Inflation at the End of 2025: Constraints on r and n s Using the Latest CMB and BAO Data
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 ± 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 ± 0.0029 , which favours monomial inflaton potentials with N ⋆ ∼ 50 over Starobinsky R 2 or Higgs inflation with N ⋆ = 51 and N ⋆ = 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 α -attractor models can predict the CMB as well as CMB+DESI n s results. 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 .
Related
- Symmetry-protected α-attractor hybrid inflation in supergravity and constraints from ACT DR6 and DESI DR2
- Revisiting the Lyth bound constraints on inflation from ACT DR6 results
- General Spin-1 Dynamics During Inflation: Microcausality Constraints and Cosmological Collider Signals
- Primordial Tensor Signatures and Gravitational Wave Constraints in Lorentz Violating Inflation with Non-Canonical Kinetics
- Cosmological constraints on single-field inflation models from ACT/SPT data and observations at sub-Mpc scales
BibTeX
@article{balkenhol2026inflation,
title = {{Inflation at the End of 2025: Constraints on r and n s Using the Latest CMB and BAO Data}},
author = {L. Balkenhol and E. Camphuis and Fabio Finelli and K. Benabed and François R. Bouchet and Julien Carron and S. Galli and Eric F. Hivon and A. R. Khalife and Lloyd Knox and Christian L. Reichardt and A. Vitrier and W. L. K. Wu},
journal = {The Open Journal of Astrophysics},
year = {2026},
month = jul,
doi = {10.33232/001c.164435},
url = {https://doi.org/10.33232/001c.164435},
note = {CC BY},
}
RIS
TY - JOUR
TI - Inflation at the End of 2025: Constraints on r and n s Using the Latest CMB and BAO Data
AU - L. Balkenhol
AU - E. Camphuis
AU - Fabio Finelli
AU - K. Benabed
AU - François R. Bouchet
AU - Julien Carron
AU - S. Galli
AU - Eric F. Hivon
AU - A. R. Khalife
AU - Lloyd Knox
AU - Christian L. Reichardt
AU - A. Vitrier
AU - W. L. K. Wu
PY - 2026
DA - 2026/07/01
JO - The Open Journal of Astrophysics
DO - 10.33232/001c.164435
UR - https://doi.org/10.33232/001c.164435
AB - 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 ± 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 ± 0.0029 , which favours monomial inflaton potentials with N ⋆ ∼ 50 over Starobinsky R 2 or Higgs inflation with N ⋆ = 51 and N ⋆ = 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 α -attractor models can predict the CMB as well as CMB+DESI n s results. 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 .
SN - 2565-6120
ER -