You are confusing the observable universe with the entire Universe. We can only observe a finite subset of the Universe because if something was farther away than that, the light would not have had time to reach us since the Big Bang. The observable universe is a sphere centered on us, where the radius is the horizon distance, which is the maximum distance light could have traveled since the Big Bang. The volume of space within the observable universe increases as time goes on simply because the length of time since the Big Bang increases as time goes on. This has nothing to do with the expansion of the universe. In the 1920s, Vesto Slipher and Edwin Hubble noticed the redshift of the galaxies, which is explained by saying that the average distance between the galaxies is increasing. Imagine coins glued to surface of a balloon being blown up. The average distance between each coin increases over time. It would not be a good analogy if the galaxies were drawn on the surface of the balloon because then they themselves would expand, which doesn't happen. In the 1990s, by looking at the redshifts of Type Ia supernova, it was found that not only is the universe expanding but the expansion itself is accelerating, which we now attribute to dark energy. Does this mean that as time goes on, the Universe contains "more space"? No! We believe that the Universe is infinite, which means that it always contains the exact same amount of space, which is infinite. When we say that the Universe is expanding, we do not mean that it contains more space as time goes on. We mean the average distance between the galaxies increases as time goes on.
We know that traveling backwards in time is intrinsically impossible, no matter what, because it violates causality, which is famously described by the grandfather paradox. If you went backwards in time, and killed your grandfather, then you would not exist, which means that you would not be able to go backwards in time to kill your grandfather, and thus the paradox.
Despite what others have said here, there is strong evidence for the multiverse. There are many fundamental constants or parameters in the Universe, where if they had slightly different values, life would not be possible. If gravity was either weaker or stronger, life would not be possible. Without the multiverse, how would you explain the following?
In the second and third generation of fermions, the quark with 2/3 charge is heavier than the quark with -1/3 charge. If that were also true in the first generation, which you would logically expect to be the case since that's the pattern, the up quark would be heavier than the down quark, so the proton (uud) would be heavier than the neutron (udd), so then the proton could decay into a neutron, and the proton would be unstable outside the nucleus, so in the early Universe, all protons would quickly decay, and there would be no atoms at all. The most likely explanation is that that indeed is what happens in the vast majority of universes that have a particle spectrum resembling the Standard Model, but those universes have no physicists. We are in a rare exceptional universe in which the pattern is broken, enabling us to be here.
How could else could you possibly explain this without the multiverse?
There are many possible ways that you could have a multiverse. People often think of the Everett Many Words Principle, but that's not the only way. It could be as simple as regions of space that are outside our observable universe. You can have eternal chaotic inflation, where as time goes on, small patches of space suddenly undergo inflation, resulting in a local Big Bang, which results in a new universe, and this process goes on forever. Each universe could occupy a different place within the string landscape, and thus have different low energy physics, different particles, different coupling constants, etc. Another possibility is brane world cosmology where our universe is a 3-brane within higher dimensional space. There reason to assume that there would be only one 3-brane, and if there are many, each will be a different universe.
However, none of this changes the fact that traveling backwards in time is utterly intrinsically impossible, no matter what, because it violates causality.
Time travel has nothing to do with the multiverse. The multiverse has nothing to do with time travel.
The fact that you brought up the multiverse as an argument for time travel makes me suspect that you were using the phrase "traveling backwards in time" to mean "traveling to a universe that coincidentally looks identical to what our universe looked like at some specific point in the past".
Traveling backwards in time is not the same thing as traveling to another universe!
Traveling to another universe is not the same thing as traveling backwards in time!
The only thing that these two different things have in common is that they are both impossible!
First of all, depending on what version of the multiverse that you are invoking, it is unlikely that there is another universe that looks the same as ours did at some point in the past.
Second of all, even if there were such a universe, there would be no way to get there.
Third of all, even if you could, that would still not be time travel. You would be traveling through space to a different place, not a different time.
