Related papers: Listening to Celestial Algebras
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
We present an eight-dimensional even sub-algebra of the ${2^4=16}$-dimensional associative Clifford algebra ${\mathrm{Cl}_{4,0}}$ and show that its eight-dimensional multivectors ${\bf X}$ and ${\bf Y}$ respect the composition law ${||{\bf…
We provide a bird's-eye view of neutron-star seismology, which aims to probe the extreme physics associated with these objects, in the context of gravitational-wave astronomy. Focussing on the fundamental mode of oscillation, which is an…
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…
We review the current observational status of string cosmology when confronted with experimental datasets. We begin by defining common observational parameters and discuss how they are determined for a given model. Then we review the…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal…
The apparent accelerating expansion of the Universe is forcing us to examine the foundational aspects of the standard model of cosmology -- in particular, the fact that dark energy is a direct consequence of the homogeneity assumption. We…
This article briefly summarizes the motivations for -- and recent progress in -- searching for cosmological configurations within string theory, with a focus on how much we might reasonably hope to learn about fundamental physics from…
The modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy.It implies extension of particle symmetry beyond the Standard model. Studies of physical basis of the modern cosmology combine direct searches…
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
The number of cosmic strings in the observable universe is relevant in determining the probability of detecting such cosmic defects through their gravitational signatures. In particular, we refer to the observation of gravitational lensing…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for…
Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and…
The new millennium will see the upcoming of several ground-based interferometric gravitational wave antennas. Within the next decade a space-based antenna may also begin to observe the distant Universe. These gravitational wave detectors…
These lecture notes concentrate on a few specific topics concerning the distribution of galaxies on scales from 0.1 to nearly 1000/h Mpc. The main aim is to provide the students with the information and tools to familiarize with a few basic…
The comparison of the Standard Cosmological Model (SCM) with astronomical observations, i.e. theory versus experiment, and with the Minimal Standard Model (MSM) in particle physics, i.e. theory versus theory, is discussed. The main issue of…