Related papers: Noncommutative Geometry and Cosmology
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an…
Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
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…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
In this letter we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage…
We explore the effects of background cosmology on large scale structures with non-spherical symmetry by using the concept of quasi-equilibrium which allows certain internal properties (e.g. angular velocity) of the bodies to change with…
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly…
The status of quantum cosmologies as testable models of the early universe is assessed in the context of inflation. While traditional Wheeler-DeWitt quantization is unable to produce sizable effects in the cosmic microwave background, the…
Motivated by describing time-evolutions of noncommutative worlds, I discuss symmetry-preserving evolutions of noncommutative worlds of finite dimensional representation spaces. An interesting issue in such evolutions is that there can be…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
In this paper we consider generalization of classical and quantum mechanics that directly follows from the causality principle and topology of a system state space. In generalized mechanics, the Hamiltonian/Schrodinger equations remain the…
Noncommutative geometry can provide effective description of physics at very short distances taking into account generic effects of quantum gravity. Inflation amplifies tiny quantum fluctuations in the early universe to macroscopic scales…