Cosmic horizon of 42-billion light-years?

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SUMMARY

The observable universe extends to a radius of 42 billion light-years, despite the Big Bang occurring approximately 14 billion years ago. This discrepancy arises from the expansion of space, which allows light from distant objects to reach us over time. The formula for calculating the radius of the observable universe is given by ro = 3 c to, where ro represents the radius, c is the speed of light in a vacuum, and to is the age of the universe. This mathematical relationship clarifies the observed distance and aligns with current cosmological models.

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I recently read the new Scientific American and in one of the articles it says that the observable universe can see a distance of 42 billion light-years away but my question is that the big bang is predicted to have occurred at approximately 14 billion years ago, so how can the observable universe be 42 billion light-years?
 
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There is a well written FAQ on this:

https://www.physicsforums.com/showthread.php?t=506987

In mathematical terms, the radius of the observable universe is (REF: Introduction to Modern Cosmology, Eqn. A1.12):

ro = 3 c to

ro = radius of observable universe
c = speed of light in vacuum
to = age of universe

This formula will match your numbers.
 
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