(spoilers, obviously) It's a predestination paradox -- so, as with all predestination paradoxes in fiction, the story is a little too in love with the use of it -- but the movie sets the ground rule that the only way to communicate backwards is to manipulate gravity, therefore that's how they're going to have to accomplish it.

As for the love-powered part, everyone's a little too hung up on that set of dialog. There's nothing in the plot that relies on it. Sufficiently advanced magic gravity technology is more than enough. Is any advancement of the plot motivated by more than the fact that he wants to see his daughter again? Sure, if they had listened to Brand's feelings they wouldn't have ended up with crazy guy and would have ended up on a (seemingly) habitable planet, but the human race also would have died on earth and lived on entirely from the test tube embryos.

The whole tesseract section doesn't entirely fit with the tone of the rest of the movie but it's not powered by love.