Has inflation really solved the problems of flatness and absence of   relics?
  Among the three cosmological enigma solved by the theory of inflation, {\it viz.} (a) large scale flatness, (b) absence of monopoles and strings, and (c) structure formation, the first two are addressed from the viewpoint of the observed scales having originated from very small ones, on which the density fluctuations of the curvaton and relics are {\it inevitably} of order unity or larger. By analyzing strictly classically (and in two different gauges to ensure consistency) the density evolution of the smoothest possible pre-inflationary component -- thermal radiation -- it is found that the O(1) statistical fluctuations on the thermal wavelength scale present formidable obstacles to the linear theory of amplitude growth by the end of inflation. Since this wavelength scale exited the horizon at an early stage of inflation, it severely limits the number of e-folds of perturbative inflation. With more e-folds than $\approx 60$ there will be even larger fluctuations in the radiation density that ensures inflation keeps making `false starts'. The only `way out' is to invoke a super-homogeneous pre-inflationary fluid, at least on small scales, adding to the fine-tuning and preventing one from claiming that inflation simply `redshifts away' all the relic inhomogeneities; {\it i.e} the theory actually provided no explanation of (a) or (b), merely a tautology. 
Richard Lieu
astro-ph.CO gr-qc