Supersymmetric Hybrid Inflation with K\"{a}hler-Induced $\mathbf{R}$-Symmetry Breaking

Abstract

We explore the role of explicit nonrenormalizable $R$-symmetry breaking interactions in the context of supersymmetric hybrid inflation. In particular, we focus on scenarios where such breaking arises predominantly from the K\"{a}hler potential, while the renormalizable terms in both the superpotential and K\"{a}hler potential preserve $R$-symmetry. Incorporating radiative corrections, soft SUSY-breaking contributions, and supergravity effects, we construct a consistent and predictive inflationary framework. Notably, the presence of $R$-symmetry violating terms at the nonrenormalizable level helps resolve the common issue of light waterfall fields in grand unified theories, rendering them sufficiently heavy without disturbing gauge coupling unification. Our numerical analysis demonstrates that these $R$-symmetry breaking contributions play a crucial role in bringing the scalar spectral index $n_s$ into excellent agreement with the recent cosmological observations, particularly the Data Release 6 of the Atacama Cosmology Telescope. The tensor-to-scalar ratio remains suppressed, with $r < 10^{-5}$, below the reach of current and near-future experiments. However, observable gravitational waves with $r \lesssim 0.03$ can be achieved by allowing moderate deviations in the parameter space associated with a non-minimal K\"{a}hler potential.