Page "Inflation (cosmology)" Paragraph 9

The ekpyrotic and cyclic models are also considered adjuncts to inflation.

These models solve the horizon problem through an expanding epoch well before the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch.

The universe passes through the Big Crunch and emerges in a hot Big Bang phase.

In this sense they are reminiscent of the oscillatory universe proposed by Richard Chace Tolman: however in Tolman's model the total age of the universe is necessarily finite, while in these models this is not necessarily so.

Whether the correct spectrum of density fluctuations can be produced, and whether the universe can successfully navigate the Big Bang / Big Crunch transition, remains a topic of controversy and current research.

They also provide no explanation of the magnetic monopole problem.

Unfortunately, as things stand-there is no evidence of any ' slowing down ' of the expansion.