A What distance is used in Hubble's Law.

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Hubble's Law is based on the concept of "proper distance," which is the distance measured at the time of observation. This distance accounts for the expansion of the universe, meaning it reflects the real distance of a galaxy at the moment light reaches us, rather than when it was emitted. The redshift observed measures the expansion that has occurred since the light was emitted, rather than simply a Doppler effect. Therefore, understanding Hubble's constant requires theoretical calculations based on the redshift data collected from when the light was emitted. This discussion highlights the complexities of measuring cosmic distances and the implications of cosmic expansion on our observations.
Javier Chornet
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Hello,

I was thinking about the Hubble's law and I know that it's determined as H(t)=\frac{1}{a(t)}\frac{da(t)}{dt} and then, thinking in the derivate of the scale factor as the speed, we've de usual formula v(t)=H(t)D
But my question is: the distance is the distance we observe the object (so now it's in farther because of the time that takes the light to go across these distance) or the real distance of the object?
In other worlds: is the distance of the galaxy when the light was emmited or the real distance at the moment of observation (despite we observe it nearest)?

I was thinking on it and trying to solve it using the derivation of the formula but I'm not convinced on any option.

Thanks,
Javier Chornet.
 
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The distance that's used for this purpose is known as the "proper distance". This is the distance that would be measured by a ruler at the time of observation.

If you want an in-depth view of distance measures in cosmology, see here:
http://arxiv.org/abs/astro-ph/9905116
 
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Chalnoth said:
The distance that's used for this purpose is known as the "proper distance". This is the distance that would be measured by a ruler at the time of observation.

If you want an in-depth view of distance measures in cosmology, see here:
http://arxiv.org/abs/astro-ph/9905116
So the used disance is the real distance of the galaxy at the moment of the observation (further than the distance we observe because the finite spee light).
Thank you! Your answer was so iluminating, and the paper you've referred is great!
Thanks again!
 
Chalnoth said:
The distance that's used for this purpose is known as the "proper distance". This is the distance that would be measured by a ruler at the time of observation.

If you want an in-depth view of distance measures in cosmology, see here:
http://arxiv.org/abs/astro-ph/9905116
Sorry again,
But then, if I measure the redshift, I'm measuring the speed that the galaxy had when she emmited the light. So for knowing the speed at the proper distance for know the value of Hubble's constant, you must calculate it theoretically based on the data collected from when the ligth was emmited, musn't you?
 
Javier Chornet said:
Sorry again,
But then, if I measure the redshift, I'm measuring the speed that the galaxy had when she emmited the light. So for knowing the speed at the proper distance for know the value of Hubble's constant, you must calculate it theoretically based on the data collected from when the ligth was emmited, musn't you?
Actually, the redshift measures the amount of expansion between the time the light was emitted and the current time.

There is some change in the redshift due to the movement of us and the far-away galaxy relative to the background expansion. But for the most part the redshift can't really be understood as a doppler shift at all. Rather, as the universe expands, the wavelength of the photon also increases along with the expansion.
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
Why was the Hubble constant assumed to be decreasing and slowing down (decelerating) the expansion rate of the Universe, while at the same time Dark Energy is presumably accelerating the expansion? And to thicken the plot. recent news from NASA indicates that the Hubble constant is now increasing. Can you clarify this enigma? Also., if the Hubble constant eventually decreases, why is there a lower limit to its value?
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