Expanding the Quiescent Cosmology Framework: A study of Isotropy, Anisotropy and Gravitational Entropy

Abstract

Motivated by the large-scale regularity of the observable universe, Barrow's quiescent cosmology was an early attempt to describe the structure of today's universe as a natural consequence of an isotropic initial singularity. Quiescent cosmology assumes that this isotropic initial singularity, driven by gravitational entropy, has evolved into the near-homogeneous and quasi-isotropic universe we observe today. The universe is still somewhat regular because we are still at a relatively early stage of its evolution towards an anisotropic future. While significant effort has been directed to better understand the isotropic initial singularity, the same level of attention has not been afforded to the possible anisotropic future states of quiescent cosmology. This lack of attention is what underpins this thesis -- a desire to: refine and extend existing results from the literature; gain a deeper understanding of the anisotropic structures and; where possible, synthesise quiescent cosmology with other fields of cosmology.

Much like previous authors in this field before us, we use example cosmologies to further our understanding of, and challenge pre-conceived assumptions within quiescent cosmology. In this thesis, we double quiescent cosmology's library of solutions (see Chapter 3) and in doing so provide a grand suite of examples for future researchers to use to advance this framework. The example solutions all admit at least one structure from quiescent cosmology and also contain geometric or kinematic properties not previously studied in quiescent cosmology. We also prove that a curvature invariant associated with gravitational entropy is monotonic in regions of particular importance (see Section 5.3), extending the work of previous authors and supporting broader conjectures about the Weyl Curvature Hypothesis from the literature.

Faced with an otherwise isotropic cosmology being shown to obey an anisotropic definition in quiescent cosmology (see Section 6.1), we conduct the most rigorous analysis of anisotropy and degeneracy within quiescent cosmology to date (see Section 6.2). We show that there are inherent flaws with the existing anisotropic definitions as they stand and provide an extended discussion of the flaws, hoping to influence future research to solve the problems. Furthermore, we dedicate a significant amount of time to prove that important physical curvature invariants do not vanish at cosmological origins or futures within a large class of non-causally degenerate conformal spacetimes.

We know that quiescent cosmology is but one approach to describing the universe around us. Recognising the importance of sharing knowledge, we synthesise results from quiescent cosmology with complementary ones from other fields of cosmology. We demonstrate that the isotropic structures of quiescent cosmology can correspond to cosmological events in the Friedmann-Robertson-Walker (FRW) cosmologies (see Section 4.2), and also show which FRW models cannot be represented by the existing structures of quiescent cosmology (see Sections 4.3 and 4.4). We also offer a detailed analysis of which perfect fluid solutions that admit structures from quiescent cosmology agree with the energy conditions of general relativity (see Section 4.5). Lastly, we make the first known attempt to present quiescent cosmology structures under the guise of the dynamical systems approach to cosmology (see Chapter 7). Although this attempt is embryonic, it serves as an opportunity for others to extend and expand upon our work. Show more