How Do Photons from Very Old Galaxies Reach the Hubble Telescope?

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Photons from ancient galaxies can reach the Hubble Space Telescope after traveling for up to 10 billion years due to the expansion of the universe. When light emitted 4.5 billion years ago began its journey, the universe was significantly smaller, but as it traveled, the cosmos expanded, extending the distance it covered. This phenomenon is akin to running up a down escalator, where the effective distance traveled can be much greater than the physical distance. The discussion emphasizes that the expansion of space allows light from distant galaxies to reach us despite the universe's earlier size. Understanding this concept is crucial for grasping how we observe ancient cosmic events.
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With the Hubble telescope now able to see back in time by as much as 10 billion years, can anyone explain the path of the photons from very old galaxies entering the HST during the last 10 billion years and particulary where they were around 4,500 million years ago?
 
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I'm guessing you're wondering how they could be traveling for 10Gy if, 4.5Gy ago the universe was a mere 4.5Gly wide.

Think about running up a 'down' escalator. If you do it right, you can run for a half mile on an escalator that is only 100 yards long.

While light from a galaxy 4.5Gy ago may have started out only a few Mly away, the universe has expanded greatly in the time it traveled here, so its jounrey was vastly extended.
 

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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##.
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Thread 'Hubble Constant, Dark Energy and the Expanding Universe'

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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