Constraints on the canonical single-field slow-roll inflation model from observations

Abstract In this work, we employ two complementary approaches to constrain the canonical single‑field slow‑roll inflation scenario. The first method makes explicit use of the analytic dependence of the primordial perturbations on the slow‑roll parameters, while the second adopts a phenomenological parameterization of the scalar and tensor primordial spectra. Using the latest observational datasets: Planck satellite data, BICEP/Keck measurements, baryon acoustic oscillation data, and the recent DESI Data Release 2, we derive direct constraints on the slow‑roll parameters. A key advantage of this strategy is that it allows us to compute the predictions of single‑field slow‑roll inflation directly from the constrained parameter values. We illustrate the resulting predictions for the parameters that characterize the scalar power spectrum and place constraints on several representative inflationary models. Our analysis shows that monomial‑potential inflation is disfavoured, while models with a concave potential, such as the Starobinsky model and brane inflation, are preferred. From the constraints on the slow‑roll parameters, we obtain a tensor spectral index in the single‑field slow‑roll framework that is very small, $|n_t|\lesssim 4.9\times 10^{-3}$, a value that will be challenging to measure with CMB data alone in the foreseeable future. Moreover, the absolute value of the derived running of the tensor spectral index does not exceed $1.91\times 10^{-4}$ at $95\%$ confidence level, based on the combination of CMB+BAO+DESI datasets.