Specifically, I am wondering if some areas of the universe expand faster than other areas and whether the faster expanding areas diffuse the expansion through the slower expanding areas or does the expansion occur at a uniform rate throughout the entire universe.
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What's outside the observable Universe, we can't say anything about, but averaged over large enough scales ($\gtrsim$ a billion lightyears), it does indeed seem to be expanding uniformly.
However, the presence of mass, or more generally energy, retards the expansion. This means that on the scale of clusters of galaxies, the Universe expands more slowly, and on the scale of galaxy groups, the galaxies' mutual gravitational attraction will prevent them from receding from each other. This is also why our galaxy, Solar system, planet, and bicycles will never get torn apart (unless the cosmological constant is not a constant).
Conversely, in mass underdensities, i.e. the huge voids between clusters and filaments of gas and galaxies, expansion is increased (relative to denser regions). In fact, it has been hypothesized that the observed accelerated expansion of the Universe is not due to dark energy, but could be an "illusion" from accidentally living in the center of a huge underdensity (e.g. Zibin et al. 2008). More recent observations seem to rule out this possibility, though.
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$\begingroup$ Is the value of the Hubble parameter everywhere exactly the same in the observable universe? Or does it depend on the concentration of mass in a particular zone? $\endgroup$– set5Commented Sep 5, 2015 at 14:30
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1$\begingroup$ @mick: The value of the Hubble parameter $H_0$ is an average of all of the Universe, since it's calculated on the basis of several observables in all directions, and at various distances. $H_0$ does not describe the expansion rate in different regions of the Universe, it describes the overall expansion rate. Locally, galaxies may recede from each other faster or slower than 68 km/s/Mpc, but the term $H_0$ describes the average expansion rate at distances so large that peculiar velocities can be neglected (i.e. velocities due to local kinematics like two galaxies orbiting each other). $\endgroup$– pelaCommented Sep 5, 2015 at 19:53
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1$\begingroup$ For instance, within the Milky Way space doesn't expand. But we wouldn't say that $H_0=0$ in the Milky Way. $\endgroup$– pelaCommented Sep 5, 2015 at 19:53
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1$\begingroup$ @JustinWaters: Not at all, you probably know more about science than I do about law :) Explaining the expansion of the Universe properly takes a bit more than what fits in a comment (also I have a deadline in 41 hours), but briefly: BHs definitely cannot be the cause of expansion, even though gravity indeed does "diffuse" ("decrease" is a better word) non-linearly (in fact as the square of the distance). BHs, even the supermassive ones, contribute relatively little to the total mass of a galaxy. (to be cont'd in next comment) $\endgroup$– pelaCommented Sep 8, 2015 at 21:55
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1$\begingroup$ We don't see expansion in the MW, and also not in other galaxies, even those that don't have central BHs. And galaxies that are close to each other also don't recede from each other. But we do see expansion on larger scales. Galaxies that are much, much too distant too feel any gravity from MW's BH recede from us with velocities that increase with their distance from us, linearly at first, but non-linearly when you get to large distances. $\endgroup$– pelaCommented Sep 8, 2015 at 21:58