This work investigates gravitational waves in closed Roberson-Walker spacetimes in the context of Intrinsic Time Gravity which describes the Hamiltonian evolution of gravitational physics in which the fractional change of the spatial volume is used as the intrinsic time variable. Gravitational wave equation is derived, and solved for Einstein’s theory as well as for General Relativity modified by an extra Cotton-York term in the Hamiltonian. Physical transverse traceless gravitational modes are expanded in terms of spherical harmonics of spatially closed Robertson-Walker spacetimes; time-dependence of the modes are solved exactly and are found to be related to associated Legendre polynomials. Different domains corresponding to early and late times with and without Cotton-York contribution are studied and the behavior of the modes are revealed. A salient feature of Cotton-York contribution which distinguishes it from pure Einstein theory is pointed out.
摘要i
Abstract ii
誌謝iii
Table of Contents iv
List of Figures v
Chapter 1. Introduction and overview 1
Chapter 2. Intrinsic Time Gravity and Hamilton’s equations for spatial metric
evolution 3
Chapter 3. Gravitation waves in closed Robertson–Walker spacetimes 5
Chapter 4. Solving the time dependence of the modes 14
Chapter 5. Associated Legendre polynomials and their application 16
Chapter 6. Gravitational waves in Einstein’s theory and in the CottonYork
era 25
ζ → 0 . . . . . . . . . . . . . . . 25
Large ζ . . . . . . . . . . . . . . . . . . . . 28
. k large enough and x is not very large . . . . . . . . . . . . . . . . . . 28
. k and x both large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
ζ not extremely small and x is small . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 7. Conclusions and further remarks 33
References 35
Appendix A. 36
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