Q:

The Paradox Men - Cosmology

In Charles L Harness's 'The Paradox Men', a spaceship crashes on earth several years before it launches, having circumnavigated the universe faster than the speed of light.  It is a good read, but I would like to be able, as far as possible, to defend that central structure and help people suspend their disbelief even if they know a lot of physics. Unfortunately I'm pretty out of my depth with the relationship between relativity and cosmology.
My current best attempt would be something like this:
The cosmic microwave background is the most distant evidence, and the most redshifted, that the boundary of our universe is what is moving away from us at the speed of light. The boundary of our universe is also t=0. If we can travel faster than light, we blue-shift that as we accelerate until finally its the big bang and we smash through it  ...Thats it... Beyond that I can only see even more fanciful handwaving. Anyone have a suggestion?

A:

Your question is a hard one, but one which can be answered using modern cosmology and General Relativity.  I'll skip the math (which is right at the edge of what I understand, anyway.)
First, the question of time travel is separate from the question of the "edge of the universe".
In General Relativity there are a number of legitimate ways to travel through time. None are easy and all require really, really exotic conditions. (I might add that many physicists think they are in fact impossible, but so far no one had actually demonstrated this.)
In Special Relativity, if you could travel faster than light in vacuum, you could relatively easily travel backwards in time.  But we are 100% sure that you can't travel FTL.  So no time travel that way.
Now for the edge of the universe: There isn't one. We have pretty strong evidence that the universe is much larger than what we can observe. (There's observational evidence that it's at least ten times bigger in diameter than what we can observe. Basically, the observed flatness of spacetime at the largest distances we can observe means that flat spacetime must extend much further than that.)
As we look out in any direction, we see more and more distant galaxies moving away from us faster and faster and further and further back in time. Eventually, we expect to see the very first galaxies.  Finally, we see the cosmic microwave background which is the redshifted glow from the hot gasses that filled the universe when it was about 3000 years old.
What we can see is controlled by two things. First, we can't see anything further away than light can travel since the Big Bang. Nearly all of the universe is further away than that. Secondly, we can only see those parts of the universe that are moving away from us at less than the speed of light.
I know that I just said that we're 100% convinced about the impossibility of FTL travel. So how do I resolve this?  Basically, the equations of GR (which includes SR) prohibit local speed differences that exceed the speed of light: Two objects can't pass each other FTL. But there is no prohibition against space expanding so much that enough new space is created between a pair of objects that they have a relative velocity greater than that of light. And that's happening right now in our expanding universe.  We can never see those more distant objects because light emitted from them towards us actually moves away from us, dragged along by the expansion of space!
We can't see those sections of the universe and, since the universe's expansion rate seems to be increasing rather than decreasing, never will be able to see them.
So if you have FTL, you can time travel trivially without going to the edge of the universe.  And if you don't, you'll never get there.  (Much less get back!)

A:

(...) help people suspend their disbelief even if they know a lot of physics.

That is not possible, because if people know a lot of physics, they will know that you will not travel backwards in time by achieving faster than light speeds.
The idea that FTL travel will allow a visit to the past comes from an equation that is relevant for time dilation measures. In brief, if you synchronize your clock with a friend while you two are at rest (in relation to each other), and then one of you accelerates, you will notice your clock measuring time in a different tempo compared to your friends. The difference is given by this formula:
$$ {\Delta t'={\frac {\Delta t}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$$
Where $v$ is your relative speed, and $c$ is the speed of light. Notice that when $ v = c $, the denominator of the equation becomes 0. People who are not familiar with math assume that this means time stops when you reach light speed. But you cannot divide by zero.
Going faster, the denominator might become negative. For example, if you go twice as fast as light, the equation becomes:
$$ {\displaystyle \Delta t'={\frac {\Delta t}{\sqrt {1-{\frac {(2c)^{2}}{c^{2}}}}}}} = {\frac {\Delta t}{\sqrt {1 - \frac {4c^2}{c^2}}}} = {\frac {\Delta t}{\sqrt {1 - 4}}} = {\frac {\Delta t}{\sqrt {-3}}}$$
Again, people who are not familiar with math will think that this implies a negative result. Which would mean that, in relation to your own clock, your friend's clock would be going backwards, so your friend would be going "to the past". But that's not the case. The square root of a negative number is not a real number, but rather an imaginary number. From which we can conclude that:

A trip to the past is neither implied nor suggested by the equation;
We cannot even begin to imagine what would happen to the FTL traveler.

This is not to say that traveling to the past is not allowed by physics. There are ways in which it would be, in theory, possible to send energy and matter to the past. However, that would not be done by achieving superluminal (FTL) speeds alone. If FTL speeds are involved, they are just part of the solution, not the whole of it.
If you want to impress us eggheads with science, you will have to include more things such as wormholes.

But let me tell you this: I know and love all of this stuff. I also love Marvel. In his autobiography, Stan Lee speaks about the science behind the Incredible Hulk and other heroes: he is honest in saying that he knows **** about physics, and that he just used whatever buzzwords and concepts that seemed to be cool when creating his characters.
If you bath someone with gamma rays, they will not gain the power to become green beasts capable of holding tectonic plates together. Your victim might be castrated and cancerous after that. This does not keep the Hulk from being one of my favorite superheroes ever.
Don't try too hard to be scientifically correct, that is no fun. Make shameless use of handwavium. We eggheads don't care. We will love you for your writing, not for your correctude.

