If nothing can travel at the speed of light and light cannot escape the universe, then the rate of expansion of the universe should be equal to the speed of light, why it is not?

  • $\begingroup$ Because there is nothing for the light to escape into $\endgroup$ – Pranav Hosangadi Jan 14 '14 at 16:20

The rate of expansion of the universe is not a single number, but rather a function of distance from the observer.

The simplest approximation is Hubble's Law, stating that $v(D)=H_0 D$, where $D$ is the distance from us, and $H_0$ is the Hubble constant, which parametrizes the cosmic expansion and has units of $\frac{|velocity|}{|distance|}$ (these days $H_0$ is called the Hubble Parameter, because it is actually not a constant in time).

It should be clear from Hubble's Law that if the Universe is large enough, then it doesn't matter how small the number $H_0$ is - if the Universe is large enough, you can always find a distance $d$, for which $v(D \geq d) \geq c$. It should also be clear that for for small values of $D$, $v$ will also be very small, which is exactly what we are experiencing in the local Universe.

That being said, it is true what is said in the comments above: There is nothing "outside" the Universe for light to escape into.

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