Radiative symmetry breaking, cosmic strings and observable gravity waves in 𝖴(1)𝖱 symmetric 𝖲𝖴(5) × 𝖴(1)χ

Abstract

We implement shifted hybrid inflation in the framework of supersymmetric SU(5) × U(1)χ GUT model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The U(1)χ symmetry is radiatevely broken after the end of inflation at an intermediate scale, yielding topologically stable cosmic strings. The Planck's bound on the gravitational interaction strength of these strings, characterized by GNμs are easily satisfied with the U(1)χ symmetry breaking scale which depends on the initial boundary conditions at the GUT scale. The dimension-5 proton lifetime for the decay p → K+ν̅, mediated by color-triplet Higgsinos is found to satisfy current Super-Kamiokande bounds for SUSY breaking scale MSUSY ≳ 12.5 TeV. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital role in bringing the scalar spectral index n_s within the Planck's latest bounds, although with small tensor modes r ≲ 2.5 × 10-6 and SU(5) gauge symmetry breaking scale in the range (2 × 1015≲ Mα ≲ 2 × 1016) GeV. By employing non-minimal terms in the Kähler potential, the tensor-to-scalar ratio approaches observable values (r ≲ 10-3) with the SU(5) symmetry breaking scale Mα ≃ 2 × 1016 GeV.