Paul Steinhardt (Princeton cosmology expert) just gave a cogent talk at Perimeter Institute criticizing inflation. http://pirsa.org/11070029/ The talk clearly lays out the problems with expansion cosmology that inflation was invented to address and again very clearly explains the ways it is unsatisfactory as a solution. He also explores one or more alternatives, partly for comparison (one of them just as bad but in a different way.) He does a good job communicating, I think. Not all that hard to understand most of the talk. It was given at a conference/workshop on this kind of thing, so the audience is experts---but it is still not all that technical or mathy. See what you think. The conference was on Challenges for Early Universe Cosmology, and all the talks are here: http://pirsa.org/C11008 Steinhardt's talk was titled Meeting the Challenges. Roger Penrose also gave one of the talks, and it is here: http://pirsa.org/11070010/ He also dispenses with the need for inflation. Penrose's title is Conformal Cyclic Cosmology: Some Striking New Observational Support Penrose has 125 slides, and the "new observational support" is not reported until after slide #95. So if you are interested in what new evidence may have accumulated you can scroll quickly down to near the end. It looks like some of it is new, though I can't be sure.