Composite Dissipation in Warm Inflation: Implications for the Primordial Power Spectrum

Abstract: Warm inflation is a well-motivated and generalized framework of inflation, describing a coupled inflaton-radiation bath. In this work, we investigate a warm inflation model with a quartic potential and a composite dissipation coefficient $Υ(φ, T) = C_1 \frac{T^3}{M_{\text{Pl}}^2} + C_2 \frac{T^3}{φ^2}.$ The two terms in $Υ$ dominate at different scales: the first term governs the early inflationary dynamics at large (CMB) scales, while the second term becomes significant at smaller scales. The model features two distinct stages of inflation: an initial phase where strong dissipation ($Q \gg 1$) generates a red-tilted primordial spectrum consistent with CMB observations (from ACT), followed by a second phase producing a blue-tilted spectrum with a significant amplification of power at small scales, leading to primordial black hole formation. We analyze the effects of key parameters -- like the duration of each inflationary phase, the slow-roll parameter at the end of the first phase, the dissipation strength at the pivot scale, and the choice of the growth function -- on the primordial power spectrum and its spectral index. Additionally, we examine the consistency of the model with the swampland distance conjecture and trans-Planckian conjecture, needed for embedding these models with some UV complete theories. This work highlights the potential of warm inflation with a composite dissipation coefficient to reconcile large-scale CMB measurements with small-scale structure formation.