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The geometric properties of time arising from insights introduced by Hermann Minkowski are discussed. A geometric model of time yields a simpler and more natural explanation of relativistic temporal effects than prevailing ideas and better explains astrophysical empirical observations, including the apparent accelerating expansion of the Universe. It is shown that new accurate and corroborating empirical data from the two largest recent galaxy redshift surveys (2dF and SDSS) are inconsistent with the standard cosmological model, yet provide robust empirical support for a revised model based on temporal geometry arising from the principles of relativity. This dissertation also introduces several innovative and illuminating ideas related to special relativity, general relativity and quantum mechanics.