The $R^2$-Higgs inflation: $R^3$ contribution and preheating after ACT and SPT data

The $R^2$-Higgs inflation is one of the simplest yet best-fit models consistent with Planck data. The higher spectral index $n_s$ recently reported by the combined cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT), South Pole Telescope (SPT), and Planck, along with baryonic acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI), disfavors the single-field-like regime of $R^2$-Higgs inflation at approximately $2\sigma$. Following a doubly covariant formalism, we show that the $R^2$-Higgs inflation, when modified by a dimension-six $R^3$ term, can account for the high $n_s$ reported by CMB+BAO. In this regard, we find that preheating may play a pivotal role. We also show that if the nonminimal coupling between the Ricci scalar $R$ and the Higgs field is $\mathcal{O}(10)$, then preheating via the production of Higgs quanta may help explain the reported observations.