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Wikipedia mentions the radius of our observable universe based on the travel time of light from remote objects whose light’s travel time is equal to the age of the universe.

“According to calculations, the current comoving distance—proper distance, which takes into account that the universe has expanded since the light was emitted—to particles from which the cosmic microwave background radiation (CMBR) was emitted, which represents the radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light-years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light-years),[10] about 2% larger. “ (Under "Observable universe").

There is another way of thinking, along the following lines: As a result of the expansion of the Universe the relative velocity between distant objects and the Earth will increase as a function of distance and for some objects eventually reach the speed of light. This defines another observable universe. It doesn’t immediately follow that these two definitions are equal.

The first version seems to allow light from distant objects to reach us in the future whereas the other seems to be a more fundamental limit. I thought 45 billion light years was an absolute limit.

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  • $\begingroup$ As a result of the expansion of the Universe the relative velocity between distant objects and the Earth will increase as a function of distance” - This is incorrect. The relative velocity of two objects remains the same during tbe expansion (ignoring the accelerated expansion). You seem to be misinterpreting the Hubble law that refers to different objects at the same time, but not to the same two objects at different times. In other words, the Hubble parameter is not constant in time, but (approximately) reciprocal of the age of the universe. $\endgroup$ – safesphere Apr 13 at 15:25
  • $\begingroup$ ...and for some objects eventually reach the speed of light” - You seem to think that the observable universe is limited by the speed of light. This is incorrect. Objects near the edge of the observable universe recede from us faster than three times the speed of light and still remain observable. $\endgroup$ – safesphere Apr 13 at 15:29
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The second way is known as the Hubble radius. It is a numerical value, but it does not appear to be a valid concept in general relativity, in which the expansion of space is a geometrical property, and the description of objects reaching the speed of light can only be coordinate dependent (and consequently arbitrary and not well defined in this context). Those same objects are not moving in comoving coordinates. If you were to define coordinates in which they were to appear to move at the speed of light, then light would travel very much faster than the speed of light in those coordinates. I see mention of the Hubble radius in popular accounts, but I don't think it should be regarded as a good way of thinking in general relativity.

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