We know that to solve the homogeneity and isotropy problem, we invite the inflation and the inflation at early universe can make the presently observable universe much smaller than the particle horizon hence to avoid the homogeneity and isotropy problem.
But the particle horizon at any time by definition is the largest region where particles can possibly contact with us. Then how can it be possible that the region we now observed is much smaller the particle horizon?
Here is my answer, but if you have a different viewpoint, please argue against me.
(Now I think when we say that what we observed is much smaller than the particle horizon usually only means the observed particles that emitted at a particular time, e.g. at the CMB formation, are inside the particle horizon with respect to any of the observed particles at the emitted time. We shall note that the particle horizon depend on the observer. In the context of inflation, usually, the particle horizon corresponds to the one with respect to the photons at recombination. And we need that the photons we observed today are within the particle horizons of themselves at the time of recombination. Without inflation, this is not the case. Because the inflation will add up the weight of the conformal time at earlier history, hence make the photons at the CMB formation time inside the particle horizon with respect to the photons of that particular time. Equivalently, the inflation push forward the recombination to be more recent)