4.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 

4.4.3.6 Thermal Fluctuation of φ . . . . . . . . . . . 71 

4.4.3.7 Thermalization of φ . . . . . . . . . . . . . . 74 

4.4.3.8 The Field Value $^{φ}$∗ . . . . . . . . . . . . . . . 76 

4.4.3.9 Energy Density of the Thermal Waterfall Field 79 

4.4.3.10 Time of Transition from Thermal Inflation to Thermal Waterfall Field Oscillation . . . . . . 82 

4.4.3.11 Energy Density of the Oscillating Spectator Field . . . . . . . . . . . . . . . . . . . . . . . 85 

4.4.4.1 The Case α = 1 . . . . . . . . . . . . . . . . . 87 

4.4.4.2 The Case α ̸ = 1 . . . . . . . . . . . . . . . . . 98 

4.5 Modulated Decay Rate . . . . . . . . . . . . . . . . . . . . . . 100 

4.5.1 Non-Gaussianity . . . . . . . . . . . . . . . . . . . . . 102 

4.5.2 Constraining the Free Parameters . . . . . . . . . . . . 104 

4.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 

4.5.2.1 Time for φ Decay . . . . . . . . . . . . . . . . 104 

4.5.2.2 Light ψ . . . . . . . . . . . . . . . . . . . . . 105 

4.5.2.3 Energy Density of the Spectator Field . . . . 106 

5 Summary and Conclusions 109 

Appendix A Derivation of Thermal Fluctuation of φ 114 

Appendix B Field Theory Derivation of Elastic Scattering Cross- section between φ and a Thermal Bath 121 

Bibliography 125 

