Related papers: Lie Group Cosmology
For most of its history, cosmology was a qualitatively constrained discourse on the universe, shaped by limited observational access and the absence of global dynamical laws. This situation has changed decisively in recent decades. Modern…
We assume that the Universe has a non trivial topology whose compact spatial sections have a volume significantly smaller than the horizon volume. By a topological lens effect, such a "folded" space configuration generates multiple images…
We review a cosmology in which particles are fluctuationally created from a background Zero Point Field. This cosmology is consistent with recent observations of an ever expanding and accelerating universe, as also the recently confirmed…
This is an introduction to the approach to the extraction of cosmological dynamics from full quantum gravity based on group field theory condensates. We outline its general perspective, which sees cosmology as the hydrodynamics of the…
Certain results of observational cosmology cast critical doubt on the foundations of standard cosmology but leave most cosmologists untroubled. Alternative cosmological models that differ from the Big Bang have been published and defended…
In this paper we give a pedagogical review of the recent observational results in cosmology from the study of type Ia supernovae and anisotropies in the cosmic microwave background. By providing consistent constrainst on the cosmological…
A Lie group G has many left invariant metrics having drastically different curvature properties. If we regard G as a flat and globalizable absolute parallelism as in [O1], then G has a canonical metric. We study some surprising consequences…
A Lie group is an old mathematical abstract object dating back to the XIX century, when mathematician Sophus Lie laid the foundations of the theory of continuous transformation groups. As it often happens, its usage has spread over diverse…
General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
In this paper, we introduce and study five families of Lie groups in degenerate Clifford geometric algebras. These Lie groups preserve the even and odd subspaces and some other subspaces under the adjoint representation and the twisted…
This article reviews the prevailing paradigm for how galaxies and larger structures formed in the universe: gravitational instability. Basic observational facts are summarized to motivate the standard cosmological framework underlying most…
We present the derivation of the 6-dimensional Eulerian Lie group of the form SO(3,C). We describe our derivation process, which involves the creation of a finite group by using permutation matrices, and the exponentiation of the adjoint…
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
Beginning with a skew-symmetric matrix, we define a certain Poisson--Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or "Lie-Poisson") Poisson bracket. By analyzing this Poisson structure, we gather…
The hypothesis is discussed that our universe is really 5--dimensional with a nonzero cosmological constant that produces a large negative curvature. In this scenario, the observable flat 4--dimensional universe is identified with the…
A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and…
The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a…
Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory:…