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1 results

  • 25 - Applied Cosmology

  • from Part Four - Ions and Photons in the Cosmos
  • Christopher W. Churchill, New Mexico State University
  • Book:
    Quasar Absorption Lines
    Published online:
    17 December 2025
    Print publication:
    18 December 2025, pp 983-1020

  • Summary

    The fundamental quantity of the expansion dynamics of the Universe is the time-dependent scale factor. However, neither time nor the scale factor is a measurable quantity. The measurable quantity due to universal expansion is the cosmological redshift of observed radiation. This redshift gives the ratio by which the Universe has expanded relative to the present epoch. In this chapter, we rewrite the expands dynamics in terms of redshift and define proper and co-moving coordinates. Using the radial and transverse components of the Robertson-Walker metric, we derive relations for cosmic time and multiple useful distance measures as a function of redshift. These include the radial and transverse proper and co-moving distances, the angular diameter distance, the luminosity distance, and the “absorption” distance. We also derive the equations for the redshift dependence of the line-of-sight separations of gravitationally lensed quasars. The redshift path density is derived. Finally, the redshift dependence of line-of-sight peculiar velocities and cosmological recessional velocities are derived from the metric.