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No, the Hubble sphere can never extend over the cosmic event horizon; it can only asymptotically approach it. The Hubble sphere is the region within which galaxies (and other stuff) recede from us slower than light. The event horizon is the region outside which no light can ever reach us. If the Hubble sphere extended beyond the event horizon, it would mean ...

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I don't think there is any surprise at all. The upper limit of 15-20 solar masses arises in black holes that are formed from stars in a metal-rich gas. i.e. We expect an upper limit of about 20 solar masses for black holes in our own Galaxy. There is however no such constraint on black holes formed in the distant (past) universe, potentially in galaxies ...

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I think I can sort of answer your first/second question. It's a bit hard to guess what your background is, but I hope you have seen or derived somewhere that the $a_{lm}$ coefficients can be written as $$\oint \Theta(\hat{x}) Y_{lm}^*(\hat{x}) d\hat{x}$$ where $\Theta$ is the temperature fluctuation (as seen in the CMB) and $Y_{lm}^*$ is (the complex ...

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Adding onto Daddy Kropotkin excellent answer. The physical reason why you might not have expected black holes above 15 solar masses is to do with stellar mass loss (which is highly uncertain and an active area of research). Star's are constantly losing mass in their stellar winds, which lowers the final mass of the star and hence the mass of a black hole it ...

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The so-called 'mass gaps' for black holes, according to theoretical models, are between 2-5 solar masses and 50 to 150 solar masses. (Actually, I have read that there is no good theoretical reason for the lower, 2 to 5 solar-mass gap....) The lower mass-gap is suspected observationally because we have yet to observe a neutron star with mass greater than ...

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