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

TL;DR

This work proposes a composite-dissipation warm inflation (CDWI) model with a two-term dissipative coefficient $\Upsilon(\phi,T)= C_1\frac{T^3}{M_{\text{Pl}}^2}+ C_2\frac{T^3}{\phi^2}$, yielding a two-stage inflationary history in which Phase-I ($\Upsilon \propto T^3/M_{\text{Pl}}^2$) sustains strong dissipation and a red-tilted spectrum, followed by Phase-II ($\Upsilon \propto T^3/\phi^2$) that maintains strong dissipation and produces a blue-tilted, amplified spectrum at small scales. The model employs a quartic potential $V(\phi)=\lambda\phi^4$ and derives distinct evolution equations for the dissipation parameter $Q$ in each phase, with end-of-phase conditions set by slow-roll parameters. Numerical analysis shows that increasing the Phase-I duration $N_1$, and tuning the transition parameter $x$, yields ACT-consistent $n_s$ values ($\sim 0.97$) with an ultra-small tensor-to-scalar ratio $r$, while allowing a strong small-scale amplification that can trigger PBH formation, depending on the chosen growth function $G(Q)$. The background evolution indicates sub-Planckian field excursions consistent with the swampland distance conjecture, though the trans-Planckian conjecture is not satisfied in this setup; the work highlights CDWI as a framework to connect large-scale CMB measurements with small-scale structure formation, with PBH and induced GW phenomenology left for future study.

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.

Figures (5)

• Figure 1: Plots for $G_1(Q)$, $G_2(Q)$, and $G_3(Q)$, in dashed blue, solid black, and dot-dashed red, respectively. Note the logarithmic scale on the vertical axis. One can see that they agree at low values of $Q$, but they differ by many orders of magnitude at intermediate and/or higher values, probed in the current work.
• Figure 2: Primordial power spectrum as a function of number of e-folds for our CDWI models. The pivot is chosen at $N_P=50$ and the value of the dissipation parameter $Q_P=100$. The two cases considered are: (a) Phase-I lasts for 40 e-folds and Phase-II for 10 e-folds ($x=1/3$), and (b) Phase-I lasts for 35 e-folds and Phase-II for 15 e-folds ($x=1/4$). The dashed blue, solid black, and dot-dashed red lines represent the spectrum with growth factor $G_1(Q)$, $G_2(Q)$, and $G_3(Q)$, respectively.
• Figure 3: Plots of inflaton field evolution with number of e-folds for the composite dissipation models. (a) Phase-I lasts for 40 e-folds and Phase-II for 10 e-folds ($x=1/3$). (b) Phase-I lasts for 35 e-folds and Phase-II for 15 e-folds ($x=1/4$).
• Figure 4: Plots of $T/H$ with the number of e-folds for the composite dissipation model. (a) Phase-I lasts for 40 e-folds and Phase-II for 10 e-folds ($x=1/3$). (b) Phase-I lasts for 35 e-folds and Phase-II for 15 e-folds ($x=1/4$).
• Figure 5: Plots of the evolution of dissipation parameter $Q(N)$ versus the number of e-folds for the composite dissipation model. Here we consider that the combined number of e-folds are $50$ and at the pivot $N_P=50$, $Q_P=100$. (a) Phase-I lasts for 40 e-folds and Phase-II for 10 e-folds ($x=1/3$), and (b) Phase-I lasts for 35 e-folds and Phase-II for 15 e-folds ($x=1/4$).