Such technology would quickly put any space empire at the absolute top of the food chain. Depending on its limits, of course.
Transportation
If the field can be transported, a single high-speed transport would be able to move incredible amounts of materials. the size of the transport depends on how big the technology is to open and close (or 'inflate' and 'deflate', if you prefer) the space. If a 'container' can be inflated and deflated from any location, then the ship could be nanotech sized, as all it really needs is to be able to move really fast and be locatable by the right people.
But never mind moving stuff and people. How about planets? Find a nice planet, stick an inflated field in its path, and once it goes in, zip it up and take it wherever you want! Make your own solar system!
Defense
Which leads me to the next point. As Dan Smolinske pointed out, you could create a maze of large and small spaces that would make it very difficult to find your home planet. But why stop there? First, find a very chaotic part of the universe - somewhere with supernovas, black holes, new stars being born, and as much dangerous stuff as you can think of scattered around. Take that solar system you created earlier and set it up somewhere in the middle, still inside its field. Now, not only do you have a needle in a haystack, but your haystack is exploding! All the time!
To get in and out safely is a little tricky, which is why I came up with four possible scenarios:
- Make a drawbridge with a long, tubular field (or multiple fields in close proximity). Extend the fields from inside your solar system (inside the maelstrom) to outside the maelstrom. When a ship wants to enter or exit, inflate the fields; this creates a thin path for the ship to follow, surrounded by a lot of empty space. Any harmful energy or particles will get bogged down in the outside of the "drawbridge", allowing the ship in the center to pass safely.
- Make a ship in a bottle. The "bottle" is a field that surrounds the ship, protecting it from harmful energy or particles with very long distances. Similar to the drawbridge, except instead of a path, it's a point.
- Make a gate. This would be the opposite of the drawbridge; part of the maelstrom would be inside an inflated chunk of space; deflating it would open a path. When the ship is safely through, re-inflate the gates and they slam shut.
- Make a thin edge. This is the opposite of the ship in a bottle; instead of expanding the space around the ship, compress it, moving the ship from one side of the maelstrom to the other in a matter of seconds. When no ships need to pass through, the 'thin' spot can be inflated, stranding the system in the middle of a vast space.
Weapons
You can carry around an armada inside a baseball. Or a sun. Or black holes. That alone is enough to rule the universe, but there's still more; instead of destroying your enemies, you can take them hostage. Along with their homeworld. Or their home solar system. You don't even have to fire a shot.
Defense
Distance makes a great shield. If the technology is fast enough, a wearable suit (or a ship-sized net) could be designed that inflates space around the wearer when projectiles are detected; the projectile would simply travel past the wearer.
Stealth
If you can operate the technology inside the field, then your ships can shrink themselves down to a tiny point, as could operatives. Of course, you could also hide you planet like that.
And stealing information (or anything else) is easy when you can hide planets in the palm of your hand.
Living Space
Of course, you'd have all the living space you'd want; find a nice habitable planet, put it in a bubble with a lovely sun, and away you go. More people? Not a problem! Just stick some bubbles in living areas! A house could be no more than a doorway into an enlarged space. If you can stack bubbles, it's even easier; rows of doors, behind yet more rows of doors. Of course, you'll need a lot of oxygen and other resources, but as long as you have somewhere to pull those from, you can make 'shortened space' jumps to deliver it exactly where it needs to be.
In fact, if you make your spaces just so, you could literally step from one planet to another by shrinking the space between them in a small area.
Boundless trouble
Of course... none of this comes without risk. If it is the space that grows and shrinks, but not the objects inside, then a failed field could create an explosion as all the stuff inside is shoved into 'normal space'.
On the other hand, if the things inside shrink and grow with the field, you may well end up with material that isn't the same size as it used to be. A number 12 bolt may go into a field just right, but come out a little bigger. Joe Smith may take the 8:05 to work and the 5:20 home, and end up growing taller every day.
If the fields retain mass, then moving a planet around is going to be just as hard inside a field as outside, and probably harder - every time you shrink something big, you run the risk of making a tiny black hole. Or a not-so-tiny black hole, if you're shrinking solar systems.
A maze may work a little too well; if you forget the way out, you're stuck.
Communication will be almost impossible, unless you can invent something that doesn't interact with space itself. The ever-changing shape of 'space' near a field would distort radio signals, and a moving field would scramble radio signals into mush.
If something with a larger area than a cross-section of the field hit the field, the object would be torn apart; the outside dimensions would stay the same, be the inside dimensions would grow. 4 units of material stretched across 4000 units of space isn't going to last long.
And finally, great technology can put you far ahead of everyone else, but it can also make you a target. If you use this technology, weaponize it first, because everyone else is going to want to take it away from you.
