Grand Unification Higgs-$\mathcal{R}^2$ Inflation: Complementarity between Proton Decay and CMB Observables

TL;DR

The paper presents a UV-complete $SO(10)$ GUT inflation model implemented in Palatini gravity with an $ abla$R^2 term, where a GUT-singlet scalar with a Coleman–Weinberg potential drives inflation and governs intermediate-scale symmetry breaking. A partial-inflation phase dilutes GUT monopoles while preserving a connection between inflationary observables $(n_s,r)$ and grand-unification scales, yielding a robust attractor for large $\\alpha$ with $r\approx 8\times10^{-4}$ and $0.955\lesssim n_s\lesssim0.974$. The model identifies a narrow window of monopole production at intermediate scales $M_I\sim10^{13}$–$10^{14}$ GeV that can be compatible with gauge unification and proton-decay bounds, offering a testable link between CMB data and proton-decay experiments. This multi-messenger complementarity implies that a measured $r$ would pinpoint a GUT scale for proton-decay searches, while proton-decay limits would constrain the inflationary parameter space, making the scenario falsifiable with upcoming CMB, monopole, and proton-decay observations.

Abstract

We propose a predictive $SO(10)$ Grand Unified Theory (GUT) framework for cosmic inflation in the Palatini $\mathcal{R}^2$ formulation of gravity. In this model, a GUT Higgs field both drives inflation and induces intermediate-scale symmetry breaking, thereby linking primordial cosmology, gauge unification, and topological defect formation. A partial inflationary phase of $N_I \sim 10$--$17$ $e$-folds following monopole formation can dilute magnetic monopoles to abundances $Y_M \sim 10^{-35}$--$10^{-27}$. The model yields Cosmic Microwave Background (CMB) predictions of $0.955 \lesssim n_s \lesssim 0.974$, accommodating the tensions between Planck-BICEP ($n_s \approx 0.965$) and Planck+ACT ($n_s \approx 0.971$) via $φ< M$ and $φ> M$ branches repectively. The predicted tensor-to-scalar ratio $r \lesssim 8\times10^{-4}$ lies within current observational constraints and is accessible to forthcoming experiments, including the Simons Observatory and LiteBIRD. The resulting correlations between the unification scale $M_U$, the inflationary observables $(n_s, r)$, and proton-decay lifetimes highlight a complementarity between CMB measurements and proton-decay searches, with regions of parameter space testable in forthcoming experiments such as Hyper-Kamiokande and DUNE.

Figures (11)

• Figure 1: Conceptual overview of our unified Palatini $SO(10)$ Higgs--$\mathcal{R}^2$ inflationary framework. The diagram illustrates how a single theoretical framework simultaneously connects and provides complementarity predictions for inflationary dynamics, tested by CMB observations BICEP:2021xfzSPIDER:2017xxzPlanck:2018jriSimonsObservatory:2018kocHazumi_2020ACT:2025tim, GUT symmetry breaking, probed by proton decay experiments such as Super-Kamiokande Super-Kamiokande:2020wjk and the upcoming DUNE DUNE:2020lwjDUNE:2020mraDUNE:2020txwDUNE:2020ypp and Hyper-Kamiokande Dealtry:2019ldr experiments; and topological defect formation, constrained by monopole searches, including the MACRO bounds MACRO:2002jdv, as well as future probes such as Hyper-Kamiokande Dealtry:2019ldr and DUNE DUNE:2020ypp.
• Figure 2: Inflationary predictions for the spectral index $n_s$ and the tensor-to-scalar ratio $r$ are shown for different values of $M$ (in $m_{\rm Pl}$ units) and varying reheating temperatures (top), while the running of the spectral index $\alpha_s$ as a function of $n_s$ is shown in the bottom panel.
• Figure 3: The tensor-to-scalar ratio $r$ is shown for different choices of the parameter $M$ as $\xi$ varies. Results are presented for both the metric and Palatini formulations. The red shaded region indicates the parameter space excluded by Planck observational constraints Planck:2018jri, while the grey dot-dashed line shows the projected constraints from LiteBIRD Hazumi_2020.
• Figure 4: Predictions for the inflationary observables of the Coleman--Weinberg potential in the $\mathcal{R}^{2}$ Palatini formalism are shown for the $\phi > M$ case, over a range of values of the non-minimal coupling parameter $\xi$ and for different choices of the $\mathcal{R}^2$ parameter $\alpha$. We fix $M = 50\,m_{\mathrm{Pl}}$ and $\omega_r = 1/3$. The blue star corresponds to the points shown in Figs. \ref{['fig:mi_1']}, \ref{['fig:monopoles1']}, \ref{['fig:monopoles2']}, and \ref{['fig:monopoles3']}.
• Figure 5: $n_s$ as a function of $\xi$ is shown for the two considered cases in the $\mathcal{R}^2$ framework: $\phi < M$ (left) and $\phi > M$ (right). The shaded regions correspond to the viable observational constraints from Planck Planck:2018jri and Planck+ACT ACT:2025tim.