Isocurvature-induced features in multi-field Higgs-$R^2$ inflation

TL;DR

This work analyzes primordial perturbations in multi-field Higgs--$R^2$ inflation, emphasizing the role of non-minimal Higgs coupling $\xi_h$ in governing field-space dynamics and isocurvature modes. By numerically solving coupled background and perturbation equations in the Einstein frame, it identifies two regimes: (i) $\xi_h \ll 1$ with persistent isocurvature and negligible turning, and (ii) $\xi_h \sim 0.1$ where transient turns strongly couple adiabatic and isocurvature perturbations, generating localized features in the curvature spectrum that eventually decay into a purely adiabatic end state. These dynamics imprint distinctive signatures in the CMB, including low-$\ell$ suppression and oscillatory features at intermediate scales, while constraining high-$\ell$ behavior and the viability of such models. The results highlight the importance of multifield effects and provide observationally testable predictions for future CMB and isocurvature searches within Higgs--$R^2$ inflation frameworks.

Abstract

We study primordial perturbations in Higgs--$R^2$ inflation in the presence of non-minimal kinetic mixing between the Higgs field and the scalaron. By numerically solving the multifield background and linear perturbation equations, we identify distinct dynamical regimes controlled by the Higgs non-minimal coupling $ξ_h$. For $ξ_h \sim \mathcal{O}(0.1)$, transient turning of the inflationary trajectory leads to a transfer between adiabatic and isocurvature modes, generating localized features in the primordial curvature power spectrum. In contrast, in the weak-coupling regime $ξ_h \ll 1$, the curvature spectrum remains nearly featureless while isocurvature perturbations do not fully decay, resulting in a residual isocurvature component at the end of inflation. We compute the associated CMB angular power spectra and discuss the observational implications of these regimes. Our results highlight the role of multifield dynamics in shaping primordial perturbations and provide constraints on viable realizations of Higgs--$R^2$ inflation.

Figures (8)

• Figure 1: Scalar potential $V(\phi\,,h)/M_p^4$ in the Einstein frame. Left panel: Potential \ref{['potential Einstein']} using the standard parameter space $\lambda = 0.13$, $\xi_h = 4000$ and $\xi_s \simeq 10^8$. The potential exhibits a two-valley structure and a ridge at $h=0$. Right panel: The same potential \ref{['potential Einstein']} but for a coupling $\xi_h = 0.1$. We observe that the valley and ridge structure disappears in the limit $\xi_h \ll 1$.
• Figure 2: Evolution of the slow-roll parameter $\epsilon_H$, the turning rate parameter $\eta_\perp$, and the parameter $\eta_{||}$, along with the field-space trajectory and background variables ($H$, $\phi$, $h$) as a function of the number of e-folds $N_e$. We consider the parameter set $\xi_h = 0.1$, $\lambda = 10^{-10}$, and $\xi_s = 4\times10^8$, with initial conditions $\phi_0 = 5.7$ and $h_0(\phi_0) = 10^{-4}$ in Planck units. It is observed that, although inflation begins in a slow-roll regime ($\epsilon_H \ll 1$), the initial conditions produce transient peaks associated with turns in the field-space trajectory.
• Figure 3: Numerical solution of equations \ref{['R equation efolds']} and \ref{['Qs equation efolds']} for the space parameter $\xi_h= 0.1$ (top panel) and $\xi_h= 10^{-9}$ (bottom panel) with $\lambda = 10^{-10}$ and $\xi_s = 4\times 10^8$ fixed. We also fixed the initial conditions to $\phi_0 = 5.7$ and $h_0 = 10^{-4}$ in Planck units. The vertical dashed line indicates horizon crossing for the pivot scale $k_* = 0.05\,\text{Mpc}^{-1}$.
• Figure 4: Primordial power spectrum for adiabatic (left panel) and isocurvature (right panel) perturbations evaluated at the end of inflation for $\xi_h = 10^{-9}$ and $\lambda = 10^{-10}$, $\xi_s = 4\times 10^{8}$. We can see that the isocurvature perturbations remain non-zero at the end of inflation.
• Figure 5: Primordial power spectra for curvature $\mathcal{P}_{\mathcal{R}}(k)$ (top), isocurvature $\mathcal{P}_{\mathcal{S}}(k)$ (middle), and the cross-correlation spectrum (bottom) for $\xi_h = 0.1$, $\lambda = 10^{-10}$ and $\xi_s = 4\times 10^{8}$ evaluated at the end of inflation. The vertical dashed line corresponds to the scale pivot $k_* = 0.05\,{\rm Mpc}^{-1}$