In the spirit of "things could be very different than you imagine" (mentioned by Noung), there's an idea that springs to mind when one considers that not only are we in an expanding universe, but that the expansion is accelerating.
Those of you who have watched popular television science shows have seen the rubber sheet demonstration. I have seen these shows, and while I am impressed with them, there is always one aspect that has nagged me immensely. The balls only create dents in the rubber sheet because they are being pulled by Earth's gravity. A two-dimensional illustration of gravity, but it depends on a three-dimensional gravity to be effective.
The lastest scientific thinking that I've heard about rumors that the universe is expanding at an accelerating rate. If that is so, this acceleration can take the place of the Earth's gravity in the rubber sheet experiment. Balls will cause a dent in the rubber sheet, not by being gravitationally attracted to something, but by simply having inertia to work against the motion of the accelerating rubber sheet. The experiment will show the same results if the sheet is accelerating upwards as if it's stationary within a gravitational field.
Another demonstration that's shown in popular science magazines is the idea that our universe may be like a balloon that's expanding - thus, things in the universe are mutually moving away from one another without all moving away from a particular point in the universe. These two ideas can now be linked - the rubber balloon is expanding at an accelerating rate, with masses denting spacetime simply by the inertia they have. Locally the rubber-sheet model holds, and this links the inertial property of mass with the gravitational property. In that case, all the dents are pointing inwards, and massive objects are in fact closer to the centre of the universe than less massive objects or empty space.
Taking this idea to outlandish extremes... what if the acceleration of the universe were to change? Gravity would be affected. What if it has been changing? Gravity isn't what it used to be. If there is a big crunch, then there will be a point where spacetime is shrinking but the massive objects will still be moving outward. Will there be oscillation? Will it be damped? Will it be underdamped, overdamped, or critically damped?
Yes, I've probably been thinking far too much about this fanciful idea. For one thing, I've heard it said that gravitational fields cannot be expressed as scalar fields (which would probably be the case if this idea were true), they can only be expressed as tensor fields (of higher rank). But, the idea tickles the imagination.