Go to previous page Go up Go to next page

7 Asymptotics of Expanding Cosmological Models

The aim of this section is to present a picture of the dynamics of forever-expanding cosmological models, by which we mean spacetimes that are maximal globally hyperbolic developments and which can be covered by a foliation by Cauchy surfaces whose mean curvature trk is strictly negative. In contrast to the approach to the big bang considered in Section 8, the spatial topology can be expected to play an important role in the present considerations. Intuitively, it may well happen that gravitational waves have time to propagate all the way around the universe. It will be assumed, as the simplest case, that the spacetimes considered admit a compact Cauchy surface. Then the hypersurfaces of negative mean curvature introduced above have finite volume and this volume is a strictly increasing function of time.

Models with accelerated expansion are now an important subject in cosmology. They have been important for a long time in connection with the early universe, where inflation plays a key role. More recently they have acquired a new significance in view of accumulating observational evidence that the expansion of the universe is accelerating at the present epoch. For these reasons it is particularly interesting to consider solutions of the Einstein equations which are appropriate for modelling cosmic acceleration. The last four Sections 7.3 to 7.6 are devoted to various aspects of this topic. An introductory account which describes some of the physical background can be found in [305Jump To The Next Citation Point].


 7.1 Lessons from homogeneous solutions
 7.2 Inhomogeneous solutions with /\ = 0
 7.3 Homogeneous models with /\ > 0
 7.4 Acceleration due to nonlinear scalar fields
 7.5 Other models for cosmic acceleration
 7.6 Inhomogeneous spacetimes with accelerated expansion

  Go to previous page Go up Go to next page