Derivation of the formula for cosmological redshift

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Discussion Overview

The discussion centers around the derivation of the formula for cosmological redshift, specifically the relationship expressed as z = R(t0)/R(te) - 1. Participants seek a clear explanation of how this formula is derived and its connection to the expansion of the universe, with references to various academic papers and theoretical concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express frustration with the lack of a clear derivation for the cosmological redshift formula, noting that sources like Wikipedia do not provide sufficient detail.
  • One participant suggests consulting the Davis and Lineweaver paper, while another mentions the Bunn and Hogg paper as potentially helpful for understanding the derivation.
  • It is proposed that the redshift is related to the expansion of the universe, with photons being lengthened by the expansion factor, leading to the formula involving the scale parameters.
  • Another participant discusses the implications of changing rates of expansion on the validity of the redshift formula, raising questions about the assumptions made in the derivation.
  • A detailed mathematical approach is presented, involving integrals and the relationship between the periods of light as measured by different observers, leading to the conclusion that the redshift can be expressed in terms of the scale factor.
  • Concerns are raised about the applicability of the derivation at very large cosmic scales, questioning whether the assumptions hold under extreme conditions.

Areas of Agreement / Disagreement

Participants generally agree on the need for a derivation of the redshift formula, but multiple competing views remain regarding the implications of changing expansion rates and the validity of certain assumptions in the derivation process.

Contextual Notes

Some participants note limitations in their understanding of thermodynamics and the stress-energy tensor, which may affect their ability to fully engage with the derivations presented. Additionally, the discussion acknowledges that the scale factor's constancy may not hold over very long time intervals or distances.

  • #31
I think I have developed a solution to the problems with the Narlikar paper and will post it once I have written it up.
 
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  • #32
Here's the solution as a pdf version of a word-processed file. I'll try to make a TeX version that is easier to read, and replace this one with that when I've done it. Any comments would be very welcome.

The file is essentially a proof that cosmological redshift due to expansion is equivalent to Doppler redshift.
 

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