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Let 
be the time that has elapsed since the Big Bang. In
that time, one would imagine that light, traveling at speed 
, has
been able to travel a maximum distance 
. (In fact the distance
is several times more than this, because according to Einstein's theory of general relativity, space itself has been expanding while the ray of light was in transit.) The portion of the
universe that we can observe would then be a sphere of radius 
, with volume 
. Compute the rate 
at which the volume of the observable universe is increasing, and check that your answer has the right units, as
in Example.
be the time that has elapsed since the Big Bang. In
that time, one would imagine that light, traveling at speed , has
been able to travel a maximum distance . (In fact the distance
is several times more than this, because according to Einstein's theory of general relativity, space itself has been expanding while the ray of light was in transit.) The portion of the
universe that we can observe would then be a sphere of radius , with volume . Compute the rate at which the volume of the observable universe is increasing, and check that your answer has the right units, as
in Example.
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