Question: So I was just wondering about this as I finished reading about Michelson-Morley's experiment which disproved the ether theory. My question is since the Universe is constantly expanding and that too with an accelerated rate does it somehow effect the experimental conditions? If so I wanna know how because I'm unable to understand what effects would expansion of space have on the velocity of light. Is the speed of light not a constant then?

Answer: 
The expansion of the Universe has no effect on the local speed of light. Any local measurement of $c$ will yield $c$, and $c$ won't change.

There is one thing that often causes confusion about the speed of light or faster-than-light travel. A photon moving in an expanding space-time *appears* to move at an average speed faster than $c$. Consider a simplified/idealized scenario: a photon is directed at a target 2 lightyears away. It travels at $c$ for one year, covering a distance of 1 lightyear. Then the Universe it is travelling in undergoes a near-instantaneous expansion to double its previous size. Now it is 2 light years from its starting point, and 2 lightyears from its target. It keeps travelling at $c$, so it takes 2 more years to reach its target. Now suppose you decided to calculate the average speed of the photon. It is now 4 lightyears from its starting point, and it made the journey in 3 years, so its average speed was $\frac{4}{3}c$. But this is not a *local* measurement of $c$; I said before that the photon was travelling at $c$ the whole time, and any local measurement at any time would have given $c$. It's just that the space between the origin and target of the photon changed while it travelled. This "sudden" expansion is of course not very realistic and I just chose it to make my point easy to illustrate, but the same concept applies for gradual expansion, demonstrating so just requires a few integrals.
The Michelson-Morley experiment indicated (contrarily to it's original intent), that the speed of light perceived by an observer is **not** dependent on their speed relative to anything.

Along these lines, our movement in space with respect to any arbitrary point has no impact on the speed of light measured in the earth system.

Disclaimer: did not hear a course on *general* relativity yet.