Prior-Averaged Ranking of Low-Order Monomial Potentials in Low-Temperature Warm Inflation

Abstract

We compare the relative prior-averaged weights of the monomial potentials \(V_p(\phi)=\lambda_p\phi^p/p\), with \(p=2,3,4\), in low-temperature warm inflation with the dissipative coefficient fixed to \(\Upsilon=C_\phi T^3/\phi^2\). The dissipative form, background equations, primordial-spectrum prescription, and compressed observable likelihood are held fixed while the monomial power is varied. For each branch, the warm background equations, including radiation backreaction, are solved numerically, and the broadened likelihood for \((A_s,n_s,r_{0.05})\) is integrated over the adopted prior domain to obtain \(Z_{\rm eff}^{(A_s,n_s,r)}\). For the reference configuration \(N_*=55\), \(\sigma_r=0.005\), and the viability-conditioned prior A, we obtain \(\Delta\ln Z_{\rm eff}(p=2)=-32.18\) and \(\Delta\ln Z_{\rm eff}(p=3)=-6.99\) relative to \(p=4\). The same ranking is retained for the specific variations of \(N_*\), the prior domains, the random seeds, and the smoothing width of the upper-bound penalty examined here. A representative quartic trajectory gives \(n_s=0.96420\), \(r_{0.05}=0.02663\), \(Q_*=4.68\times10^{-3}\), and \(T_*/H_*=10.67\). Its scalar spectrum is evaluated using the assumed Bose--Einstein occupation prescription. A component test at this representative point indicates that the occupation term contributes more to the scalar enhancement than the fitted dissipative growth factor. Thus, within the compressed-likelihood setup, the adopted thermal-occupation prescription, and the adopted viability-conditioned priors, the prior-averaged ranking is \(p=4>p=3\gg p=2\).