Noncanonical warm inflation: A model with a general Lagrangian density

Abstract

Warm inflation is extended from the canonical field to the noncanonical field with a general Lagrangian density in the coupling form of kinetic and potential terms. In this paper, the equation of motion for the noncanonical inflaton field is developed, but the coupling term ${\mathcal{L}}_{X\ensuremath{\varphi}}{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\varphi}}}^{2}$ makes the inflation difficult to solve. It is found that there is a special field redefinition decoupling the equation of motion and the inflation can be solved in this special field representation for convenience. The relation of field redefinition is obtained between the special uncoupled field and general noncanonical field. Also, the equation of motion and slow roll approximations for noncanonical warm inflation are developed in the special field representation. Then two examples are presented to show how the translation of a general noncanonical Lagrangian density in the coupled $\ensuremath{\varphi}$ representation to the uncoupled $\ensuremath{\phi}$ representation. Finally, we calculate the cosmological perturbations generated by the new kind of warm inflation.