Non Commutative Quantum Spacetime with Topological Vortex States, and Dark Matter in the Universe

X iv :g rqc /0 31 01 36 v1 3 1 O ct 2 00 3 Non commutative quantum spacetime with topological vortex states, and dark matter in the Universe Ajay Patwardhan Physics Department, St. Xavier’s college, Mahapalika Marg, Mumbai, 400001, India Abstract Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distances and energy in between. There is a variety of physics possible till the nucleosynthesis epoch is reached. The use of topology and non commutative geometry in cosmology is a recent approach. This paper considers the possibility of topological solutions of a vortex kind given by non commutative structures. These are interpreted as dark matter, with the grand unified Yang-Mills field theory energy scale used to describe its properties. The relation of the model with other existing theories is discussed. Introduction The role of Geometry and Topology in understanding the physics of the universe of space time and matter has a century of work that is supported by observations. Inflationary cosmological models developed for creation of matter have included the small anisotropic distributions as given by COBE and WMAP observations. The models modified to create the voids and filamentary large scale structure of the early universe , with the ratios of dark energy, dark matter and normal matter are topics of active research. The non linear evolution equations of the early universe give rise to anisotropy and inhomogenity persisting at all length scales , these are observable with even finer resolution that is expected in subsequent experiments. These indicate analogies with condensed matter. Topological defects and vortex like states in rapid expansion and cooling occur in condensed matter phases. This paper develops the role of noncommutative geometry in the formation of the vortex like topological states. The typical model of the universe, a few seconds old and a few kilometers in size, is expected to have some 10 particles of normal matter, and to form a smooth geometry given by Einstein’s theory of general relativity ; with 10 parts fluctuation in matter distribution as inferred from the temperature and thermal radiation microwave measurements. [References]. The models of the early universe In the inflation models and their variations that give the later stage expanding universe models with the correct observed properties, there are topologically non trivial states possible. A rubber sheet or expanding balloon