Abstract: The assumption that time dilation must be computed using velocities relative to the local Hubble Frame has important consequences for cosmology. Four such consequences are described: (1) the impact on redshift calculations, (2) an alternate explanation of the apparent accelerated rate of expansion of the universe, (3) a reinterpretation of the period of inflation following the Big Bang, and (4) reevaluation of the computation of time dilation experienced during space travel, such as that postulated in the Twins Paradox.