Can gravity transfer to the other side of the universe? Since the speed of gravitational wave is limited by the speed of light, and a light can never transfer to the other side of the universe because it is expanding so fast. So does that means gravity will never affect the other side of the universe? My teacher said it will not because something about graviton, but since their interaction is also limited by the speed of light, how will that affect the result (plus it's a hypothetical particle).
This question is pretty much same as mine but the only answer didn't really answer my question since it doesn't consider the theory of relativity and the expansion of universe.
Does my mass really affect objects on the other side of the universe?
 A: You're right: gravity is communicated ('travels') at the same speed as light, and thus its effects are limited in the same way that we can only see a certain, near-enough region of the universe.  In particular, the gravity that we 'feel' on earth is limited to the farthest distance from which light could reach us, over the age of the universe---that distance is called the cosmic horizon / or the edge of the observable universe.
Some other questions about the cosmic horizon which might be helpful:
Is it possible to learn about an event that occurred outside of your observable universe?
How can a quasar be 29 billion light-years away from Earth if Big Bang happened only 13.8 billion years ago?
Why is the observable universe so big? 
A: Taking a different approach - 
Well, per GR, considering speed of gravity same as speed of light, gravity would be different than the light. I mean the cosmic horizon is only for light and should not be for gravity. Because gravity is curvature of space (time).
Consider the time when stuff was closer to us. At that time space (time) had a curvature. Now keep adding newly created space to it. The addition would take place along the curvature that already is/was there. So, adding more space would not get rid of the curvature that was once created. It would only stretch it along.
Light is a wave and gets created every moment and passes us each moment. Curvature remains there once created, it only keeps reducing, however small it may be. Light is there, or not there, and new light has to catch up with expansion of space. Gravity (shape of curvature) should always remain part of expansion itself, without the need of point to point communication. Light on the other hand, is point to point communication.
More advanced members, please correct me as needed.
A: I think the phrasing of "gravity" in the OP makes this difficult to understand what is being asked, and therefore, difficult to answer this clearly.
What is unambiguously true is that the gravitational effects of a change in position of a nearby object will not be felt by an object that is farther away than the edge of the visible universe.  
Different questions can have different answers, though.  If you are asking "does an object beyond the horizon feel gravitatianal effects from things on this side of the horizon, you have to consider that some of the local gravitational field was set up when the universe was very young, and if you believe in inflationary scenarios${}^{1}$, then there was a time in the distant past when the expansion rate of the universe was different, and the cosmological horizons included a much greater fraction of the mass of the universe.  The gravitational field of these distant stars depends, partially, on the positions of objects in this very distant, primordial past.
Finally, I'll add the fact that the $\frac{1}{r^{2}}$ dependence in the leading term in gravitational force makes most of these effects quite small, and causes local objects to dominate, which is why the gravity you feel is governed mostly by the Earth, and the second-order effects come from the Moon and the Sun, then the other planets, and only then, from the bulk of the Milky Way, and THEN from cosmology. Almost all of these discussions involve the dynamics that happen amongst objects that aren't bound into "small" objects like galaxies.
${}^{1}$ And most of the best evidence we have says that inflationary scenarios fit the data we have best
