Not So Minimal Warm Inflation

Abstract

An axion-like inflaton coupled to non-Abelian gauge bosons provides a compelling microphysical framework for warm inflation. Starting even from cold initial conditions, in these systems, sphaleron heating may generate thermal friction sufficient to sustain finite temperatures throughout the inflationary epoch. Insisting on shift-symmetric potentials, in this work we revisit the viability of these scenarios under the designation of Minimal Warm Inflation. We examine both observational constraints and model-building limitations on models with a hierarchy between the decay constants appearing in the friction rate and in the inflaton potential. We conclude that the popular clockwork mechanism cannot generate the required hierarchy; however, partial-wave unitarity bounds admit effective descriptions that remain consistent with observations.

Figures (8)

• Figure 1: Plot of the scalar spectral index $n_s$ versus the tensor-to-scalar ratio $r$, obtained by varying the parameter $f_b$ (setting $f_a=f_b$) with some values of $f_b$ highlighted in the curve, together with the observational range for $n_s$ and $r$ from the BK18 datasets BK18. We compare the results for $N_*=50$ and $N_*=60$, as well as the minimum and maximum values of the parameter $\alpha$.
• Figure 2: Plot of $n_s$ versus $r$ for different values of $f_a$ and $f_b$, as well as both $N_*=50$ and $N_*=60$. The curves are obtained by varying the parameter $\alpha$. The blue area marks the BK18 observational constraints on $n_s$ and $r$BK18. In each case we have highlighted the points where the dissipative ratio at horizon crossing, $Q_*$, reaches a value of $Q_*=10^{-7}$, $Q_*=10^{-5}$ and $Q_*=10^{-2}$.
• Figure 4: Plot of $\alpha_s$ versus $n_s$ for different values of $f_a$, $f_b$ and $N_*$, with CI values marked as dots in each case. The area shaded in blue marks the observational range for $n_s$BK18, the area shaded in green marks the observational range for $\alpha_s$Planck:2018jri and the dashed lines mark the regimes where the observational bound for $r$ is not fulfilled, as seen in Fig. \ref{['fig:ns-r']}.
• Figure 5: Plot of $\alpha\Lambda/f_a$ versus $n_s$. Here, the shaded gray area marks the values ruled out by the unitarity constraint (\ref{['eq:unitarity']}), while the blue area marks the observational range for $n_s$BK18. The dashed part of the curves mark the regions where $r$ is outside its observational range as seen in Fig. \ref{['fig:ns-r']}, and the dotted ones mark the analogous for $\alpha_s$ as seen in Fig. \ref{['fig:alphas-ns']}. The gray dashed line at $\alpha \Lambda/f_a=1$ shows that the clockwork condition is never fulfilled within observational range, since $\alpha\Lambda/f_a>1$ implies $\Lambda/f_a>1$.
• Figure 6: Value of the inflaton at horizon crossing, $\phi_*$ normalized by $\pi f_b$, with respect to the dissipative ratio at horizon crossing, $Q_*$. The data in this plot corresponds to $f_a=10^{12}\,\text{GeV}$, but other values of $f_a$ present the same behavior, up to very small variations. The dashed gray line marks the value $\phi_*/f_b=\pi/2$.