The Horizon Problem: why is the Universe almost, but not quite, homogeneous on the very largest distance scales?

In2003 the case for inflation was bolstered by the Wilkinson Microwave Anisotropy Probe, which made detailed measurements of "anisotropies" (slight deviations from perfect evenness) in the cosmic microwave background radiation.  The resulting "cosmic microwave background power spectrum" shows peaks and troughs whose precise features should be sensitive to many details of the very early history of the Universe.  Models that include inflation seem to fit this data very well, while those that don't, don't.

However, the mechanism behind inflation remains somewhat mysterious.  Inflation can be nicely explained using quantum field theory by positing the existence of a special particle called the "inflaton", which gave rise to extremely high negative pressure before it decayed into other particles.  This may sound wacky, but it's really not.  The only problem is that nobody has any idea how this particle fits into known physics.  For example, it's not part of the Standard Model.