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I'll include an answer that I considered satisfactory from another forum. To the point, succinct, yet comprehensive. "The Hubble Constant is not simply the inverse of the “Age of the Universe”, but an approximation. This is due to the fact that the Hubble Constant (otherwise named the “Hubble Parameter” because it is not really a constant) is a function ...

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I'm a bit uncertain if I understand your question correctly, but if I do, you're asking whether or not it's a coincidence that $1/H_0$ is roughly equal to the age of the Universe. If so, the answer is "Somewhat, but not really". Not a complete coincidence The reason it is not exactly a coincidence is that, if the Universe had expanded linearly with ...

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The brackets refer to the average, so $\left< x^2 \right>^{1/2}$ is the root-mean-square (RMS) of $x$. That is the square root of the mean (or average) of the square of multiple $x$s. The RMS average is useful when a quantity can be either negative or positive. For instance, a sine or cosine wave has an average of zero over one cycle, but its RMS ...

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