  Typically cold inflation with positive vacuum energy density dilutes all
matter except the quan- tum fluctuations which are stretched outside the Hubble
patch during inflation. However the cyclic- inflation scenario, where the
universe undergoes many many asymmetric cycles leading to an overall
exponential growth, operates in the presence of thermal matter. Thus, while
some of the nice prop- erties of cold inflation is preserved, in cyclic
inflationary models thermal excitations are continually produced and there
exists a unique opportunity of imprinting interesting thermal history in CMBR.
In particular, we will see that a phase transition can lead to observably large
higher order nongaus- sianities as the critical temperature is approached, and
that these are increasingly divergent with the order of the correlations.
