# Distance and luminosity distance

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?

• Isn't it the luminosity distance? – Kyle Kanos Jun 16 '15 at 20:04
• Exactly yes... I'll change it right away! – Worldsheep Jun 16 '15 at 20:09

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 $z$.
• 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 $H$. – Hayk Hakobyan Jun 27 '15 at 18:29
• 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. – Hayk Hakobyan Jun 27 '15 at 18:35