Inflation at the End of 2025: Constraints on $r$ and $n_s$ Using the Latest CMB and BAO Data

TL;DR

This paper constrains inflationary parameters $r$ and $n_s$ using the latest CMB and BAO data, finding tight limits on $r$ and a shift in $n_s$ that favors certain inflation models, with implications for future observations.

Contribution

It provides updated constraints on inflationary parameters using new CMB and BAO data, and discusses implications for inflation model selection.

Findings

Upper limit on $r$ is less than 0.034 at 95% confidence.

The $n_s$ value shifts upward when adding BAO data, favoring monomial potentials.

Polynomial $ ext{alpha}$-attractor models can fit the observed $n_s$ values.

Abstract

Inflation elegantly provides initial conditions for the standard model of cosmology, while solving the horizon, flatness, and magnetic monopole problems. Inflationary models make predictions for the tensor-to-scalar ratio $r$ and the spectral index $n_s$ of initial density fluctuations. In light of relevant data releases this year, we present constraints on these two parameters using the latest cosmic microwave background (CMB) and baryon acoustic oscillation data (BAO) available. Using data from Planck, the South Pole Telescope, Atacama Cosmology Telescope, and BICEP/Keck experiments, we derive $n_s=0.9682\,\pm\,0.0032$ and a 95% upper limit of $r<0.034$. This upper limit on $r$ is consistent with the official BICEP/Keck result given the numerical precision of the analyses and our choice to impose the self-consistency relation for single field slow-roll inflation on the tensor power spectrum; the $r$ constraint is not impacted by the additional CMB data. While adding DESI BAO data to the CMB data has a negligible impact on $r$, the $n_s$ constraint shifts upward to $0.9728\,\pm\,0.0029$, which favours monomial inflaton potentials with $N_\star\sim 50$ over Starobinsky $R^2$ or Higgs inflation with $N_\star = 51$ and $N_\star = 55$, respectively. This shift is caused by marginally significant differences between the CMB and DESI data that remain unexplained in the context of the standard model. We show that a class of polynomial $\alpha$-attractor models can predict the CMB and CMB+DESI $n_s$ results with $N_\star=47.1$ and $N_\star=55.1$, respectively. While future data will improve our sensitivity to $r$, robust $n_s$ constraints are just as crucial to differentiate between inflation models. We make the data needed to reproduce the new CMB and BAO results and visualisation tools for $r$-$n_s$ figures to compare to any inflation model available https://github.com/Lbalkenhol/r_ns_2025 .