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

TL;DR

This work constrains the canonical single-field slow-roll inflation model by combining analytic slow-roll parameter relations with a phenomenological spectrum parameterization, using Planck, BICEP2/Keck, and BAO data. It reports tight upper limits on the slow-roll parameter ε, a small negative η, and weak constraints on higher-order parameters ξ and σ, then derives bounds on the scalar and tensor power spectra: r ≲ 0.036–0.037, n_s ≈ 0.961–0.963, and tiny tensor features with |n_t| ≲ 4.7×10^-3 and |α_t| ≲ 1.56×10^-4 (95% CL). The results disfavor simple monomial potentials and favor concave models such as Starobinsky and brane inflation, with tensor tilt and running predicted to be too small to detect reliably with CMB data alone in the near future. Overall, the study provides a rigorous link between slow-roll dynamics and observable spectra, helping to distinguish among inflationary potentials using current cosmological observations.

Abstract

In this paper we use two methods to constrain the the canonical single-field slow-roll inflation model. The first method exploits the analytic slow-roll-parameter dependence of primordial perturbations, and the second consists of a phenomenological parameterization of the primordial spectra of both scalar and tensor perturbations. We constrain the slow-roll parameters directly by adopting the latest datasets, including Planck satellite data, BICEP2/Keck data and Baryon Acoustic Oscillation data. An advantage of this method is that we can work out the predictions of single-field slow-roll inflation model by using these constrained slow-roll parameters. We illustrate the predictions of the parameters characterizing the scalar power spectrum and constrain some inflation models. We find that the inflation model with monomial potential is disfavored, and the inflation models with a concave potential, such as the Starobinsky inflation model, brane inflation model are preferred. From the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, namely $|n_t|\lesssim 4.7\times 10^{-3}$ which will be very difficult to be measured by CMB data only in the future, and the absolute value of derived running of tensor spectral index is not larger than $1.56\times 10^{-4}$ at $95\%$ confidence level.

Figures (9)

• Figure 1: The contour plots and likelihood distributions of the slow-roll parameters $\{\epsilon,\eta\}$ are shown at the $68\%$ and $95\%$ confidence levels, derived from the combinations of CMB+BAO datasets.
• Figure 2: The contour plots and likelihood distributions of the slow-roll parameters $\{\epsilon,\eta,\xi\}$ are shown at the $68\%$ and $95\%$ confidence levels, derived from the combinations of CMB+BAO datasets.
• Figure 3: The contour plots and likelihood distributions of the slow-roll parameters $\{\epsilon,\eta,\xi, \sigma\}$ are shown at the $68\%$ and $95\%$ confidence levels, derived from the combinations of CMB+BAO datasets.
• Figure 4: The contour plots and likelihood distributions of the scalar power spectrum parameters $\{r, n_s\}$ are shown at the $68\%$ and $95\%$ confidence levels, derived from the combinations of CMB+BAO datasets. The filled black lines represent the sampled results. The dashed red lines represent the derived results.
• Figure 5: The contour plots and likelihood distributions of the scalar power spectrum parameters $\{r, n_s, \alpha_s\}$ are shown at the $68\%$ and $95\%$ confidence levels, derived from the combinations of CMB+BAO datasets. The filled black lines represent the sampled results. The dashed red lines represent the derived results.