Effects of thermal inflation on small scale density perturbations

Abstract

In this thesis, we study the cosmological scenario with thermal inflation and analyze its distinctive signatures in cosmological density perturbations. In the thermal inflation model, three additional eras, the moduli domination, the thermal inflation and the flaton domination eras, are inserted between the primordial inflation and the radiation domination of the standard scenario and change, in particular, the primordial power spectrum on small scales. After a brief introduction to the standard model of cosmology and some of its problems, we suggest the thermal inflation model to strengthen the standard scenario. Although the thermal inflation provides a clean and natural path to resolve the problems of the standard scenario, whether or not the early universe indeed experienced it can only be tested by theoretical study of its distinctive signatures and by confirming them in observational cosmology. Our main focus in this thesis is on the small scale density perturbations in the thermal inflation model. We start by finding the largest characteristic scale of thermal inflation at the comoving scale, $k_b = a_b H_b$, of the horizon size when the phase shift in expansion, $\ddot{a}_b$ = 0, occurs at the transition from moduli domination to thermal inflation.Giving some rudiments of gauge transformations and gauge-invariant observables, we move on to the evolution dynamics of the curvature perturbation via Einstein equation that relates the Riemannian geometry of the universe with the matter configuration therein. In describing the effects on the primordial power spectrum, our analysis concentrates on the evolution of curvature perturbation on radiation hypersurface during the transition from moduli domination to thermal inflation. It will be shown that the power spectrum is modified to have modulated oscillations at K ~ $k_b$ with the enhancement less than 10 times. Since $k_b ~ 1 to 10^5 Mpc^{-1}$ depending on the parameters of thermal inflation, thermal i...