Cosmology
Indefinite expansion does not determine the spatial curvature of the universe. It can be open (with negative spatial curvature), flat, or closed (positive spatial curvature), although if it is closed, sufficient dark energy must be present to counteract the gravitational attraction of matter and other forces tending to contract the universe. Open and flat universes will expand forever even in the absence of dark energy.
Observations of the cosmic background radiation by the Wilkinson Microwave Anisotropy Probe suggest that the universe is spatially flat and has a significant amount of dark energy. In this case, the universe should continue to expand at an accelerating rate. The acceleration of the universe's expansion has also been confirmed by observations of distant supernovae. If, as in the concordance model of physical cosmology (Lambda-cold dark matter or ΛCDM), the dark energy is in the form of a cosmological constant, the expansion will eventually become exponential, with the size of the universe doubling at a constant rate.
If the theory of inflation is true, the universe went through an episode dominated by a different form of dark energy in the first moments of the big bang; but inflation ended, indicating an equation of state much more complicated than those assumed so far for present-day dark energy. It is possible that the dark energy equation of state could change again resulting in an event that would have consequences which are extremely difficult to parametrize or predict.
Read more about this topic: Future Of An Expanding Universe