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In measurements concerning distances, luminosity, etc. to evaluate the Hubble's parameter, do scientists take into considerations the fact that the light, emitted from a star, and received by a detector, is actually not representing the actual distance of the star? Thus when we say the current value of the Hubble's parameter is wrong, in a sense, it reflects measurements obtained from past events.

For example, if we denote (D), (O) for detector and object respectively,

(D)----$d_0$-----(O) -perceived

(D)-----$d$---------(O) -actual

then the actual distance $d=d_0(1+v/c)$.

PseudoYousef
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  • Yes, see https://physics.stackexchange.com/questions/552056/why-cant-we-directly-observe-homogeneity-because-we-observe-down-the-past-ligh which asks about a different topic that assumes what you are asking (observing down the "past light cone"). – Allure Jun 22 '20 at 06:05

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The answer is yes. Hubble's law relates the "velocity of recession" to the proper distance - which is the distance to the other galaxy now.

That is not usually the distance we measure, as you have identified.

The difference between the two is very small at low redshifts, but becomes larger at higher redshifts, and depends on the expansion history of the universe and hence the cosmological parameters like $\Omega_M$, $\Omega_\Lambda$ as well as $H_0$.

ProfRob
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  • So, In a perfect theoretical cosmological model, if we use $t_{age}$ (the age of the universe), then $H(t_{age})$ should be different than $H_0 \approx 70$. – PseudoYousef Jun 22 '20 at 12:44
  • Yes @PseudoYousef $H_0$ means the Hubble parameter now. It varies with cosmic epoch. – ProfRob Jun 22 '20 at 13:09