Power spectra in warm G-inflation and its consistency: stochastic approach

Recently, it has been realized that the so-called G-inflation model inspired by supplementing a generalized covariant Galileon-like non-linear derivative self-interacting term to the standard kinetic term should be ruled out from inflationary models. This is due to the fact that it suffers from lack of an oscillatory phase at the end of the inflationary regime which is typically accompanied by the appearance of a negative squared propagation speed of the scalar mode leading to instabilities of small-scale perturbations. In this regard, the warm G-inflation scenario is proposed where for G-inflation to survive, the Galileon scalar field is coupled to the radiation field through a dissipation term which results in removing the reheating period due to the characteristics of warm inflationary scenario. In so doing, a linear stability analysis is first performed to obtain the appropriate slow-roll conditions in such a proposal. Cosmological perturbations of the model are then investigated by utilizing fluctuation-dissipation theorem and analytical expressions are derived for observable quantities; the power spectrum, tilt spectral index and tensor-to-scalar ratio in terms of $PSR$ parameters and Galileon flow functions. Finally, the model is solved for chaotic self-interacting potentials, particularly the renormalizable Higgs potential $\frac{\lambda}{4} \phi^{4}$, and shown to be consistent with observations in the weak dissipation $Q \ll 1+ 3\frac{\delta_{GX}}{\delta_{X}}$ and G-dominant $3\frac{\delta_{GX}}{\delta_{X}}\gg 1$ regime despite its large self-coupling, since the energy scale at the horizon crossing is depressed by the synergy of Galileon and thermal effects.