Derivation of the formula for cosmological redshift

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SUMMARY

The discussion centers on the derivation of the cosmological redshift formula, z = R(t0)/R(te) - 1, and the relationship between redshift and the expansion of the universe. Participants reference key papers, including Davis and Lineweaver (2003) and Bunn and Hogg, which provide insights into the derivation and implications of the formula. The conversation emphasizes the importance of understanding how the scale factor affects photon wavelengths and energy density in an expanding universe. Additionally, it addresses the validity of the formula over varying cosmic scales and the potential for future observational studies to test these models.

PREREQUISITES
  • Understanding of cosmological scale factors and their role in redshift calculations.
  • Familiarity with the concepts of photon energy density and the stress-energy tensor.
  • Basic knowledge of calculus, particularly limits and integrals.
  • Awareness of key astrophysical papers, specifically Davis and Lineweaver (2003) and Bunn and Hogg.
NEXT STEPS
  • Study the derivation of the cosmological redshift in Bunn and Hogg's paper on arXiv.
  • Explore the implications of varying cosmic expansion rates on redshift calculations.
  • Research the stress-energy tensor and its application to photon gases in cosmology.
  • Investigate observational techniques for measuring redshift drift over time, as discussed in recent astrophysical studies.
USEFUL FOR

Astronomers, astrophysicists, and students of cosmology seeking a deeper understanding of redshift phenomena and the mathematical foundations of cosmological models.

  • #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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