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In my cosmology lecture notes I read that a way to measure distances in cosmology is to use standard candles and the comparison between "absolute luminosity" of the candle and the apparent luminosity. Comparing these two quantities you end up having (1 = time of emission of a pulse, 0 = time of observation): $$d_L = \frac{R^2(t_0)}{R(t_1)}\bar r_1$$ where $\bar r_1$ is the comoving distance between us and the candle. Finally to first order: $$d_L \approx \frac{z}{H}$$ I guess that the point is that now I know $H$ and I can measure $z$ in order to get $d_L$.

The question is, what is physically $d_L$? How knowing $d_L$ helps me knowing the physical distance between me and the candle?

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  • $\begingroup$ Isn't it the luminosity distance? $\endgroup$
    – Kyle Kanos
    Commented Jun 16, 2015 at 20:04
  • $\begingroup$ Exactly yes... I'll change it right away! $\endgroup$
    – Worldsheep
    Commented Jun 16, 2015 at 20:09

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The luminosity distance is like a hypothetical distance, how far would this object, with this luminosity, have to be in a Euclidean universe without time dilation, to be observed the way we observe it.

Our observations of luminous objects are distorted by the expansion of space and time dilation. If it weren't for those effects, the object would have to be farther away for it to be appear that way. That hypothetical distance is luminosity distance.

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Say, if you have a SNIa standard candle, with the help of its luminosity curve, you can recreate its absolute luminosity. By knowing the absolute luminosity $L$ and the visible flux $F$, one can calculate the luminosity distance $d_{\rm L}=\sqrt{L/4\pi F}$. What is a physical distance? There is a Hubble distance, luminosity distance, angular diameter distance etc. All of these, including $d_{\rm L}$, are different physical distances. That's why cosmologists mostly speak in terms of redshift $z$.

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  • $\begingroup$ You seem to have avoided the question as to what the luminosity distance really is; all you've done is restate it & name other distance measures. $\endgroup$
    – Kyle Kanos
    Commented Jun 27, 2015 at 18:26
  • $\begingroup$ What does the word "really" stand for in your "what the luminosity distance really is"? Really, it is some sort of physically feasible distance, that you can measure and compare it with $z$ and $H$. $\endgroup$
    – hayk
    Commented Jun 27, 2015 at 18:29
  • $\begingroup$ The only thing I wanted to say, is that there is no physical distance concept. The luminosity distance is a physical distance example. $\endgroup$
    – hayk
    Commented Jun 27, 2015 at 18:30
  • $\begingroup$ Is it an actual distance? Is it a measure of a distance? (i.e., is it an approximation) Does it measure something else that isn't a length? There's a parameter space of cosmological terms that could be meant, and you've simply ignored it despite the fact that it's what the OP wanted in the first place. $\endgroup$
    – Kyle Kanos
    Commented Jun 27, 2015 at 18:31
  • $\begingroup$ Again, what is an actual distance? It is not an approximation, of course. When talking about inflating non-stationary Universe, there is no such meaning, as actual distance. You only have possible physical measures, like comoving distance, luminosity distance etc. You can't just take two coordinates, say, $r_1$ and $r_2$, and substract them to get a distance. $\endgroup$
    – hayk
    Commented Jun 27, 2015 at 18:35

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