Three channel dissipative warm Higgs inflation with global inference via genetic algorithms

TL;DR

This work develops a three-channel dissipative framework for Warm Higgs Inflation (WHI), decomposing the total dissipation coefficient $Υ(h,T)$ into low-temperature, high-temperature, and threshold-activated contributions. A genetic algorithm with structural priors (mixing and entropy) is used to perform global numerical inference on a 14-parameter model, exposing multi-channel dissipation and mitigating dominant-channel degeneracy. A layered warmness criterion based on $Q=Υ/(3H)$ and $T/H$ decouples model selection from cosmological observables, enabling transparent priors and robust energy-consistency checks. The results show the pivot-scale state is genuinely mixed, with channel-relay dynamics during evolution and energy conservation controlled to $O(10^{-7}-10^{-4})$, establishing a reliable pipeline for inferring multi-channel WHI backgrounds and their perturbation spectra.

Abstract

This paper constructs and analyzes a three channel dissipative framework for Warm Higgs Inflation, wherein the total dissipation coefficient, $Υ(h,T)$, is decomposed into low temperature, high temperature, and threshold activated contributions. A genetic algorithm is employed for the global numerical solution and statistical inference of the background field dynamics. To overcome the single channel dominance degeneracy in high dimensional parameter scans, two classes of structural priors are introduced into the objective function: a \texttt{mixing} prior to suppress extreme channel fractions and an \texttt{entropy} prior to favor multi channel coexistence. Furthermore, the adoption of a layered warmness criterion (e.g., $Q \equiv Υ/3H$) decouples model selection from cosmological observables, thereby enhancing analytical transparency. The complete workflow is demonstrated on a $14$ dimensional phenomenological model. An ablation study of the priors (\texttt{noprior} vs. \texttt{mixing} vs. \texttt{mixing+entropy}) yields $18871$ viable parameter points, revealing that the priors significantly enhance the discovery probability of non-trivial multi channel solutions within a parameter space naturally biased towards single channel dominance. After imposing the observational constraint $r < 0.036$, the number of retained solutions for each scenario is $14485$, $1889$, and $1971$, respectively. A typical best fit solution exhibits a "channel relay" dynamical feature during its evolution and a genuinely mixed state at the pivot scale (e.g., $f_{{\rm HT},*}\simeq 0.399480$, $f_{{\rm th},*}\simeq 0.600517$), implying that the microscopic origin of dissipation need not be unique within a single inflationary history.

Figures (5)

• Figure 1: Background evolution for the benchmark multi channel WHI solution, shown as a function of the number of e-folds $N$. The panels display: the Hubble slow-roll parameter $\epsilon_H(N)$ (top left), the temperature-to-Hubble ratio $T/H(N)$ (top right), the inflaton field trajectory $h(N)$ (bottom left), and the dissipation ratio $Q(N)$ (bottom right, scaled by $10^3$ for readability). Dashed lines indicate the $\epsilon_H=1$ and $T/H=1$ thresholds.
• Figure 2: Energy conservation diagnostic for the benchmark solution. The plot shows the absolute fractional energy balance residual, $|\mathcal{R}_E(N)|$, as a function of the number of e-folds $N$ (logarithmic vertical axis). The quantity $\mathcal{R}_E$ quantifies the instantaneous mismatch in the Friedmann equation as determined by the numerical integrator. Smaller values indicate better energy closure. The oscillatory pattern reflects the adaptive step-sizing of the integrator, while the sharp increase at the end corresponds to the increased stiffness of the system as it exits inflation.
• Figure 3: Evolution of the fractional dissipation channel contributions, $f_i(N)$, along the background trajectory. The left panel uses a linear scale to emphasize the dominant partition, while the right panel uses a logarithmic scale to resolve subdominant components and diagnose sharp transitions.
• Figure 4: Scatter plot of viable warm solutions in the $(n_s, r)$ plane for three inference settings: noprior (left), mixing (middle), and mixing+entropy (right). Each point corresponds to a solution passing the warm-selection criteria, colored by $\log_{10} Q_*$. The orange horizontal line denotes the reference upper bound $r = 0.036$BICEP:2021xfz, while the purple vertical dashed line marks the scale-invariant limit $n_s = 1$. The blue vertical bands indicate the Planck-allowed intervals for $n_s$BICEP:2021xfz.
• Figure 5: Distributions of the channel dominance statistic $f_{\max,*}$ (left) and the normalized entropy $H_n$ (right) for warm viable solutions, comparing the three inference settings. These diagnostics provide complementary measures of degeneracy: $f_{\max,*} \to 1$ and $H_n \to 0$ indicate single channel dominance, while smaller $f_{\max,*}$ and larger $H_n$ indicate more balanced multi channel coexistence.