Interpretation of the Cosmological Metric

Abstract

The cosmological Robertson-Walker metric of general relativity is often said to have the consequences that (1) the recessional velocity $v$ of a galaxy at proper distance $\ell$ obeys the Hubble law $v=H\ell$, and therefore galaxies at sufficiently great distance $\ell$ are receding faster than the speed of light $c$; (2) faster than light recession does not violate special relativity theory because the latter is not applicable to the cosmological problem, and because ``space itself is receding'' faster than $c$ at great distance, and it is velocity relative to local space that is limited by $c$, not the velocity of distant objects relative to nearby ones; (3) we can see galaxies receding faster than the speed of light; and (4) the cosmological redshift is not a Doppler shift, but is due to a stretching of photon wavelength during propagation in an expanding universe. We present a particular Robertson-Walker metric (an empty universe metric) for which a coordinate transformation shows that none of these interpretation necessarily holds. The resulting paradoxes of interpretation lead to a deeper understanding of the meaning of the cosmological metric.

REVTeX 4, 20 pages, accepted for publication in Am. J. Phys. Comments: edited version that will appear in the Am. J. Phys

References in corpus (6)

• Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
• Is space expanding in the Friedmann universe models?
• Joining the Hubble Flow: Implications for Expanding Space
• Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects
• Cosmology under Milne's shadow
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• Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies
• Evidence for the Fifth Element Astrophysical status of Dark Energy
• The kinematic component of the cosmological redshift
• Expanding space, quasars and St. Augustine's fireworks
• A Measurement of the Cosmic Expansion Within our Lifetime
• Harrison's interpretation of the cosmological redshift revisited
• Tantalizing New Physics from the Cosmic Purview
• A physical interpretation of Hubble's law and the cosmological redshift from the perspective of a static observer
• Teaching cosmology with special relativity: Piecewise inertial frames as a model for cosmic expansion
• The equivalence principle and the relative velocity of local inertial frames
• Can an Infinitely Long Object Fit in an Expanding Universe?
• Relations between Newtonian and relativistic cosmology