Modeling Cosmological Perturbations of Thermal Inflation

Abstract

We consider a simple system consisting of matter, radiation and vacuum components to model the impact of thermal inflation on the evolution of primordial perturbations. The vacuum energy magnifies the primordial modes entering the horizon before its domination, making them potentially observable, and the resulting transfer function reflects the phase changes and energy contents. To determine the transfer function, we follow the curvature perturbation from well outside the horizon during radiation domination to well outside the horizon during vacuum domination and evaluate it on a constant radiation density hypersurface, as is appropriate for the case of thermal inflation. The shape of the transfer function is determined by the ratio of vacuum energy to radiation at matter-radiation equality, which we denote by upsilon , and has two characteristic scales, ka and kb , corresponding to the horizon sizes at matter radiation equality and the beginning of the inflation, respectively. If upsilon MUCH LESS-THAN1 , the Universe experiences radiation, matter and vacuum domination eras and the transfer function is flat for kMUCH LESS-THANkb , oscillates with amplitude 1/5 for kbMUCH LESS-THANkMUCH LESS-THANka and oscillates with amplitude 1 for k >> ka . For upsilon >> 1 , the matter domination era disappears, and the transfer function reduces to being flat for kMUCH LESS-THANkb and oscillating with amplitude 1 for k >> kb .