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

TL;DR

This paper presents a Grand Unified Theory-based inflation model linking cosmic inflation, gauge unification, and proton decay, with specific predictions for CMB observables and proton decay experiments, offering testable links between cosmology and particle physics.

Contribution

It introduces a predictive $SO(10)$ GUT inflation model within the Palatini $ ^2$ gravity framework, connecting inflationary predictions with proton decay and unification scale measurements.

Findings

Predicted $n_s$ between 0.955 and 0.974 consistent with observations.

Tensor-to-scalar ratio $r \,\lesssim 8\times 10^{-4}$ within experimental reach.

Correlations between unification scale, inflation observables, and proton decay lifetimes.

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 $\phi < M$ and $\phi > M$ 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.