Related papers: Lie Group Cosmology
The early universe provides an opportunity for quantum gravity to connect to observation by explaining the large-scale structure of the Universe. In the group field theory (GFT) approach, a macroscopic universe is described as a GFT…
The changing universe model (CUM) describes galaxy parameter relationships (SESAPS '03, session EB 2). The CUM must be successfully applied to cosmological scale observations to be considered a cosmological model. A major component of…
By considering suitable Poisson groupoids, we develop an approach to obtain Lie group structures on (subgroups of) the Poisson diffeomorphism groups of various classes of Poisson manifolds. As applications, we show that the Poisson…
The author studies the G\"odel Universe as the Lie group with left-invariant Lorentz metric. The expressions for timelike and isotropic geodesics in elementary functions are found by methods of geometric theory of optimal control for the…
A coarse graining operation of spatially homogeneous quantum states based on an SU(1,1) Lie group structure has recently been proposed in [1] and used in [2] to compute an explicit renormalisation group flow in the context of loop quantum…
Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory.…
Orthogonal Lie algebras in dimension 4 are identified as current Lie algebras, thus producing a natural decomposition for them over any field.
A relativistic modified gravity (MOG) theory leads to a self-consistent, stable gravity theory that can describe the solar system, galaxy and clusters of galaxies data and cosmology.
In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…
In this essay we discuss the difference in views of the Universe as seen by two different observers. While one of the observers follows a geodesic congruence defined by the geometry of the cosmological model, the other observer follows the…
A class of interacting classical random fields is constructed using deformed *-algebras of creation and annihilation operators. The fields constructed are classical random field versions of "Lie fields". A vacuum vector is used to construct…
We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate"…
Recently, some authors removed the big-bang singularity and predicted an infinite age of our universe. In this paper, we show that the same result can be obtained in string theory and M-theory; however, the shape of universe changes in…
We study Lie group structures on groups of the form C^\infty(M,K)}, where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra…
We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup.
We study the Newman--Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this topology. To obtain…
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie…
A mildly inhomogeneous universe with a cosmological constant may look like it contains evolving dark energy. We show that could be the case by modelling the inhomogeneities and their effects in three different ways: as clumped matter…
Dark Matter that is composed of WIMP remnants of incomplete particle-antiparticle annihilation in the early universe experiences ongoing annihilation in gravitationally bound large scale structure. This annihilation will have important…
Our universe appears to have been created not out of nothing but from a strange space-time dust. Quantum geometry (loop quantum gravity) makes it possible to avoid the ominous beginning of our universe with its physically unrealistic (i.e.…