Perturbation spectra in the warm $k$-inflation

TL;DR

This paper explores how entropy perturbations influence the spectra in warm $k$-inflation, highlighting the role of dissipation and thermal fluctuations in shaping cosmological perturbations.

Contribution

It introduces the analysis of entropy perturbations in warm $k$-inflation and examines their effects on the evolution of curvature perturbations and the resulting spectra.

Findings

Entropy perturbations can be neglected in the weak dissipation limit.

Thermal fluctuations dominate density perturbations over vacuum fluctuations.

The tensor-to-scalar ratio is smaller than in cold inflation models.

Abstract

We investigate the cosmological perturbation theory and calculate the perturbation spectra in the warm $k$-inflation. Unlike the scalar perturbations of $k$-inflation in the cold inflationary scenario, entropy perturbations should be considered in our model. We study how the entropy perturbations affect the evolution of curvature perturbation $\mathcal{R}$ on the comoving hypersurfaces and find the dissipation coefficient $\Gamma$ plays a central role in the entropy perturbations and the evolution equation of $\mathcal{R}$. In the weak dissipation condition, entropy perturbations on the large scale can be neglected such that the primordial spectrum of cosmological perturbations is due only to adiabatic perturbations. Like general warm inflationary models, density fluctuations also mainly originated from the thermal fluctuations of the inflaton field rather than the vacuum fluctuations in our model. Finally, we calculate the perturbation spectra and the tensor-to-scalar ratio, then find the tensor-to-scalar ratio is smaller than that in the $k$-inflation or the general potential-driven cold inflationary models.