A general solution to mimetic dust with astrophysical and cosmological applications -

Abstract

The purpose of this thesis is to investigate solutions for the recently proposed model of dark matter, mimetic dark matter. The model, proposed by Chamseddine and Mukhanov in 2013[15], suggests a reformulation of Einstein’s Theory of Gravitation through isolating the conformal degree of freedom in a covariant way. In order to perform that, the physical metric is written in terms of an auxiliary metric and a scalar field appearing through its first derivatives. As a result, the conformal degree of freedom becomes dynamic even in the absence of matter. The extra degree of freedom has been shown to imitate the potential motion of dust. This thesis provides a review of Einstein’s Theory of Relativity in addition to astrophysical and cosmological applications. Furthermore, it examines the mimetic dust and provides particular and general solutions for specific behavior of this dust by specifying an arbitrary function f(r), related to the initial conditions. The aim of this thesis is to prove that mimetic matter indeed behaves as dust. As expected for regular dust, this mimetic dust will undergo gravitational collapse. As for the cosmological implications, it will be shown that mimetic dust provides a mean of describing a spatially flat, “matter dominated” universe. Finally, further directions of research will be indicated.