Tuesday, 9 March 2021

Redshifts and Distances

Still working on the magic Killing tensor ##K_{\mu\nu}=a^2\left(g_{\mu\nu}+U_\mu U_\nu\right)## in FLRW spacetime:
  • We use ##K_{\mu\nu}## to show that interstellar gas cools in an expanding universe.
  • Then we use it to show that as the universe expands the observed frequency of a photon will decrease. 
  • Cosmologist measure the redshift, ##z##, of distant objects and we show how this tells us the scale factor ##a## when the object emitted the light being measured. 
  • I then looked up some galactic distances and redshifts to compare them (pictured). Extrapolating the graph indicates the size of the visible universe is ~15 Gly.
  • Carroll then seems to ramble a bit and goes back to a non-relativistic redshift. The history of Doppler and Hubble, which he does not mention, is quite interesting.
  • Getting back on track Carrol shows that the nearby universe can be thought of as flat and we are able to use proper distance meaningfully and derive Hubble's law. I think he is overcomplicated.
  • Next step other distances!

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