Inflation (2025)

Abstract

This is a review article for The Review of Particle Physics 2026 (aka the Particle Data Book), appearing as Chapter 23. It forms a compact review of our understanding of cosmological inflation near the end of 2025. Topics included are Scalar Field Cosmology; Primordial Perturbations from Inflation; Models; Model Comparison; Constraints on Reheating; Beyond Single-Field Inflation; Initial-conditions and Fine-tuning; Future Probes of Inflation.

Figures (5)

• Figure 1: The marginalized joint 68 and 95% CL regions for the tilt in the scalar perturbation spectrum, $n_{\rm s}$, and the relative magnitude of the tensor perturbations, $r$, obtained from the Planck 2018 and lensing data alone, and their combinations with BICEP2/Keck Array (BK15) and (optionally) BAO data, confronted with the predictions of some of the inflationary models discussed in this review. This figure is taken from Ref.Akrami:2018odb.
• Figure 2: The result of reconstructing a single-field inflaton potential using a cubic-spline power-spectrum mode expansion and the full Planck, lensing, BK15 and BAO data set. This figure is taken from Refs. Akrami:2018odb.
• Figure 3: Inflationary potential $V$ in the ${\mathrm{R}}^2$ model (solid black line) compared with its form in various no-scale models discussed in detail in Ref. Ellis:2013xoa (dashed coloured lines).
• Figure 4: Bayes factors calculated in Refs. Martin:2016oykMartin:2024qnn for 287 single-field inflationary models using Planck 2018 data Planck:2018jri in combination with other CMB and BAO measurements. Those highlighted in yellow are featured in this review, according to the numbers listed in the text (the models labeled "2" and "3" lie outside the plot frame because of their low Bayesian evidence). On the vertical axis, the information gain on the reheating parameter, i.e. the $k$-independent terms in the right-hand side of Eq. \ref{['inflation:eq:nefolds']}, is displayed in units of bits for the Kullback-Leibler divergence between its prior and posterior distributions Martin:2016oyk.
• Figure 5: lllustration of the impact of the BICEP/Keck BICEPKeck:2021gln and other constraints on the inflaton decay coupling, $y$, and the number of e-folds at a scale $0.05$ Mpc$^{-1}$, $N_{0.05}$, in $\alpha$-attractor models of inflation. The horizontal blue lines are 68% and 95% C.L. lower limits on $n_{\rm s}$. The left and right axes show the relation between $N_{0.05}$ and $n_{\rm s}$ and the top and bottom scales show the relation between the inflaton coupling, $y$, and the reheating temperature, $T_{\rm reh}$. The diagonal dashed, solid and dotted black lines illustrate the correlations between these quantities for $\alpha$-attractor models with $\alpha = 0.1$, $1$, and $5$. We also include the lower limit on $y$ from Big-Bang nucleosynthesis (red line), the constraint that $T_{\rm reh}$ be no smaller than the electroweak scale (gray line), and a constraint from gravitino production (purple line) for $\alpha = 1$, which strengthens for smaller $\alpha$. Plot taken from Ref. Ellis:2021kad.