
The emergence of $R^2$ (Starobinsky) inflation from the semi-classical modification of gravity due to matter quantum fields (trace anomaly) clearly points out the importance of fundamental physics and the first principles in the…
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already…
We propose that at the beginning of the universe gravity existed in a limbo either because it was switched off or because it was only conformally coupled to all particles. This picture can be reverse-engineered from the requirement that the…
Doppler peaks in the cosmic microwave background may allow us to distinguish among the two classes of theories-inflationary models and topological defect scenarios-which attempt to explain the origin of structure formation in the universe.…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
We introduce \emph{Information Topology}: a framework that unifies information theory and algebraic topology by treating \emph{cycle closure} as the primitive operation of inference. The starting point is the \emph{dot-cycle dichotomy},…
The laws of Physics are time-reversible, making no qualitative distinction between the past and the future -- yet we can only go towards the future. This apparent contradiction is known as the "arrow of time problem". Its current resolution…
The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in…
We discuss early cosmology in theories where the fundamental Planck mass is close to the TeV scale. In such theories the standard model fields are localized to a (3+1)-dimensional wall with n new transverse sub-millimeter sized spatial…
Models of cosmic inflation suggest that our universe underwent an early phase of accelerated expansion, driven by the dynamics of one or more scalar fields. Inflationary models make specific, quantitative predictions for several observable…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…