SINGULARITIES IN INFLATIONARY COSMOLOGY - A REVIEW

We review here some recent results that show that inflationary cosmolo gical models must contain initial singularities. We also present a new singularity theorem. The question of the initial singularity re-emerg es in inflationary cosmology because inflation is known to be generica lly future-eternal. It is natural to ask, therefore, if inflationary m odels can be continued into the infinite past in a non-singular way. T he results that we discuss show that the answer to the question is ''n o.'' This means that we cannot use inflation as a way of avoiding the question of the birth of the Universe. We also argue that our new theo rem suggests - in a sense that we explain in the paper - that the Univ erse cannot be infinitely old.