Echoes of $R^3$ modification and Goldstone preheating in the CMB-BAO landscape

The $R^2$ and the single-field-like regime of $R^2$-Higgs inflation are disfavored by the observed high spectral index $n_s$ from the combined cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) measurements at the $\sim 2\sigma$ level. The addition of a dimension-six $R^3$ term in the action helps alleviate this tension. We show that the parameter space accounting for the observed high $n_s$ also induces rapid Goldstone and Higgs preheating. The preheating, especially from Goldstone modes, helps match the CMB and inflationary scales, which in turn supports the observed $n_s$.