I am very grateful to many friends and colleagues for their important inputs, and for sharing their thoughts with me relating to the cosmo-logical scheme that I am putting forward here. Most importantly, detailed discussions with Paul Tod, concerning the formulation of his proposal for a conformal-extension version of the Weyl curvature hypothesis have been crucially influential, and many aspects of his analysis have proved vital to the detailed development of the equations of conformal cyclic cosmology, as I am putting them forward here. At the other end of things, Helmut Friedrich's powerful analysis of conformal infinity, particularly his work on the case where there is a positive cosmological constant, has lent a strong support to the mathematical viability of this scheme. Another who has contributed an important input over a great many years is Wolfgang Rindler, particularly for his seminal understanding of cosmo-logical horizons, but also for his long collaboration with me on the 2-spinor formalism, and also for discussions on the role of inflationary cosmology.

Significant input has come from Florence Tsou (Sheung Tsun) and Hong-Mo Chan for sharing with me their ideas concerning the nature of mass in particle physics, and James Bjorken also provided a crucial insight in relation to this. Among the many others who have importantly influenced me are David Spergel, Amir Hajian, James Peebles, Mike Eastwood, Ed Speigel, Abhay Ashtekar, Neil Turok, Pedro Ferreira, Vahe

Gurzadyan, Lee Smolin, Paul Steinhardt, Andrew Hodges, Lionel Mason, and Ted Newman. Richard Lawrence's heroic editorial support has been invaluable, as has the vital input from Thomas Lawrence in providing much missing information, particularly concerning Part 1. Thanks are due to Paul Nash for indexing.

For her deep support, love and understanding, under frequently difficult circumstances, I am profoundly indebted to my wife Vanessa, whom I thank also for immediately providing some needed graphs at short notice, but more particularly for guiding me through some of the continual frustrations of modern electronic technology that would otherwise have completely defeated me with regard to the diagrams. Finally, our 10-year-old son Max is to be thanked not only for his continual encouragement and good cheer, but also for playing his own part in helping me through this bewildering technology.

I am grateful to the M.C. Escher Company, Holland, for permission to reprint the images used in Fig. 2.3. Thanks go to the Institute of Theoretical Physics, University of Heidelberg for Fig. 2.6. I give thanks, in addition, to NSF for support under PHY00-90091.

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